From 01d01ab5ec8be3d499a9519983a27544c5b9a75b Mon Sep 17 00:00:00 2001 From: bozenne Date: Tue, 4 Jul 2023 11:58:17 +0200 Subject: [PATCH] ... minor fix ... --- DESCRIPTION | 2 +- R/S4-BuyseTest-confint.R | 149 +- inst/doc-software/overview.aux | 87 +- inst/doc-software/overview.log | 1730 ++++++++++--------- inst/doc-software/overview.org | 722 +++++--- inst/doc-software/overview.pdf | Bin 568241 -> 504309 bytes inst/doc-software/overview.tex | 812 +++++---- tests/testthat/test-BuyseTest-previousBug.R | 6 +- tests/testthat/test-BuyseTest-resampling.R | 25 +- 9 files changed, 1976 insertions(+), 1557 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 3b49943..81d3a50 100755 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -2,7 +2,7 @@ Package: BuyseTest Type: Package Title: Generalized Pairwise Comparisons Version: 3.0.0 -Date: 2023-07-03 +Date: 2023-07-04 Authors@R: c( person("Brice", "Ozenne", role = c("aut", "cre"), email = "brice.mh.ozenne@gmail.com", comment = c(ORCID = "0000-0001-9694-2956")), person("Julien", "Peron", role = "ctb"), diff --git a/R/S4-BuyseTest-confint.R b/R/S4-BuyseTest-confint.R index 5e4135f..eb4de05 100644 --- a/R/S4-BuyseTest-confint.R +++ b/R/S4-BuyseTest-confint.R @@ -4,7 +4,7 @@ ## Created: maj 19 2018 (23:37) ## Version: ## By: Brice Ozenne -## Update #: 978 +## Update #: 1019 ##---------------------------------------------------------------------- ## ### Commentary: @@ -129,6 +129,7 @@ setMethod(f = "confint", option <- BuyseTest.options() D <- length(object@endpoint) method.inference <- object@method.inference + add.halfNeutral <- object@add.halfNeutral if(is.null(statistic)){ statistic <- option$statistic } @@ -136,7 +137,11 @@ setMethod(f = "confint", transformation <- option$transformation } if(is.null(conf.level)){ - conf.level <- option$conf.level + if(!attr(method.inference,"permutation")){ + conf.level <- option$conf.level + }else{ + conf.level <- NA + } } if(is.null(alternative)){ alternative <- option$alternative @@ -224,13 +229,6 @@ setMethod(f = "confint", refuse.NA = FALSE, valid.length = 1, method = "confint[S4BuyseTest]") - if(is.na(conf.level)){ - method.inference[] <- "none" ## uses [] to not remove the attributs of method.inference - attr(method.inference,"permutation") <- FALSE - attr(method.inference,"bootstrap") <- FALSE - attr(method.inference,"studentized") <- FALSE - attr(method.inference,"ustatistic") <- FALSE - } alpha <- 1-conf.level ## alternative @@ -285,14 +283,7 @@ setMethod(f = "confint", if(!is.null(cluster) && any(object@weightObs!=1)){ stop("Cannot handle clustered observations when observations are weighted. \n") } - perm.null <- switch(statistic, - "netBenefit" = 0, - "winRatio" = 1, - "favorable" = 0.5, - "unfavorable" = 0.5) - if(attr(method.inference,"permutation") && !is.null(null) && null!=perm.null){ - stop("Cannot specify the null hypothesis when using permutation tests. \n") } - + ## ** extract estimate all.endpoint <- names(object@endpoint) Delta <- coef(object, statistic = statistic, cumulative = cumulative, stratified = stratified, endpoint = endpoint) @@ -349,7 +340,7 @@ setMethod(f = "confint", } ## ** null hypothesis - if(attr(method.inference,"permutation")){ + if(attr(method.inference,"permutation") && !add.halfNeutral && is.null(null) && statistic %in% c("favorable","unfavorable")){ null <- NA }else if(is.null(null)){ null <- switch(statistic, @@ -359,6 +350,7 @@ setMethod(f = "confint", "unfavorable" = 1/2) }else { validNumeric(null, valid.length = 1, + refuse.NA = !attr(method.inference,"permutation"), min = if("statistic"=="netBenefit"){-1}else{0}, max = if("statistic"=="winRatio"){Inf}else{1}) } @@ -544,7 +536,7 @@ setMethod(f = "confint", } ## ** export - if(attr(method.inference,"permutation")){ + if(attr(method.inference,"permutation") && !is.na(conf.level)){ if(is.null(attr(conf.level,"warning.permutation")) || !identical(attr(conf.level,"warning.permutation"),FALSE)){ warning("Confidence intervals are computed under the null hypothesis and therefore may not be valid. \n") } @@ -571,22 +563,28 @@ confint_percentilePermutation <- function(Delta, Delta.resampling, outTable[,"se"] <- apply(backtransform.delta(Delta.resampling), MARGIN = 2, FUN = stats::sd, na.rm = TRUE) ## ** confidence interval - Delta.resamplingH0 <- apply(Delta.resampling, MARGIN = 2, FUN = scale, scale = FALSE, center = TRUE) - outTable[,"lower.ci"] <- backtransform.delta(switch(alternative, - "two.sided" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = alpha/2, na.rm = TRUE), - "less" = -Inf, - "greater" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = alpha, na.rm = TRUE) - )) + if(!is.na(alpha)){ + Delta.resamplingH0 <- apply(Delta.resampling, MARGIN = 2, FUN = scale, scale = FALSE, center = TRUE) + outTable[,"lower.ci"] <- backtransform.delta(switch(alternative, + "two.sided" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = alpha/2, na.rm = TRUE), + "less" = -Inf, + "greater" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = alpha, na.rm = TRUE) + )) - outTable[,"upper.ci"] <- backtransform.delta(switch(alternative, - "two.sided" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha/2, na.rm = TRUE), - "less" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha, na.rm = TRUE), - "greater" = Inf - )) + outTable[,"upper.ci"] <- backtransform.delta(switch(alternative, + "two.sided" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha/2, na.rm = TRUE), + "less" = Delta + apply(Delta.resamplingH0, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha, na.rm = TRUE), + "greater" = Inf + )) + } - ## ** p-value + ## ** null + if(any(is.na(null))){ + null[is.na(null)] <- apply(Delta.resampling,2,stats::median)[is.na(null)] + } outTable[,"null"] <- backtransform.delta(null) + ## ** p-value add.1 <- BuyseTest.options()$add.1.presample outTable[,"p.value"] <- sapply(1:n.endpoint, FUN = function(iE){ ## iE <- 1 test.alternative <- switch(alternative, # test whether each sample is has a cumulative proportions in favor of treatment more extreme than the point estimate @@ -618,17 +616,19 @@ confint_percentileBootstrap <- function(Delta, Delta.resampling, outTable[,"se"] <- apply(Delta.resampling, MARGIN = 2, FUN = stats::sd, na.rm = TRUE) ## ** confidence interval - outTable[,"lower.ci"] <- switch(alternative, - "two.sided" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = alpha/2, na.rm = TRUE), - "less" = -Inf, - "greater" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = alpha, na.rm = TRUE) - ) + if(!is.na(alpha)){ + outTable[,"lower.ci"] <- switch(alternative, + "two.sided" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = alpha/2, na.rm = TRUE), + "less" = -Inf, + "greater" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = alpha, na.rm = TRUE) + ) - outTable[,"upper.ci"] <- switch(alternative, - "two.sided" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha/2, na.rm = TRUE), - "less" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha, na.rm = TRUE), - "greater" = Inf - ) + outTable[,"upper.ci"] <- switch(alternative, + "two.sided" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha/2, na.rm = TRUE), + "less" = apply(Delta.resampling, MARGIN = 2, FUN = stats::quantile, probs = 1 - alpha, na.rm = TRUE), + "greater" = Inf + ) + } ## ** p.values outTable[,"null"] <- backtransform.delta(null) @@ -668,17 +668,20 @@ confint_gaussian <- function(Delta, Delta.resampling, outTable[,"se"] <- apply(backtransform.delta(Delta.resampling), MARGIN = 2, FUN = stats::sd, na.rm = TRUE) ## ** confidence interval - outTable[,"lower.ci"] <- backtransform.delta(switch(alternative, - "two.sided" = Delta + stats::qnorm(alpha/2) * Delta.se, - "less" = -Inf, - "greater" = Delta + stats::qnorm(alpha) * Delta.se - )) + if(!is.na(alpha)){ + outTable[,"lower.ci"] <- backtransform.delta(switch(alternative, + "two.sided" = Delta + stats::qnorm(alpha/2) * Delta.se, + "less" = -Inf, + "greater" = Delta + stats::qnorm(alpha) * Delta.se + )) - outTable[,"upper.ci"] <- backtransform.delta(switch(alternative, - "two.sided" = Delta + stats::qnorm(1-alpha/2) * Delta.se, - "less" = Delta + stats::qnorm(1-alpha) * Delta.se, - "greater" = Inf - )) + outTable[,"upper.ci"] <- backtransform.delta(switch(alternative, + "two.sided" = Delta + stats::qnorm(1-alpha/2) * Delta.se, + "less" = Delta + stats::qnorm(1-alpha) * Delta.se, + "greater" = Inf + )) + } + ## ** p-value outTable[,"null"] <- backtransform.delta(null) outTable[,"p.value"] <- switch(alternative, @@ -712,7 +715,7 @@ confint_studentPermutation <- function(Delta, Delta.se, Delta.resampling, Delta. outTable[,"se"] <- backtransform.se(Delta, se = Delta.se) ## ** critical quantile - if(length(index.var)>0){ + if(!is.na(alpha) && length(index.var)>0){ Delta.statH0.resampling <- apply(Delta.resampling[,index.var,drop=FALSE], MARGIN = 2, FUN = scale, scale = FALSE, center = TRUE)/Delta.se.resampling[,index.var,drop=FALSE] Delta.qInf <- switch(alternative, @@ -728,7 +731,7 @@ confint_studentPermutation <- function(Delta, Delta.se, Delta.resampling, Delta. } ## ** confidence interval - if(length(index.var)>0){ + if(!is.na(alpha) && length(index.var)>0){ outTable[index.var,"lower.ci"] <- backtransform.delta(Delta[index.var] + Delta.qInf * Delta.se[index.var]) outTable[index.var,"upper.ci"] <- backtransform.delta(Delta[index.var] + Delta.qSup * Delta.se[index.var]) } @@ -738,16 +741,20 @@ confint_studentPermutation <- function(Delta, Delta.se, Delta.resampling, Delta. outTable[index.novar,"upper.ci"] <- backtransform.delta(Delta[index.novar]) } - ## ** p.value + ## ** null + if(any(is.na(null))){ + null[is.na(null)] <- apply(Delta.resampling,2,stats::median)[is.na(null)] + } outTable[,"null"] <- backtransform.delta(null) + ## ** p.value add.1 <- BuyseTest.options()$add.1.presample if(length(index.var)>0){ Delta.stat <- (Delta-null)/Delta.se Delta.stat.resampling <- (Delta.resampling-null)/Delta.se.resampling outTable[index.var,"p.value"] <- sapply(index.var, FUN = function(iE){ ## iE <- 1 test.alternative <- switch(alternative, # test whether each sample is has a cumulative proportions in favor of treatment more extreme than the point estimate - "two.sided" = abs(Delta.stat[iE]) <= abs(Delta.stat.resampling[,iE] - null[iE]), + "two.sided" = abs(Delta.stat[iE]) <= abs(Delta.stat.resampling[,iE]), "less" = Delta.stat[iE] >= Delta.stat.resampling[,iE], "greater" = Delta.stat[iE] <= Delta.stat.resampling[,iE] ) @@ -791,27 +798,31 @@ confint_studentBootstrap <- function(Delta, Delta.se, Delta.resampling, Delta.se if(length(index.var)>0){ Delta.statH0.resampling <- apply(Delta.resampling[,index.var,drop=FALSE], MARGIN = 2, FUN = scale, scale = FALSE, center = TRUE)/Delta.se.resampling[,index.var,drop=FALSE] - Delta.qInf <- switch(alternative, - "two.sided" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = alpha/2), - "less" = -Inf, - "greater" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = alpha) - ) - Delta.qSup <- switch(alternative, - "two.sided" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = 1-alpha/2), - "less" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = 1-alpha), - "greater" = Inf - ) + if(!is.na(alpha)){ + + Delta.qInf <- switch(alternative, + "two.sided" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = alpha/2), + "less" = -Inf, + "greater" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = alpha) + ) + Delta.qSup <- switch(alternative, + "two.sided" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = 1-alpha/2), + "less" = apply(Delta.statH0.resampling, MARGIN = 2, FUN = stats::quantile, na.rm = TRUE, probs = 1-alpha), + "greater" = Inf + ) + } + } ## ** confidence interval ## normal case - if(length(index.var)>0){ + if(!is.na(alpha) && length(index.var)>0){ outTable[index.var,"lower.ci"] <- backtransform.delta(Delta[index.var] + Delta.qInf * Delta.se[index.var]) outTable[index.var,"upper.ci"] <- backtransform.delta(Delta[index.var] + Delta.qSup * Delta.se[index.var]) } ## special case - if(length(index.novar)>0){ + if(!is.na(alpha) && length(index.novar)>0){ test.diff <- colSums(Delta.resampling[,index.novar,drop=FALSE] != matrix(Delta, nrow = NROW(Delta.resampling), ncol = length(Delta), byrow = TRUE)) outTable[index.novar[test.diff],c("lower.ci","upper.ci")] <- NA outTable[index.novar[test.diff==0],c("lower.ci","upper.ci")] <- backtransform.delta(Delta[index.novar[test.diff==0]]) @@ -822,7 +833,7 @@ confint_studentBootstrap <- function(Delta, Delta.se, Delta.resampling, Delta.se outTable[, "null"] <- backtransform.delta(null) add.1 <- BuyseTest.options()$add.1.presample - for(iE in index.var){ ## iE <- 2 + for(iE in index.var){ ## iE <- 1 outTable[iE, "p.value"] <- boot2pvalue(stats::na.omit(Delta[iE] + Delta.se[iE] * Delta.statH0.resampling[,iE]), null = null[iE], estimate = Delta[iE], ## note: estimate is not used to produce the ci, just for knowing the sign @@ -859,6 +870,7 @@ confint_Ustatistic <- function(Delta, Delta.se, statistic, null, outTable[,"se"] <- backtransform.se(Delta, se = Delta.se) ## ** confidence interval + if(!is.na(alpha)){ outTable[,"lower.ci"] <- backtransform.delta(switch(alternative, "two.sided" = Delta + stats::qnorm(alpha/2) * Delta.se, "less" = -Inf, @@ -870,6 +882,7 @@ confint_Ustatistic <- function(Delta, Delta.se, statistic, null, "less" = Delta + stats::qnorm(1-alpha) * Delta.se, "greater" = Inf )) + } ## ** p-value outTable[,"null"] <- backtransform.delta(null) diff --git a/inst/doc-software/overview.aux b/inst/doc-software/overview.aux index 5735f67..1150062 100644 --- a/inst/doc-software/overview.aux +++ b/inst/doc-software/overview.aux @@ -20,54 +20,56 @@ \citation{peron2018extension} \citation{buyse2010generalized} \@writefile{toc}{\contentsline {section}{\numberline {1}Performing generalized pairwise comparisons (GPC) using the \texttt {BuyseTest} function}{4}{section.1}\protected@file@percent } -\newlabel{sec:org6608846}{{1}{4}{Performing generalized pairwise comparisons (GPC) using the \texttt {BuyseTest} function}{section.1}{}} +\newlabel{sec:orgfecca0d}{{1}{4}{Performing generalized pairwise comparisons (GPC) using the \texttt {BuyseTest} function}{section.1}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Displaying the results}{5}{subsection.1.1}\protected@file@percent } -\newlabel{sec:orgad6051f}{{1.1}{5}{Displaying the 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options}{40}{section.6}\protected@file@percent } +\newlabel{sec:orgdc6f3fa}{{6}{40}{Modifying default options}{section.6}{}} \bibstyle{apalike} \bibdata{bibliography} \bibcite{brunner2018rank}{{1}{2018}{{Brunner et~al.}}{{}}} @@ -77,5 +79,4 @@ \bibcite{peron2018extension}{{5}{2018}{{P{\'e}ron et~al.}}{{}}} \bibcite{peron2021correcting}{{6}{2021}{{P{\'e}ron et~al.}}{{}}} \bibcite{verbeeck2019generalized}{{7}{2019}{{Verbeeck et~al.}}{{}}} -\newlabel{sec:orgf87f212}{{6}{38}{}{lstnumber.-98.1}{}} -\gdef \@abspage@last{38} +\newlabel{sec:orgbe6c6b4}{{6}{41}{}{lstnumber.-107.1}{}} diff --git a/inst/doc-software/overview.log b/inst/doc-software/overview.log index e43497d..3241992 100644 --- a/inst/doc-software/overview.log +++ b/inst/doc-software/overview.log @@ -1,64 +1,66 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.23 (MiKTeX 21.8) (preloaded format=pdflatex 2021.8.26) 30 JUN 2023 12:23 +This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 206. @@ -1132,23 +1130,27 @@ LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 206. LaTeX Font Info: ... okay on input line 206. LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 206. 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The issue c @@ -1189,23 +1191,24 @@ loading the todonotes package. on input line 206. * \@reversemarginfalse * (1in=72.27pt=25.4mm, 1cm=28.453pt) +\AtBeginShipoutBox=\box128 Package hyperref Info: Link coloring ON on input line 206. -(C:\Program Files\MiKTeX 2.9\tex/latex/hyperref\nameref.sty -Package: nameref 2021-04-02 v2.47 Cross-referencing by name of section +(/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty +Package: nameref 2019/09/16 v2.46 Cross-referencing by name of section -(C:\Users\hpl802\AppData\Roaming\MiKTeX\2.9\tex/latex/refcount\refcount.sty +(/usr/share/texlive/texmf-dist/tex/latex/refcount/refcount.sty Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO) ) -(C:\Users\hpl802\AppData\Roaming\MiKTeX\2.9\tex/generic/gettitlestring\gettitle -string.sty +(/usr/share/texlive/texmf-dist/tex/generic/gettitlestring/gettitlestring.sty Package: gettitlestring 2019/12/15 v1.6 Cleanup title references (HO) ) -\c@section@level=\count379 +\c@section@level=\count365 ) LaTeX Info: Redefining \ref on input line 206. LaTeX Info: Redefining \pageref on input line 206. LaTeX Info: Redefining \nameref on input line 206. - (overview.out) (overview.out) + +(./overview.out) (./overview.out) \@outlinefile=\write5 \openout5 = `overview.out'. @@ -1214,26 +1217,25 @@ Package caption Info: float package is loaded. Package caption Info: End \AtBeginDocument code. 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PDF statistics: - 877 PDF objects out of 1000 (max. 8388607) - 430 named destinations out of 1000 (max. 500000) - 209 words of extra memory for PDF output out of 10000 (max. 10000000) + 963 PDF objects out of 1000 (max. 8388607) + 866 compressed objects within 9 object streams + 470 named destinations out of 1000 (max. 500000) + 313 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/inst/doc-software/overview.org b/inst/doc-software/overview.org index 00f6fab..b851110 100644 --- a/inst/doc-software/overview.org +++ b/inst/doc-software/overview.org @@ -22,16 +22,18 @@ right-censoring. When considering a single endpoint, the GPC procedure can be summarized as follow. Denote the endpoint by \(Y\) in the treatment group and by \(X\) in the control group. Given a threshold of clinical relevance \(\tau\), the aim of GPC is to estimate the -proportion in favor of treatment \(\Prob[Y \geq X + \tau]\) and the -proportion in favor of control \(\Prob[X \geq Y + \tau]\). Other -statistics such as the net benefit \(\Prob[Y \geq X + \tau]-\Prob[X -\geq Y + \tau]\) or the win ratio \(\frac{\Prob[Y \geq X + -\tau]}{\Prob[X \geq Y + \tau]}\) can then be deduced. The vignette is -written for readers familar with the GPC framework [fn::if not, -cite:buyse2010generalized is a good place to start.], e.g. prioritized -endpoints, pair, net benefit, win ratio, threshold of clinical -relevance, \ldots, since it focuses on the software aspect -of the *BuyseTest* package (not on the underlying statistical model). +proportion in favor of treatment[fn::in absence of ties this equals +the Wilcoxon-Mann-Whitney parameter] \(\Prob[Y \geq X + \tau]\) and +the proportion in favor of control \(\Prob[X \geq Y + \tau]\). Their +difference \(\Prob[Y \geq X + \tau]-\Prob[X \geq Y + \tau]\) leads to +the net benefit and their ratio \(\frac{\Prob[Y \geq X + +\tau]}{\Prob[X \geq Y + \tau]}\) to the win ratio (in absence of +ties). The vignette is written for readers familar with the GPC +framework [fn::if not, cite:buyse2010generalized is a good place to +start.], e.g. prioritized endpoints, pair, net benefit, win ratio, +threshold of clinical relevance, \ldots, since it focuses on the +software aspect of the *BuyseTest* package (not on the underlying +statistical model). \bigskip @@ -46,6 +48,7 @@ The *BuyseTest* package contains three main functions: + =confint= to extract estimates, confidence intervals, and p.values. + =plot= for a graphical display of the scoring of the pair per endpoint. + =sensitivity= to perform a sensitivity analysis on the choice of the threshold(s). + + =nobs= to extract the number of observations and pairs. + =getIid= to extract the iid decomposition of the estimator. + =getPairScore= to extract the contribution of each pair to the net benefit/win ratio. + =getSurvival= to extract the estimates of the survival used for right-censored endpoints. @@ -72,17 +75,18 @@ To illustrate the functionalities of the package, we will used the #+BEGIN_SRC R :exports both :results output :session *R* :cache no data(cancer, package = "survival") veteran <- cbind(id = 1:NROW(veteran), veteran) +veteran$trt <- factor(veteran$trt,1:2,c("Pl","Exp")) head(veteran) #+END_SRC #+RESULTS: : id trt celltype time status karno diagtime age prior -: 1 1 1 squamous 72 1 60 7 69 0 -: 2 2 1 squamous 411 1 70 5 64 10 -: 3 3 1 squamous 228 1 60 3 38 0 -: 4 4 1 squamous 126 1 60 9 63 10 -: 5 5 1 squamous 118 1 70 11 65 10 -: 6 6 1 squamous 10 1 20 5 49 0 +: 1 1 Pl squamous 72 1 60 7 69 0 +: 2 2 Pl squamous 411 1 70 5 64 10 +: 3 3 Pl squamous 228 1 60 3 38 0 +: 4 4 Pl squamous 126 1 60 9 63 10 +: 5 5 Pl squamous 118 1 70 11 65 10 +: 6 6 Pl squamous 10 1 20 5 49 0 See =?veteran= for a presentation of the database. @@ -96,7 +100,7 @@ utils::packageVersion("BuyseTest") #+END_SRC #+RESULTS: -: [1] '3.0.0' +: [1] ‘3.0.0’ For completness, the details of the R session used to generate this document are: @@ -106,35 +110,38 @@ sessionInfo() #+RESULTS: #+begin_example -R version 4.2.0 (2022-04-22 ucrt) -Platform: x86_64-w64-mingw32/x64 (64-bit) -Running under: Windows 10 x64 (build 19045) +R version 4.2.0 (2022-04-22) +Platform: x86_64-pc-linux-gnu (64-bit) +Running under: Ubuntu 20.04.4 LTS Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0 locale: -[1] LC_COLLATE=Danish_Denmark.utf8 LC_CTYPE=Danish_Denmark.utf8 -[3] LC_MONETARY=Danish_Denmark.utf8 LC_NUMERIC=C -[5] LC_TIME=Danish_Denmark.utf8 + [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8 + [4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 + [7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C +[10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: -[1] data.table_1.14.2 BuyseTest_3.0.0 Rcpp_1.0.8.3 prodlim_2019.11.13 -[5] ggplot2_3.4.2 survival_3.3-1 +[1] data.table_1.14.2 BuyseTest_3.0.0 Rcpp_1.0.9 prodlim_2019.11.13 +[5] ggplot2_3.4.0 survival_3.5-0 loaded via a namespace (and not attached): - [1] pillar_1.9.0 compiler_4.2.0 tools_4.2.0 digest_0.6.31 - [5] lifecycle_1.0.3 tibble_3.2.1 gtable_0.3.1 lattice_0.20-45 - [9] pkgconfig_2.0.3 rlang_1.1.0 Matrix_1.5-1 cli_3.6.0 -[13] parallel_4.2.0 SparseM_1.81 withr_2.5.0 dplyr_1.1.0 -[17] MatrixModels_0.5-0 generics_0.1.3 vctrs_0.5.2 globals_0.16.2 -[21] stats4_4.2.0 grid_4.2.0 tidyselect_1.2.0 glue_1.6.2 -[25] listenv_0.9.0 R6_2.5.1 future.apply_1.10.0 fansi_1.0.4 -[29] parallelly_1.34.0 lava_1.7.2.1 magrittr_2.0.3 scales_1.2.1 -[33] codetools_0.2-18 splines_4.2.0 future_1.31.0 colorspace_2.1-0 -[37] utf8_1.2.3 munsell_0.5.0 + [1] pillar_1.8.1 compiler_4.2.0 tools_4.2.0 digest_0.6.31 + [5] lifecycle_1.0.3 tibble_3.1.8 gtable_0.3.1 lattice_0.20-45 + [9] pkgconfig_2.0.3 rlang_1.0.6 Matrix_1.4-1 DBI_1.1.3 +[13] cli_3.5.0 parallel_4.2.0 SparseM_1.81 withr_2.5.0 +[17] dplyr_1.0.10 MatrixModels_0.5-0 generics_0.1.3 vctrs_0.5.1 +[21] globals_0.16.1 stats4_4.2.0 grid_4.2.0 tidyselect_1.2.0 +[25] glue_1.6.2 listenv_0.8.0 R6_2.5.1 future.apply_1.9.1 +[29] fansi_1.0.3 parallelly_1.32.1 lava_1.7.2 magrittr_2.0.3 +[33] scales_1.2.1 codetools_0.2-18 splines_4.2.0 assertthat_0.2.1 +[37] future_1.28.0 colorspace_2.0-3 utf8_1.2.2 munsell_0.5.0 #+end_example \clearpage @@ -147,7 +154,7 @@ To perform generalized pairwise comparisons, the =BuyseTest= function needs: - the type of each endpoint \hfill - argument =type= - the variable defining the two treatment groups \hfill - argument =treatment= -The =BuyseTest= function has many optional arguments to specify for example: +The =BuyseTest= function has many optional arguments. For example: - the threshold of clinical relevance associated to each endpoint \hfill - argument =threshold= - the censoring associated to each endpoint (for time to event endpoints) \hfill - argument =status= @@ -171,7 +178,7 @@ BT <- BuyseTest(data = veteran, Generalized Pairwise Comparisons Settings - - 2 groups : Control = 1 and Treatment = 2 + - 2 groups : Control = Pl and Treatment = Exp - 1 endpoint: priority endpoint type operator threshold event 1 time time to event higher is favorable 20 status (0 1) @@ -226,7 +233,7 @@ summary(BT) - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta @@ -235,10 +242,33 @@ summary(BT) [-0.2735;0.1045] 0.37162 #+end_example - To display the number of pairs instead of the percentage of pairs -that are favorable/unfavorable/neutral/uniformative, set the argument -=percentage= to =FALSE=. The =model.tables= method returns the table -displayed at the end of the =summary= in a =data.frame= format: + +It displays information about each endpoint, percentage of pairs +classified as favorable, unfavorable, neutral, and uninformative, as +well as the estimated net benefit (column =Delta=), its confidence +interval, and the corresponding p-value testing the absence of a group +difference. Other To display the number of pairs instead of the +percentage of pairs that are +favorable/unfavorable/neutral/uniformative, set the argument +=percentage= to =FALSE=. See =help(S4BuyseTest-summary)= for more +details about the =summary= method, its input and output. For a more +concise display of the results, consider using the =print= method: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +print(BT, percentage = FALSE) +#+END_SRC + +#+RESULTS: +: endpoint threshold total favorable unfavorable neutral uninf Delta CI [2.5% ; 97.5%] +: time 20 4692 1772.59 2183.89 735.52 0 -0.0877 [-0.2735;0.1045] +: p.value +: 0.37162 + +\bigskip + +To access these values, we recommand using the =model.tables= method +that outputs the information from the previous table in a =data.frame= +format: + #+BEGIN_SRC R :exports both :results output :session *R* :cache no model.tables(BT, percentage = FALSE) #+END_SRC @@ -269,32 +299,6 @@ coef(BT) : time_t20 : -0.08765836 -By default =summary= displays results relative to the net benefit. To -get results for the win ratio set the argument =statistic= to -"winRatio": -#+BEGIN_SRC R :exports both :results output :session *R* :cache no -summary(BT, statistic = "winRatio") -#+END_SRC - -#+RESULTS: -#+begin_example - Generalized pairwise comparisons with 1 endpoint - - - statistic : win ratio (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 1 - - confidence level: 0.95 - - inference : H-projection of order 1 after log transformation - - treatment groups: 2 (treatment) vs. 1 (control) - - censored pairs : probabilistic score based on the survival curves - - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta - time 20 100 37.78 46.54 15.68 0 0.8117 - CI [2.5% ; 97.5%] p.value - [0.5134;1.2833] 0.37195 -#+end_example - -See =help(S4BuyseTest-summary)= for more details about the =summary= -method and its output. \clearpage @@ -314,13 +318,14 @@ BTstrata <- BuyseTest(ffstrata, data = veteran, trace = 0) #+RESULTS: Not being wrapped by =bin=, =cont= or =tte= differentiates it from -endpoint variables. When doing a stratified analysis, the summary -method displays strata-specific and global results[fn::the -strata-specific results can be removed by setting the argument -=strata= to ="global"= when calling =summary=.]: +endpoint variables. When doing a stratified analysis, the summary method +displays strata-specific and global results[fn::the strata-specific +results can be removed by setting the argument =strata= to ="global"= +when calling =summary=.]: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -summary(BTstrata, type.display = c("endpoint","threshold","strata", - "total","favorable","unfavorable","delta","Delta")) +keep.colStrata <- c("endpoint","strata", "total", + "favorable","unfavorable","neutral","uninf","delta","Delta") +summary(BTstrata, type.display = keep.colStrata) #+END_SRC #+RESULTS: @@ -331,30 +336,106 @@ summary(BTstrata, type.display = c("endpoint","threshold","strata", - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - strata weights : 26.38%, 34.63%, 18.47%, 20.52% - censored pairs : probabilistic score based on the survival curves - uninformative pairs: no contribution - results - endpoint threshold strata total(%) favorable(%) unfavorable(%) delta Delta - time 20 global 100.00 36.70 46.66 -0.0997 -0.0997 - squamous 25.38 14.33 8.77 0.2193 - smallcell 45.69 12.69 20.88 -0.1792 - adeno 13.71 4.74 6.15 -0.1034 - large 15.23 4.30 9.97 -0.3722 + endpoint strata total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) delta Delta + time global 100.00 36.06 45.77 17.33 0.85 -0.0997 -0.0997 + squamous 25.38 14.33 8.77 2.28 0.00 0.2193 + smallcell 45.69 12.69 20.88 11.27 0.85 -0.1792 + adeno 13.71 4.74 6.15 2.81 0.00 -0.1034 + large 15.23 4.30 9.97 0.96 0.00 -0.3722 #+end_example -Note that here the numbers in the total/favorable/unfavorable/ columns -are relative to the overall sample while the delta is only relative to -the strata. The global delta is a sum of the strata specific delta -weighted by the empirical proportion of pairs for each strata. The -weight of each strata is by default proportional to the number of -pairs. This behavior can be changed with the argument =pool.strata=: + +The percentage of pairs in the +total/favorable/unfavorable/neutral/uninf columns are relative to the +overall number of pairs whereas the column =delta= presents the +strata-specific net benefits (in the last 4 lines). The last column +(=Delta=) displays the overall net benefit. + +\bigskip + +\Warning With this weighting scheme the proportion of favorable pairs +minus the proportion of unfavorable pairs does not equal the +stata-specific nor the global net benefit. To retrieve the net +benefits, we first extract the number of pairs per strata using the +method =nobs=: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +strata.obs <- nobs(BTstrata, stratified = TRUE) +strata.obs +#+END_SRC + +#+RESULTS: +: Pl Exp pairs +: squamous 15 20 300 +: smallcell 30 18 540 +: adeno 9 18 162 +: large 15 12 180 + +and use the method =model.tables= to extract the number of favorable and unfavorable +pairs per strata: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +dfStrata <- model.tables(BTstrata, percentage = FALSE, + strata = c("squamous","smallcell","adeno","large"), + columns = c("strata","total","favorable","unfavorable")) +dfStrata +#+END_SRC + +#+RESULTS: +: strata total favorable unfavorable +: 2 squamous 300 169.40260 103.6104 +: 3 smallcell 540 150.00000 246.7778 +: 4 adeno 162 56.00000 72.7500 +: 5 large 180 50.83333 117.8333 + +We retrieve the strata-specific net benefits by comparing, in each +strata, the number of favorable and unfavorable pairs relative to the +number of pairs[fn::Alernatively one could compute, from the \texttt{summary}, the difference +between the percentage of favorable and unfavorable pairs relative to +the percentage of pairs in the strata, e.g. \((14.33\%-8.77\%)/25.38\% +\approx 21.93\%\)]: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +delta <- (dfStrata$favorable - dfStrata$unfavorable)/strata.obs$pairs +delta +#+END_SRC + +#+RESULTS: +: [1] 0.2193074 -0.1792181 -0.1033951 -0.3722222 + + + +The global net benefit is then the sum of the strata-specific net +benefits weighted by the strata weights: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +weightCMH <- strata.obs$pairs/(strata.obs$Pl + strata.obs$Exp) + +list(estimate = sum(delta * weightCMH/sum(weightCMH)), + weight = 100*weightCMH/sum(weightCMH)) +#+END_SRC + +#+RESULTS: +: $estimate +: [1] -0.09967584 +: +: $weight +: [1] 26.38329 34.62807 18.46830 20.52034 + + + +The default weighting scheme is =CMH=, standing for +Cochran-Mantel-Haenszel, which has been recommaned in the litterature +citep:dong2018stratified. It is efficient under the assumption of a +common multiplicative effect (across strata) on the odds ratio +scale. If the effect is thought additive, one should instead weight +proportionnaly to the number of pairs. This can be +achieved by specifying the argument =pool.strata=: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -BTstrataCMH <- BuyseTest(ffstrata, data = veteran, trace = 0, pool.strata = "CMH") -summary(BTstrataCMH, type.display = c("endpoint","threshold","strata", - "total","favorable","unfavorable","delta","Delta")) +BTstrata2 <- BuyseTest(ffstrata, data = veteran, trace = 0, pool.strata = "buyse") +summary(BTstrata2, type.display = keep.colStrata) #+END_SRC #+RESULTS: @@ -365,49 +446,35 @@ summary(BTstrataCMH, type.display = c("endpoint","threshold","strata", - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) - - strata weights : 26.38%, 34.63%, 18.47%, 20.52% + - treatment groups: Exp (treatment) vs. Pl (control) + - strata weights : 25.38%, 45.69%, 13.71%, 15.23% - censored pairs : probabilistic score based on the survival curves - uninformative pairs: no contribution - results - endpoint threshold strata total(%) favorable(%) unfavorable(%) delta Delta - time 20 global 100.00 36.70 46.66 -0.0997 -0.0997 - squamous 25.38 14.33 8.77 0.2193 - smallcell 45.69 12.69 20.88 -0.1792 - adeno 13.71 4.74 6.15 -0.1034 - large 15.23 4.30 9.97 -0.3722 + endpoint strata total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) delta Delta + time global 100.00 36.06 45.77 17.33 0.85 -0.0971 -0.0971 + squamous 25.38 14.33 8.77 2.28 0.00 0.2193 + smallcell 45.69 12.69 20.88 11.27 0.85 -0.1792 + adeno 13.71 4.74 6.15 2.81 0.00 -0.1034 + large 15.23 4.30 9.97 0.96 0.00 -0.3722 #+end_example -=CMH= stands for Cochran-Mantel-Haenszel whose weighted scheme has -been advocated in the litterature citep:dong2018stratified. We can -retrieve the weights by evalating the number of individual per strata -and treatment group: -#+BEGIN_SRC R :exports both :results output :session *R* :cache no -nStrata <- table(veteran$celltype, veteran$trt) -nStrata -#+END_SRC - -#+RESULTS: -: -: 1 2 -: squamous 15 20 -: smallcell 30 18 -: adeno 9 18 -: large 15 12 - +The weighting scheme only affect the evaluation of the overall net +benefit, which now equals the difference between the overall +proportion of favorable vs. unfavorable pairs. As before the +strata-specific net benefits are still not equal to the difference +between the proportion of favorable and unfavorable pairs. While +extractors will by default output global estimates (i.e. after pooling +the results over strata) #+BEGIN_SRC R :exports both :results output :session *R* :cache no -nPairStrata <- nStrata[,1]*nStrata[,2] -wStrata <- rbind(default = nPairStrata, - CMH = nPairStrata/rowSums(nStrata)) -round(100*wStrata/rowSums(wStrata),2) +confint(BTstrata2) #+END_SRC #+RESULTS: -: squamous smallcell adeno large -: default 25.38 45.69 13.71 15.23 -: CMH 26.38 34.63 18.47 20.52 +: estimate se lower.ci upper.ci null p.value +: time_t20 -0.09706901 0.0977929 -0.2829348 0.09582321 0 0.323961 -It is also possible to output strata specific results: +one can specify the argument =stratified= to extract strata-specific estimates: #+BEGIN_SRC R :exports both :results output :session *R* :cache no confint(BTstrata, stratified = TRUE) #+END_SRC @@ -421,7 +488,6 @@ confint(BTstrata, stratified = TRUE) \clearpage - ** Using multiple endpoints More than one endpoint can be considered by indicating a vector of endpoints, types, and thresholds. In the formula interface, the @@ -441,7 +507,7 @@ summary(BT.H) - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - neutral pairs : re-analyzed using lower priority endpoints - results @@ -514,7 +580,7 @@ summary(BT.nH) - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results endpoint threshold weight total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) delta @@ -569,6 +635,128 @@ confint(BT.nHw, cumulative = FALSE) \clearpage +** Statistical inference + +Several methods are available in =BuyseTest= to quantify uncertainty +about the estimates: +- *permutation test* setting the argument =method.inference= to + ="permutation"=. Assuming exchangeability under the null hypothesis, + this approach gives valid p-values (regardless to the sample size) + for testing the absence of a difference between the groups. +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +BT.perm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = 0, method.inference = "permutation", + seed = 10) +summary(BT.perm) +#+END_SRC + +#+RESULTS: +#+begin_example + Generalized pairwise comparisons with 1 endpoint + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : permutation test with 1000 samples + p-value computed using the permutation distribution + - treatment groups: Exp (treatment) vs. Pl (control) + - censored pairs : probabilistic score based on the survival curves + - results + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta p.value + time 20 100 37.78 46.54 15.68 0 -0.0877 0.35265 +#+end_example + +- *bootstrap resampling* setting the argument =method.inference= to + ="bootstrap"=. In large enough samples, this approach gives valid + p-values and confidence intervals. + +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +BT.boot <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = 0, method.inference = "bootstrap", + seed = 10) +summary(BT.boot) +#+END_SRC + +#+RESULTS: +#+begin_example + Generalized pairwise comparisons with 1 endpoint + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : bootstrap resampling with 1000 samples + CI computed using the percentile method; p-value by test inversion + - treatment groups: Exp (treatment) vs. Pl (control) + - censored pairs : probabilistic score based on the survival curves + - results + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta + time 20 100 37.78 46.54 15.68 0 -0.0877 + CI [2.5% ; 97.5%] p.value + [-0.2721;0.1034] 0.38362 +#+end_example + +- *asymptotic distribution* setting the argument =method.inference= to + ="u-statistic"=. In large enough samples, this approach gives valid + p-values and confidence intervals citep:ozenne2021asymptotic. + +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +BT.ustat <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = 0, method.inference = "u-statistic") +summary(BT.ustat) +#+END_SRC + +#+RESULTS: +#+begin_example + Generalized pairwise comparisons with 1 endpoint + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : H-projection of order 1 after atanh transformation + - treatment groups: Exp (treatment) vs. Pl (control) + - censored pairs : probabilistic score based on the survival curves + - results + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta + time 20 100 37.78 46.54 15.68 0 -0.0877 + CI [2.5% ; 97.5%] p.value + [-0.2735;0.1045] 0.37162 +#+end_example + +The first two approaches require simulating a large number of samples +and applying the GPC to each of these samples. The =seed= argument is +used to generate a seed for each sample. The number of samples is set +using the arugment =n.resampling= and it should large enough to limit +the Monte Carlo error when estimating the p-value. Typically should be +at least 10000 to get, roughtly, 2-digit precision, as examplified +below: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +set.seed(10) +sapply(1:10, function(i){mean(rbinom(1e4, size = 1, prob = 0.05))}) +#+END_SRC + +#+RESULTS: +: [1] 0.0511 0.0491 0.0489 0.0454 0.0516 0.0522 0.0468 0.0483 0.0491 0.0508 +Indeed, here we get a reasonnable approximation of =0.05= (if we round +and only keep 2 digits). Note that to get 3 digits precision we would +need more samples. The last method does not rely on resampling but on +the computation of the influence function of the +estimator. Fortunately, when using the Gehan's scoring rule, this does +not really involve any extra-calculations and this is therefore very +fast to perform. When using the Peron's scoring rule, more serious +extra-calculations are involved so the computation time is expected to +increase by a factor 5 to 10 compared to the point estimate alone +(i.e. =method.inference= equal to ="none"=). + +\bigskip + +Note: it is possible to relax the exchangeability assumption using a +studentized permutation. A studentized bootstrap is also possible to +improve on the better small samples properties of the bootstrap +confidence intervals. Both rely on the asymptotic approach to estimate +standard errors and are more numerically intensive. + +\clearpage + ** What if smaller is better? By default =BuyseTest= will always assume that higher values of an endpoint are favorable. This behavior can be changed by specifying =operator = "<0"= @@ -587,7 +775,7 @@ summary(BTinv) - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta @@ -670,124 +858,115 @@ So in this case no pair is analyzed at second priority. \clearpage -** What about p-value and confidence intervals? +** What about other summary statistics than the net benefit? -Several methods are available in =BuyseTest= to perform statistical inference: -- *permutation test* setting the argument =method.inference= to - ="permutation"=. Assuming exchangeability under the null hypothesis, - this approach gives valid p-values (regardless to the sample size) - for testing the absence of a difference between the groups. +By default methods such as =summary= display results relative to the +net benefit. Three other summary statistics are accessible: proportion +in favor of treatment \(\Prob[Y\geq X + \tau]\), proportion in favor +of control \(\Prob[X\geq Y + \tau]\), and their ratio \(\Prob[X\geq +Y + \tau]\). They can be access via the argument +=statistic=, e.g.: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -BT.perm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), - data = veteran, trace = 0, method.inference = "permutation", - seed = 10) -summary(BT.perm) +summary(BT, statistic = "winRatio") #+END_SRC #+RESULTS: #+begin_example Generalized pairwise comparisons with 1 endpoint - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 + - statistic : win ratio (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 1 - confidence level: 0.95 - - inference : permutation test with 1000 samples - p-value computed using the permutation distribution - - treatment groups: 2 (treatment) vs. 1 (control) + - inference : H-projection of order 1 after log transformation + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta p.value - time 20 100 37.78 46.54 15.68 0 -0.0877 0.35265 + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta + time 20 100 37.78 46.54 15.68 0 0.8117 + CI [2.5% ; 97.5%] p.value + [0.5134;1.2833] 0.37195 #+end_example -- *bootstrap resampling* setting the argument =method.inference= to - ="bootstrap"=. In large enough samples, this approach gives valid - p-values and confidence intervals. - +\Warning In presence of ties, it is recommanded to use another +definition for the proportion in favorable of treatment/control as +their null distribution depends on the data generative mechanism and +the threshold of clinical relevance. The =confint= method will use a +value of 0.5 for the null hypothesis: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -BT.boot <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), - data = veteran, trace = 0, method.inference = "bootstrap", - seed = 10) -summary(BT.boot) +confint(BT, statistic = "favorable") #+END_SRC #+RESULTS: -#+begin_example - Generalized pairwise comparisons with 1 endpoint +: estimate se lower.ci upper.ci null p.value +: time_t20 0.3777905 0.04902199 0.2874747 0.477467 0.5 0.01673643 - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 - - confidence level: 0.95 - - inference : bootstrap resampling with 1000 samples - CI computed using the percentile method; p-value by test inversion - - treatment groups: 2 (treatment) vs. 1 (control) - - censored pairs : probabilistic score based on the survival curves - - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta - time 20 100 37.78 46.54 15.68 0 -0.0877 - CI [2.5% ; 97.5%] p.value - [-0.2721;0.1034] 0.38362 -#+end_example +But this value does not correspond to the location of the null +distribution: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +BT.perm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = FALSE, + method.inference = "permutation", seed = 10) +confint(BT.perm, statistic = "favorable") +#+END_SRC -- *asymptotic distribution* setting the argument =method.inference= to - ="u-statistic"=. In large enough samples, this approach gives valid - p-values and confidence intervals citep:ozenne2021asymptotic. +#+RESULTS: +: estimate se lower.ci upper.ci null p.value +: time_t20 0.3777905 0.04770182 NA NA 0.4205855 0.3556444 +which, in this example, is around 0.42. Therefore the null hypotheses +tested by =confint= is generally not meaningful and the p-value should +generally be disregarded. For statistical testing we therefore +recommand defining the proportion in favor of treatment as +\(\Prob[Y\geq X + \tau] + 0.5\Prob[|Y- X| < \tau]\) which matches the +definition of the Wilcoxon-Mann-Whitney parameter. To do so, one +should set the argument =add.halfNeutral= to =TRUE= when calling +=BuyseTest=: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -BT.ustat <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), - data = veteran, trace = 0, method.inference = "u-statistic") -summary(BT.ustat) +BT.half <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = FALSE, add.halfNeutral = TRUE) +confint(BT.half, statistic = "favorable") #+END_SRC #+RESULTS: -#+begin_example - Generalized pairwise comparisons with 1 endpoint - - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 - - confidence level: 0.95 - - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) - - censored pairs : probabilistic score based on the survival curves - - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta - time 20 100 37.78 46.54 15.68 0 -0.0877 - CI [2.5% ; 97.5%] p.value - [-0.2735;0.1045] 0.37162 -#+end_example +: estimate se lower.ci upper.ci null p.value +: time_t20 0.4561708 0.04880921 0.3632263 0.5522714 0.5 0.3716632 -The first two approaches require simulating a large number of samples -and applying the GPC to each of these samples. The =seed= argument is -used to generate a seed for each sample. The number of samples is set -using the arugment =n.resampling= and it should large enough to limit -the Monte Carlo error when estimating the p-value. Typically should be -at least 10000 to get, roughtly, 2-digit precision, as examplified -below: +Note that the win ratio is also often defined that way, i.e. as +\(\frac{\Prob[Y\geq X + \tau] + 0.5\Prob[|Y- X| < \tau]}{\Prob[X\geq Y + +\tau] + 0.5\Prob[|Y- X| < \tau]}\), leading to: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -set.seed(10) -sapply(1:10, function(i){mean(rbinom(1e4, size = 1, prob = 0.05))}) +confint(BT.half, statistic = "winRatio") #+END_SRC #+RESULTS: -: [1] 0.0511 0.0491 0.0489 0.0454 0.0516 0.0522 0.0468 0.0483 0.0491 0.0508 -Indeed, here we get a reasonnable approximation of =0.05= (if we round -and only keep 2 digits). Note that to get 3 digits precision we would -need more samples. The last method does not rely on resampling but on -the computation of the influence function of the -estimator. Fortunately, when using the Gehan's scoring rule, this does -not really involve any extra-calculations and this is therefore very -fast to perform. When using the Peron's scoring rule, more serious -extra-calculations are involved so the computation time is expected to -increase by a factor 5 to 10 compared to the point estimate alone -(i.e. =method.inference= equal to ="none"=). +: estimate se lower.ci upper.ci null p.value +: time_t20 0.8388127 0.1650208 0.5704361 1.233454 1 0.3716211 -\bigskip +Testing a Net Benefit of 0, a Win Ratio of 1, and a +Wilcoxon-Mann-Whitney parameter of 0.5 corresponds to the same +hypothesis and therefore the same p-value should be obtained. The +(small) discrepancy in p-values observed in this example (0.371617 +vs. 0.3716211 vs. 0.3716632) are due to large sample +approximation. Such discrepancies will not arise when using +permutation tests, e.g.: +#+BEGIN_SRC R :exports both :results output :session *R* :cache no +BT.halfperm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = FALSE, add.halfNeutral = TRUE, + method.inference = "permutation", seed = 10) +Mstat <- rbind(netBenefit = confint(BT.halfperm, statistic = "netBenefit"), + winRatio = confint(BT.halfperm, statistic = "winRatio"), + favorable = confint(BT.halfperm, statistic = "favorable")) +Mstat +#+END_SRC -Note: it is possible to relax the exchangeability assumption using a -studentized permutation. A studentized bootstrap is also possible to -improve on the better small samples properties of the bootstrap -confidence intervals. Both rely on the asymptotic approach to estimate -standard errors and are more numerically intensive. +#+RESULTS: +: estimate se lower.ci upper.ci null p.value +: netBenefit -0.08765836 0.09535235 NA NA 0.0 0.3526474 +: winRatio 0.83881270 0.19924455 NA NA 1.0 0.3526474 +: favorable 0.45617082 0.04767618 NA NA 0.5 0.3526474 + +This approach has two drawbacks though: no (reliable) confidence +intervals and greater computation time. \clearpage @@ -796,12 +975,8 @@ standard errors and are more numerically intensive. Yes, as with any other statistical method. Having a pre-defined statistical plan (i.e. written before looking at the data) specifying the hierarchy of endpoints, their threshold of clinical relevance is -recommanded. - -\bigskip - -This being said, there are mainly two way to conclude about results -from running multiple GPC: +recommanded. When planning multiple GPC, summarize the results can be +done via one of two principles: - *intersection union principle*: one rejects the (global) null hypothesis if there is evidence for an effect in all the GPC analyses. This is typically a sensitivity analysis: checking that @@ -856,7 +1031,7 @@ Here we look at whether there is a benefit in survival alone (first priority =time_t20=) or a benefit over both endpoint (second priority =karno=). Setting the argument =cumulative= to =FALSE= when considering non-hierarchical GPC analyses enables to efficiently -adjust endpoint specific GPC for multiple comparisons: +adjust endpoint-specific GPC for multiple comparisons: #+BEGIN_SRC R :exports both :results output :session *R* :cache no BuyseMultComp(BT.nH, cumulative = FALSE, endpoint = 1:2) #+END_SRC @@ -872,17 +1047,17 @@ BuyseMultComp(BT.nH, cumulative = FALSE, endpoint = 1:2) One can also consider the global endpoint of two different GPC analyses: #+BEGIN_SRC R :exports both :results output :session *R* :cache no -BuyseMultComp(list(hierchical = BT.H, Obrien = BT.nH), cluster = "id") +BuyseMultComp(list(hierarchical = BT.H, Obrien = BT.nH), cluster = "id") #+END_SRC #+RESULTS: : - Univariate tests: -: estimate se lower.ci upper.ci null p.value lower.band upper.band -: hierchical -0.10092285 0.09971277 -0.2901336 0.09588144 0 0.3147770 -0.3014645 0.1081696 -: Obrien -0.05949414 0.08700807 -0.2266953 0.11111326 0 0.4951361 -0.2368800 0.1217304 -: adj.p.value -: hierchical 0.3831444 -: Obrien 0.5851872 +: estimate se lower.ci upper.ci null p.value lower.band +: hierarchical -0.10092285 0.09971277 -0.2901336 0.09588144 0 0.3147770 -0.3014645 +: Obrien -0.05949414 0.08700807 -0.2266953 0.11111326 0 0.4951361 -0.2368800 +: upper.band adj.p.value +: hierarchical 0.1081696 0.3831444 +: Obrien 0.1217304 0.5851872 Finally the =sensitivity= method can also be used to adjust for multiple comparisons over multiple thresholds: @@ -897,16 +1072,16 @@ BTse.ustat[,c("time","estimate", #+RESULTS: #+begin_example time estimate lower.ci upper.ci p.value lower.band upper.band adj.p.value -1 0.00000 -0.08752774 -0.27851884 0.11012263 0.3858177 -0.32450860 0.1597923 0.7746620 -2 55.55556 -0.08095829 -0.25229456 0.09530004 0.3682107 -0.29401340 0.1397613 0.7528122 -3 111.11111 -0.03170177 -0.17629003 0.11422560 0.6712414 -0.21223939 0.1509285 0.9810295 -4 166.66667 0.01896964 -0.10713643 0.14447503 0.7688360 -0.13892698 0.1759257 0.9969925 -5 222.22222 0.03315614 -0.07506821 0.14060850 0.5486177 -0.10250127 0.1676028 0.9257172 -6 277.77778 0.04217485 -0.04914025 0.13279075 0.3653982 -0.07236883 0.1556205 0.7492675 -7 333.33333 0.04112991 -0.03631838 0.11808708 0.2979105 -0.05604663 0.1375345 0.6544816 -8 388.88889 0.04075638 -0.02402114 0.10519310 0.2174545 -0.04053858 0.1215153 0.5206881 -9 444.44444 0.04097871 -0.01844156 0.10011054 0.1764199 -0.03359858 0.1151022 0.4429140 -10 500.00000 0.03517173 -0.01915553 0.08929191 0.2044340 -0.03301187 0.1030295 0.4967546 +1 0.00000 -0.08752774 -0.27851884 0.11012263 0.3858177 -0.32448885 0.1597708 0.7745625 +2 55.55556 -0.08095829 -0.25229456 0.09530004 0.3682107 -0.29399544 0.1397420 0.7528122 +3 111.11111 -0.03170177 -0.17629003 0.11422560 0.6712414 -0.21222383 0.1509125 0.9810274 +4 166.66667 0.01896964 -0.10713643 0.14447503 0.7688360 -0.13891317 0.1759120 0.9969926 +5 222.22222 0.03315614 -0.07506821 0.14060850 0.5486177 -0.10248934 0.1675911 0.9257172 +6 277.77778 0.04217485 -0.04914025 0.13279075 0.3653982 -0.07235871 0.1556106 0.7492675 +7 333.33333 0.04112991 -0.03631838 0.11808708 0.2979105 -0.05603803 0.1375260 0.6545176 +8 388.88889 0.04075638 -0.02402114 0.10519310 0.2174545 -0.04053138 0.1215082 0.5203739 +9 444.44444 0.04097871 -0.01844156 0.10011054 0.1764199 -0.03359197 0.1150957 0.4429140 +10 500.00000 0.03517173 -0.01915553 0.08929191 0.2044340 -0.03300583 0.1030235 0.4967546 #+end_example Here by setting the argument =band= to =TRUE= (and =adj.p.value= to @@ -1001,8 +1176,8 @@ ggsave(autoplot(BTse.H, col = NA), filename = file.path("figures","gg-sensitivit #+END_SRC #+RESULTS: -Note that the autoplot function cannot be used when more than 2 -thresholds are varied at the same time. +The autoplot function can only be used when 1 or 2 thresholds are +varied at the same time. #+RESULTS: \clearpage @@ -1038,18 +1213,18 @@ getPairScore(BT.keep, endpoint = 1) #+RESULTS: #+begin_example - index.1 index.2 favorable unfavorable neutral uninf weight - 1: 1 70 1 0 0 0 1 - 2: 2 70 1 0 0 0 1 - 3: 3 70 1 0 0 0 1 - 4: 4 70 1 0 0 0 1 - 5: 5 70 1 0 0 0 1 - --- -4688: 65 137 0 1 0 0 1 -4689: 66 137 0 1 0 0 1 -4690: 67 137 0 1 0 0 1 -4691: 68 137 0 1 0 0 1 -4692: 69 137 0 1 0 0 1 + index.Pl index.Exp favorable unfavorable neutral uninf weight + 1: 1 70 1 0 0 0 1 + 2: 2 70 1 0 0 0 1 + 3: 3 70 1 0 0 0 1 + 4: 4 70 1 0 0 0 1 + 5: 5 70 1 0 0 0 1 + --- +4688: 65 137 0 1 0 0 1 +4689: 66 137 0 1 0 0 1 +4690: 67 137 0 1 0 0 1 +4691: 68 137 0 1 0 0 1 +4692: 69 137 0 1 0 0 1 #+end_example Each line corresponds to different comparison between a pair from the @@ -1066,8 +1241,8 @@ veteran[c(70,1),] #+RESULTS: : id trt celltype time status karno diagtime age prior -: 70 70 2 squamous 999 1 90 12 54 10 -: 1 1 1 squamous 72 1 60 7 69 0 +: 70 70 Exp squamous 999 1 90 12 54 10 +: 1 1 Pl squamous 72 1 60 7 69 0 For the first pair, the event was observed for both observations and @@ -1149,10 +1324,10 @@ getPairScore(BT.keep2, endpoint = 1, rm.withinStrata = FALSE)[91] #+END_SRC #+RESULTS: -: index.1 index.2 indexWithinStrata.1 indexWithinStrata.2 favorable unfavorable neutral -: 1: 22 71 22 2 0 0.6950827 0.3049173 -: uninf weight -: 1: 0 1 +: index.Pl index.Exp indexWithinStrata.Pl indexWithinStrata.Exp favorable unfavorable +: 1: 22 71 22 2 0 0.6950827 +: neutral uninf weight +: 1: 0.3049173 0 1 In the dataset this corresponds to: #+BEGIN_SRC R :exports both :results output :session *R* :cache no @@ -1161,8 +1336,8 @@ veteran[c(22,71),] #+RESULTS: : id trt celltype time status karno diagtime age prior -: 22 22 1 smallcell 97 0 60 5 67 0 -: 71 71 2 squamous 112 1 80 6 60 0 +: 22 22 Pl smallcell 97 0 60 5 67 0 +: 71 71 Exp squamous 112 1 80 6 60 0 The observation from the control group is censored at 97 while the observation from the treatment group has an event at 112. Since the @@ -1268,10 +1443,10 @@ getPairScore(BT.keep2, endpoint = 1, rm.withinStrata = FALSE)[148] #+END_SRC #+RESULTS: -: index.1 index.2 indexWithinStrata.1 indexWithinStrata.2 favorable unfavorable neutral -: 1: 10 72 10 3 0.5058685 0.3770426 0.1170889 -: uninf weight -: 1: 0 1 +: index.Pl index.Exp indexWithinStrata.Pl indexWithinStrata.Exp favorable unfavorable +: 1: 10 72 10 3 0.5058685 0.3770426 +: neutral uninf weight +: 1: 0.1170889 0 1 which corresponds to the observations: #+BEGIN_SRC R :exports both :results output :session *R* :cache no @@ -1280,8 +1455,8 @@ veteran[c(10,72),] #+RESULTS: : id trt celltype time status karno diagtime age prior -: 10 10 1 squamous 100 0 70 6 70 0 -: 72 72 2 squamous 87 0 80 3 48 0 +: 10 10 Pl squamous 100 0 70 6 70 0 +: 72 72 Exp squamous 87 0 80 3 48 0 The probability in favor of the treatment (\(p_F\)) and control (\(p_{UF}\)) can be computed as: @@ -1730,8 +1905,8 @@ s.correction <- model.tables(e.correction, column = c("favorable","unfavorable", #+END_SRC #+RESULTS: -: Advarselsbesked: -: I .BuyseTest(envir = envirBT, iid = outArgs$iid, method.inference = "none", : +: Warning message: +: In .BuyseTest(envir = envirBT, iid = outArgs$iid, method.inference = "none", : : Some of the survival curves for endpoint(s) "timeC" are unknown beyond a survival of 0.25. : The correction of uninformative pairs assume that uninformative pairs would on average behave like informative pairs. : This can be a strong assumption and have substantial impact when the tail of the survival curve is unknown. @@ -1884,7 +2059,7 @@ summary(powerW) Simulation study with Generalized pairwise comparison with 1000 samples - - statistic : net benefit (null hypothesis Delta=0) + - net benefit statistic (null hypothesis Delta=0) endpoint threshold n.T n.C mean.estimate sd.estimate mean.se rejection.rate Y 1e-12 5 5 0.2484 0.359 0.3395 0.069 10 10 0.2471 0.2551 0.2464 0.137 @@ -1950,10 +2125,13 @@ summary(nW) #+RESULTS: #+begin_example - Simulation study with Generalized pairwise comparison - with 1000 samples + Sample size calculation with Generalized pairwise comparison + for a power of 0.8 and type 1 error rate of 0.05 + + - estimated sample size (mean [min;max]): 89 [60;145] controls + 89 [60;145] treated - - statistic : net benefit (null hypothesis Delta=0) + - net benefit statistic (null hypothesis Delta=0) endpoint threshold n.T n.C mean.estimate sd.estimate mean.se rejection.rate Y 1e-12 89 89 0.2452 0.0854 0.0834 0.806 diff --git a/inst/doc-software/overview.pdf b/inst/doc-software/overview.pdf index 75d561bb5a3cae64fc4325870e88d8c7a0ea5793..702223df0f6a20b118a76fca7add3d81f42fd954 100644 GIT binary patch delta 319524 zcmb@tV~{367bV=bZB3g`+qSJ~+qULu+cu{)ZQJIwZQJHI@4NeFBR1mOh}|Dmkx`YA zC-U4|Q5PrcmdPIXiQ;k797(`Pltn}wJV|r_Bmfd-z<)12I3@`PXFD}7M>7&;I3{@` zS7)n#GnoI)`1k%l_kS}~%v>DYoK4JJNZ9{9QGsKUGqbmFwIpF?CrR6FgQh{8N1j%q zp56fif&K)&Nt^A2LQk_G0i*f9hU5C*!jb$haByb!rY^3|W=3}Z895kR!*Tx?T;>0E 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-214,16 +214,18 @@ can be summarized as follow. Denote the endpoint by \(Y\) in the treatment group and by \(X\) in the control group. Given a threshold of clinical relevance \(\tau\), the aim of GPC is to estimate the -proportion in favor of treatment \(\Prob[Y \geq X + \tau]\) and the -proportion in favor of control \(\Prob[X \geq Y + \tau]\). Other -statistics such as the net benefit \(\Prob[Y \geq X + \tau]-\Prob[X -\geq Y + \tau]\) or the win ratio \(\frac{\Prob[Y \geq X + -\tau]}{\Prob[X \geq Y + \tau]}\) can then be deduced. The vignette is -written for readers familar with the GPC framework \footnote{if not, -\cite{buyse2010generalized} is a good place to start.}, e.g. prioritized -endpoints, pair, net benefit, win ratio, threshold of clinical -relevance, \ldots, since it focuses on the software aspect -of the \textbf{BuyseTest} package (not on the underlying statistical model). +proportion in favor of treatment\footnote{in absence of ties this equals +the Wilcoxon-Mann-Whitney parameter} \(\Prob[Y \geq X + \tau]\) and +the proportion in favor of control \(\Prob[X \geq Y + \tau]\). Their +difference \(\Prob[Y \geq X + \tau]-\Prob[X \geq Y + \tau]\) leads to +the net benefit and their ratio \(\frac{\Prob[Y \geq X + +\tau]}{\Prob[X \geq Y + \tau]}\) to the win ratio (in absence of +ties). The vignette is written for readers familar with the GPC +framework \footnote{if not, \cite{buyse2010generalized} is a good place to +start.}, e.g. prioritized endpoints, pair, net benefit, win ratio, +threshold of clinical relevance, \ldots, since it focuses on the +software aspect of the \textbf{BuyseTest} package (not on the underlying +statistical model). \bigskip @@ -240,6 +242,7 @@ \item \texttt{confint} to extract estimates, confidence intervals, and p.values. \item \texttt{plot} for a graphical display of the scoring of the pair per endpoint. \item \texttt{sensitivity} to perform a sensitivity analysis on the choice of the threshold(s). +\item \texttt{nobs} to extract the number of observations and pairs. \item \texttt{getIid} to extract the iid decomposition of the estimator. \item \texttt{getPairScore} to extract the contribution of each pair to the net benefit/win ratio. \item \texttt{getSurvival} to extract the estimates of the survival used for right-censored endpoints. @@ -270,17 +273,18 @@ \begin{lstlisting} data(cancer, package = "survival") veteran <- cbind(id = 1:NROW(veteran), veteran) +veteran$trt <- factor(veteran$trt,1:2,c("Pl","Exp")) head(veteran) \end{lstlisting} \begin{verbatim} id trt celltype time status karno diagtime age prior -1 1 1 squamous 72 1 60 7 69 0 -2 2 1 squamous 411 1 70 5 64 10 -3 3 1 squamous 228 1 60 3 38 0 -4 4 1 squamous 126 1 60 9 63 10 -5 5 1 squamous 118 1 70 11 65 10 -6 6 1 squamous 10 1 20 5 49 0 +1 1 Pl squamous 72 1 60 7 69 0 +2 2 Pl squamous 411 1 70 5 64 10 +3 3 Pl squamous 228 1 60 3 38 0 +4 4 Pl squamous 126 1 60 9 63 10 +5 5 Pl squamous 118 1 70 11 65 10 +6 6 Pl squamous 10 1 20 5 49 0 \end{verbatim} @@ -297,7 +301,7 @@ \end{lstlisting} \begin{verbatim} -[1] '3.0.0' +[1] ‘3.0.0’ \end{verbatim} @@ -309,41 +313,44 @@ \end{lstlisting} \begin{verbatim} -R version 4.2.0 (2022-04-22 ucrt) -Platform: x86_64-w64-mingw32/x64 (64-bit) -Running under: Windows 10 x64 (build 19045) +R version 4.2.0 (2022-04-22) +Platform: x86_64-pc-linux-gnu (64-bit) +Running under: Ubuntu 20.04.4 LTS Matrix products: default +BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0 +LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0 locale: -[1] LC_COLLATE=Danish_Denmark.utf8 LC_CTYPE=Danish_Denmark.utf8 -[3] LC_MONETARY=Danish_Denmark.utf8 LC_NUMERIC=C -[5] LC_TIME=Danish_Denmark.utf8 + [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8 + [4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 + [7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C +[10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: -[1] data.table_1.14.2 BuyseTest_3.0.0 Rcpp_1.0.8.3 prodlim_2019.11.13 -[5] ggplot2_3.4.2 survival_3.3-1 +[1] data.table_1.14.2 BuyseTest_3.0.0 Rcpp_1.0.9 prodlim_2019.11.13 +[5] ggplot2_3.4.0 survival_3.5-0 loaded via a namespace (and not attached): - [1] pillar_1.9.0 compiler_4.2.0 tools_4.2.0 digest_0.6.31 - [5] lifecycle_1.0.3 tibble_3.2.1 gtable_0.3.1 lattice_0.20-45 - [9] pkgconfig_2.0.3 rlang_1.1.0 Matrix_1.5-1 cli_3.6.0 -[13] parallel_4.2.0 SparseM_1.81 withr_2.5.0 dplyr_1.1.0 -[17] MatrixModels_0.5-0 generics_0.1.3 vctrs_0.5.2 globals_0.16.2 -[21] stats4_4.2.0 grid_4.2.0 tidyselect_1.2.0 glue_1.6.2 -[25] listenv_0.9.0 R6_2.5.1 future.apply_1.10.0 fansi_1.0.4 -[29] parallelly_1.34.0 lava_1.7.2.1 magrittr_2.0.3 scales_1.2.1 -[33] codetools_0.2-18 splines_4.2.0 future_1.31.0 colorspace_2.1-0 -[37] utf8_1.2.3 munsell_0.5.0 + [1] pillar_1.8.1 compiler_4.2.0 tools_4.2.0 digest_0.6.31 + [5] lifecycle_1.0.3 tibble_3.1.8 gtable_0.3.1 lattice_0.20-45 + [9] pkgconfig_2.0.3 rlang_1.0.6 Matrix_1.4-1 DBI_1.1.3 +[13] cli_3.5.0 parallel_4.2.0 SparseM_1.81 withr_2.5.0 +[17] dplyr_1.0.10 MatrixModels_0.5-0 generics_0.1.3 vctrs_0.5.1 +[21] globals_0.16.1 stats4_4.2.0 grid_4.2.0 tidyselect_1.2.0 +[25] glue_1.6.2 listenv_0.8.0 R6_2.5.1 future.apply_1.9.1 +[29] fansi_1.0.3 parallelly_1.32.1 lava_1.7.2 magrittr_2.0.3 +[33] scales_1.2.1 codetools_0.2-18 splines_4.2.0 assertthat_0.2.1 +[37] future_1.28.0 colorspace_2.0-3 utf8_1.2.2 munsell_0.5.0 \end{verbatim} \clearpage \section{Performing generalized pairwise comparisons (GPC) using the \texttt{BuyseTest} function} -\label{sec:org6608846} +\label{sec:orgfecca0d} To perform generalized pairwise comparisons, the \texttt{BuyseTest} function needs: \begin{itemize} @@ -353,7 +360,7 @@ \section{Performing generalized pairwise comparisons (GPC) using the \texttt{Buy \item the variable defining the two treatment groups \hfill - argument \texttt{treatment} \end{itemize} -The \texttt{BuyseTest} function has many optional arguments to specify for example: +The \texttt{BuyseTest} function has many optional arguments. For example: \begin{itemize} \item the threshold of clinical relevance associated to each endpoint \hfill - argument \texttt{threshold} \item the censoring associated to each endpoint (for time to event endpoints) \hfill - argument \texttt{status} @@ -381,7 +388,7 @@ \section{Performing generalized pairwise comparisons (GPC) using the \texttt{Buy Generalized Pairwise Comparisons Settings - - 2 groups : Control = 1 and Treatment = 2 + - 2 groups : Control = Pl and Treatment = Exp - 1 endpoint: priority endpoint type operator threshold event 1 time time to event higher is favorable 20 status (0 1) @@ -423,7 +430,7 @@ \section{Performing generalized pairwise comparisons (GPC) using the \texttt{Buy \end{lstlisting} \subsection{Displaying the results} -\label{sec:orgad6051f} +\label{sec:org15a4b64} The results of the GPC can be displayed using the \texttt{summary} method: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} @@ -438,7 +445,7 @@ \subsection{Displaying the results} - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta @@ -447,10 +454,36 @@ \subsection{Displaying the results} [-0.2735;0.1045] 0.37162 \end{verbatim} - To display the number of pairs instead of the percentage of pairs -that are favorable/unfavorable/neutral/uniformative, set the argument -\texttt{percentage} to \texttt{FALSE}. The \texttt{model.tables} method returns the table -displayed at the end of the \texttt{summary} in a \texttt{data.frame} format: + +It displays information about each endpoint, percentage of pairs +classified as favorable, unfavorable, neutral, and uninformative, as +well as the estimated net benefit (column \texttt{Delta}), its confidence +interval, and the corresponding p-value testing the absence of a group +difference. Other To display the number of pairs instead of the +percentage of pairs that are +favorable/unfavorable/neutral/uniformative, set the argument +\texttt{percentage} to \texttt{FALSE}. See \texttt{help(S4BuyseTest-summary)} for more +details about the \texttt{summary} method, its input and output. For a more +concise display of the results, consider using the \texttt{print} method: +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +print(BT, percentage = FALSE) +\end{lstlisting} + +\begin{verbatim} +endpoint threshold total favorable unfavorable neutral uninf Delta CI [2.5% ; 97.5%] + time 20 4692 1772.59 2183.89 735.52 0 -0.0877 [-0.2735;0.1045] +p.value +0.37162 +\end{verbatim} + + +\bigskip + +To access these values, we recommand using the \texttt{model.tables} method +that outputs the information from the previous table in a \texttt{data.frame} +format: + \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} model.tables(BT, percentage = FALSE) @@ -490,37 +523,11 @@ \subsection{Displaying the results} \end{verbatim} -By default \texttt{summary} displays results relative to the net benefit. To -get results for the win ratio set the argument \texttt{statistic} to -"winRatio": -\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} -\begin{lstlisting} -summary(BT, statistic = "winRatio") -\end{lstlisting} - -\begin{verbatim} - Generalized pairwise comparisons with 1 endpoint - - - statistic : win ratio (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 1 - - confidence level: 0.95 - - inference : H-projection of order 1 after log transformation - - treatment groups: 2 (treatment) vs. 1 (control) - - censored pairs : probabilistic score based on the survival curves - - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta - time 20 100 37.78 46.54 15.68 0 0.8117 - CI [2.5% ; 97.5%] p.value - [0.5134;1.2833] 0.37195 -\end{verbatim} - -See \texttt{help(S4BuyseTest-summary)} for more details about the \texttt{summary} -method and its output. \clearpage \subsection{Stratified GPC} -\label{sec:org7ce1c98} +\label{sec:orgf07e3aa} GPC can be performed for subgroups of a categorical variable \hfill - argument \texttt{strata} \newline For instance, the celltype may have huge @@ -535,14 +542,15 @@ \subsection{Stratified GPC} \end{lstlisting} Not being wrapped by \texttt{bin}, \texttt{cont} or \texttt{tte} differentiates it from -endpoint variables. When doing a stratified analysis, the summary -method displays strata-specific and global results\footnote{the -strata-specific results can be removed by setting the argument -\texttt{strata} to \texttt{"global"} when calling \texttt{summary}.}: +endpoint variables. When doing a stratified analysis, the summary method +displays strata-specific and global results\footnote{the strata-specific +results can be removed by setting the argument \texttt{strata} to \texttt{"global"} +when calling \texttt{summary}.}: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -summary(BTstrata, type.display = c("endpoint","threshold","strata", - "total","favorable","unfavorable","delta","Delta")) +keep.colStrata <- c("endpoint","strata", "total", + "favorable","unfavorable","neutral","uninf","delta","Delta") +summary(BTstrata, type.display = keep.colStrata) \end{lstlisting} \begin{verbatim} @@ -552,89 +560,160 @@ \subsection{Stratified GPC} - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - strata weights : 26.38%, 34.63%, 18.47%, 20.52% - censored pairs : probabilistic score based on the survival curves - uninformative pairs: no contribution - results - endpoint threshold strata total(%) favorable(%) unfavorable(%) delta Delta - time 20 global 100.00 36.70 46.66 -0.0997 -0.0997 - squamous 25.38 14.33 8.77 0.2193 - smallcell 45.69 12.69 20.88 -0.1792 - adeno 13.71 4.74 6.15 -0.1034 - large 15.23 4.30 9.97 -0.3722 + endpoint strata total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) delta Delta + time global 100.00 36.06 45.77 17.33 0.85 -0.0997 -0.0997 + squamous 25.38 14.33 8.77 2.28 0.00 0.2193 + smallcell 45.69 12.69 20.88 11.27 0.85 -0.1792 + adeno 13.71 4.74 6.15 2.81 0.00 -0.1034 + large 15.23 4.30 9.97 0.96 0.00 -0.3722 \end{verbatim} -Note that here the numbers in the total/favorable/unfavorable/ columns -are relative to the overall sample while the delta is only relative to -the strata. The global delta is a sum of the strata specific delta -weighted by the empirical proportion of pairs for each strata. The -weight of each strata is by default proportional to the number of -pairs. This behavior can be changed with the argument \texttt{pool.strata}: +The percentage of pairs in the +total/favorable/unfavorable/neutral/uninf columns are relative to the +overall number of pairs whereas the column \texttt{delta} presents the +strata-specific net benefits (in the last 4 lines). The last column +(\texttt{Delta}) displays the overall net benefit. + +\bigskip + +\Warning With this weighting scheme the proportion of favorable pairs +minus the proportion of unfavorable pairs does not equal the +stata-specific nor the global net benefit. To retrieve the net +benefits, we first extract the number of pairs per strata using the +method \texttt{nobs}: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -BTstrataCMH <- BuyseTest(ffstrata, data = veteran, trace = 0, pool.strata = "CMH") -summary(BTstrataCMH, type.display = c("endpoint","threshold","strata", - "total","favorable","unfavorable","delta","Delta")) +strata.obs <- nobs(BTstrata, stratified = TRUE) +strata.obs \end{lstlisting} \begin{verbatim} - Generalized pairwise comparisons with 1 endpoint and 4 strata + Pl Exp pairs +squamous 15 20 300 +smallcell 30 18 540 +adeno 9 18 162 +large 15 12 180 +\end{verbatim} - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 - - confidence level: 0.95 - - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) - - strata weights : 26.38%, 34.63%, 18.47%, 20.52% - - censored pairs : probabilistic score based on the survival curves - - uninformative pairs: no contribution - - results - endpoint threshold strata total(%) favorable(%) unfavorable(%) delta Delta - time 20 global 100.00 36.70 46.66 -0.0997 -0.0997 - squamous 25.38 14.33 8.77 0.2193 - smallcell 45.69 12.69 20.88 -0.1792 - adeno 13.71 4.74 6.15 -0.1034 - large 15.23 4.30 9.97 -0.3722 + +and use the method \texttt{model.tables} to extract the number of favorable and unfavorable +pairs per strata: +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +dfStrata <- model.tables(BTstrata, percentage = FALSE, + strata = c("squamous","smallcell","adeno","large"), + columns = c("strata","total","favorable","unfavorable")) +dfStrata +\end{lstlisting} + +\begin{verbatim} + strata total favorable unfavorable +2 squamous 300 169.40260 103.6104 +3 smallcell 540 150.00000 246.7778 +4 adeno 162 56.00000 72.7500 +5 large 180 50.83333 117.8333 \end{verbatim} -\texttt{CMH} stands for Cochran-Mantel-Haenszel whose weighted scheme has -been advocated in the litterature \citep{dong2018stratified}. We can -retrieve the weights by evalating the number of individual per strata -and treatment group: + +We retrieve the strata-specific net benefits by comparing, in each +strata, the number of favorable and unfavorable pairs relative to the +number of pairs\footnote{Alernatively one could compute, from the \texttt{summary}, the difference +between the percentage of favorable and unfavorable pairs relative to +the percentage of pairs in the strata, e.g. \((14.33\%-8.77\%)/25.38\% +\approx 21.93\%\)}: +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +delta <- (dfStrata$favorable - dfStrata$unfavorable)/strata.obs$pairs +delta +\end{lstlisting} + +\begin{verbatim} +[1] 0.2193074 -0.1792181 -0.1033951 -0.3722222 +\end{verbatim} + + + + +The global net benefit is then the sum of the strata-specific net +benefits weighted by the strata weights: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -nStrata <- table(veteran$celltype, veteran$trt) -nStrata +weightCMH <- strata.obs$pairs/(strata.obs$Pl + strata.obs$Exp) + +list(estimate = sum(delta * weightCMH/sum(weightCMH)), + weight = 100*weightCMH/sum(weightCMH)) \end{lstlisting} \begin{verbatim} +$estimate +[1] -0.09967584 - 1 2 -squamous 15 20 -smallcell 30 18 -adeno 9 18 -large 15 12 +$weight +[1] 26.38329 34.62807 18.46830 20.52034 \end{verbatim} + + +The default weighting scheme is \texttt{CMH}, standing for +Cochran-Mantel-Haenszel, which has been recommaned in the litterature +\citep{dong2018stratified}. It is efficient under the assumption of a +common multiplicative effect (across strata) on the odds ratio +scale. If the effect is thought additive, one should instead weight +proportionnaly to the number of pairs. This can be +achieved by specifying the argument \texttt{pool.strata}: + \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -nPairStrata <- nStrata[,1]*nStrata[,2] -wStrata <- rbind(default = nPairStrata, - CMH = nPairStrata/rowSums(nStrata)) -round(100*wStrata/rowSums(wStrata),2) +BTstrata2 <- BuyseTest(ffstrata, data = veteran, trace = 0, pool.strata = "buyse") +summary(BTstrata2, type.display = keep.colStrata) \end{lstlisting} \begin{verbatim} - squamous smallcell adeno large -default 25.38 45.69 13.71 15.23 -CMH 26.38 34.63 18.47 20.52 + Generalized pairwise comparisons with 1 endpoint and 4 strata + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : H-projection of order 1 after atanh transformation + - treatment groups: Exp (treatment) vs. Pl (control) + - strata weights : 25.38%, 45.69%, 13.71%, 15.23% + - censored pairs : probabilistic score based on the survival curves + - uninformative pairs: no contribution + - results + endpoint strata total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) delta Delta + time global 100.00 36.06 45.77 17.33 0.85 -0.0971 -0.0971 + squamous 25.38 14.33 8.77 2.28 0.00 0.2193 + smallcell 45.69 12.69 20.88 11.27 0.85 -0.1792 + adeno 13.71 4.74 6.15 2.81 0.00 -0.1034 + large 15.23 4.30 9.97 0.96 0.00 -0.3722 \end{verbatim} +The weighting scheme only affect the evaluation of the overall net +benefit, which now equals the difference between the overall +proportion of favorable vs. unfavorable pairs. As before the +strata-specific net benefits are still not equal to the difference +between the proportion of favorable and unfavorable pairs. While +extractors will by default output global estimates (i.e. after pooling +the results over strata) +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +confint(BTstrata2) +\end{lstlisting} + +\begin{verbatim} + estimate se lower.ci upper.ci null p.value +time_t20 -0.09706901 0.0977929 -0.2829348 0.09582321 0 0.323961 +\end{verbatim} -It is also possible to output strata specific results: + +one can specify the argument \texttt{stratified} to extract strata-specific estimates: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} confint(BTstrata, stratified = TRUE) @@ -651,9 +730,8 @@ \subsection{Stratified GPC} \clearpage - \subsection{Using multiple endpoints} -\label{sec:org3ef3f1c} +\label{sec:org64aceea} More than one endpoint can be considered by indicating a vector of endpoints, types, and thresholds. In the formula interface, the different endpoints must be separated with a "+" on the right hand @@ -672,7 +750,7 @@ \subsection{Using multiple endpoints} - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - neutral pairs : re-analyzed using lower priority endpoints - results @@ -729,7 +807,7 @@ \subsection{Using multiple endpoints} - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results endpoint threshold weight total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) delta @@ -791,10 +869,142 @@ \subsection{Using multiple endpoints} \end{verbatim} +\clearpage + +\subsection{Statistical inference} +\label{sec:org928b7f7} + +Several methods are available in \texttt{BuyseTest} to quantify uncertainty +about the estimates: +\begin{itemize} +\item \textbf{permutation test} setting the argument \texttt{method.inference} to +\texttt{"permutation"}. Assuming exchangeability under the null hypothesis, +this approach gives valid p-values (regardless to the sample size) +for testing the absence of a difference between the groups. +\end{itemize} +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +BT.perm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = 0, method.inference = "permutation", + seed = 10) +summary(BT.perm) +\end{lstlisting} + +\begin{verbatim} + Generalized pairwise comparisons with 1 endpoint + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : permutation test with 1000 samples + p-value computed using the permutation distribution + - treatment groups: Exp (treatment) vs. Pl (control) + - censored pairs : probabilistic score based on the survival curves + - results + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta p.value + time 20 100 37.78 46.54 15.68 0 -0.0877 0.35265 +\end{verbatim} + +\begin{itemize} +\item \textbf{bootstrap resampling} setting the argument \texttt{method.inference} to +\texttt{"bootstrap"}. In large enough samples, this approach gives valid +p-values and confidence intervals. +\end{itemize} + +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +BT.boot <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = 0, method.inference = "bootstrap", + seed = 10) +summary(BT.boot) +\end{lstlisting} + +\begin{verbatim} + Generalized pairwise comparisons with 1 endpoint + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : bootstrap resampling with 1000 samples + CI computed using the percentile method; p-value by test inversion + - treatment groups: Exp (treatment) vs. Pl (control) + - censored pairs : probabilistic score based on the survival curves + - results + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta + time 20 100 37.78 46.54 15.68 0 -0.0877 + CI [2.5% ; 97.5%] p.value + [-0.2721;0.1034] 0.38362 +\end{verbatim} + +\begin{itemize} +\item \textbf{asymptotic distribution} setting the argument \texttt{method.inference} to +\texttt{"u-statistic"}. In large enough samples, this approach gives valid +p-values and confidence intervals \citep{ozenne2021asymptotic}. +\end{itemize} + +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +BT.ustat <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = 0, method.inference = "u-statistic") +summary(BT.ustat) +\end{lstlisting} + +\begin{verbatim} + Generalized pairwise comparisons with 1 endpoint + + - statistic : net benefit (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 0 + - confidence level: 0.95 + - inference : H-projection of order 1 after atanh transformation + - treatment groups: Exp (treatment) vs. Pl (control) + - censored pairs : probabilistic score based on the survival curves + - results + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta + time 20 100 37.78 46.54 15.68 0 -0.0877 + CI [2.5% ; 97.5%] p.value + [-0.2735;0.1045] 0.37162 +\end{verbatim} + +The first two approaches require simulating a large number of samples +and applying the GPC to each of these samples. The \texttt{seed} argument is +used to generate a seed for each sample. The number of samples is set +using the arugment \texttt{n.resampling} and it should large enough to limit +the Monte Carlo error when estimating the p-value. Typically should be +at least 10000 to get, roughtly, 2-digit precision, as examplified +below: +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +set.seed(10) +sapply(1:10, function(i){mean(rbinom(1e4, size = 1, prob = 0.05))}) +\end{lstlisting} + +\begin{verbatim} +[1] 0.0511 0.0491 0.0489 0.0454 0.0516 0.0522 0.0468 0.0483 0.0491 0.0508 +\end{verbatim} + +Indeed, here we get a reasonnable approximation of \texttt{0.05} (if we round +and only keep 2 digits). Note that to get 3 digits precision we would +need more samples. The last method does not rely on resampling but on +the computation of the influence function of the +estimator. Fortunately, when using the Gehan's scoring rule, this does +not really involve any extra-calculations and this is therefore very +fast to perform. When using the Peron's scoring rule, more serious +extra-calculations are involved so the computation time is expected to +increase by a factor 5 to 10 compared to the point estimate alone +(i.e. \texttt{method.inference} equal to \texttt{"none"}). + +\bigskip + +Note: it is possible to relax the exchangeability assumption using a +studentized permutation. A studentized bootstrap is also possible to +improve on the better small samples properties of the bootstrap +confidence intervals. Both rely on the asymptotic approach to estimate +standard errors and are more numerically intensive. + \clearpage \subsection{What if smaller is better?} -\label{sec:org6e41682} +\label{sec:org2f4818a} By default \texttt{BuyseTest} will always assume that higher values of an endpoint are favorable. This behavior can be changed by specifying \texttt{operator = "<0"} for an endpoint: @@ -812,7 +1022,7 @@ \subsection{What if smaller is better?} - null hypothesis : Delta == 0 - confidence level: 0.95 - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta @@ -828,7 +1038,7 @@ \subsection{What if smaller is better?} \clearpage \subsection{Stopping comparison for neutral pairs} -\label{sec:org4b1a2e3} +\label{sec:org303c889} In presence of neutral pairs, \texttt{BuyseTest} will, by default, continue the comparison on the endpoints with lower priority. For instance let consider a dataset with one observation in each treatment arm: @@ -899,149 +1109,142 @@ \subsection{Stopping comparison for neutral pairs} \clearpage -\subsection{What about p-value and confidence intervals?} -\label{sec:org4598fce} +\subsection{What about other summary statistics than the net benefit?} +\label{sec:org8094779} -Several methods are available in \texttt{BuyseTest} to perform statistical inference: -\begin{itemize} -\item \textbf{permutation test} setting the argument \texttt{method.inference} to -\texttt{"permutation"}. Assuming exchangeability under the null hypothesis, -this approach gives valid p-values (regardless to the sample size) -for testing the absence of a difference between the groups. -\end{itemize} +By default methods such as \texttt{summary} display results relative to the +net benefit. Three other summary statistics are accessible: proportion +in favor of treatment \(\Prob[Y\geq X + \tau]\), proportion in favor +of control \(\Prob[X\geq Y + \tau]\), and their ratio \(\Prob[X\geq +Y + \tau]\). They can be access via the argument +\texttt{statistic}, e.g.: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -BT.perm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), - data = veteran, trace = 0, method.inference = "permutation", - seed = 10) -summary(BT.perm) +summary(BT, statistic = "winRatio") \end{lstlisting} \begin{verbatim} Generalized pairwise comparisons with 1 endpoint - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 + - statistic : win ratio (delta: endpoint specific, Delta: global) + - null hypothesis : Delta == 1 - confidence level: 0.95 - - inference : permutation test with 1000 samples - p-value computed using the permutation distribution - - treatment groups: 2 (treatment) vs. 1 (control) + - inference : H-projection of order 1 after log transformation + - treatment groups: Exp (treatment) vs. Pl (control) - censored pairs : probabilistic score based on the survival curves - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta p.value - time 20 100 37.78 46.54 15.68 0 -0.0877 0.35265 + endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta + time 20 100 37.78 46.54 15.68 0 0.8117 + CI [2.5% ; 97.5%] p.value + [0.5134;1.2833] 0.37195 \end{verbatim} -\begin{itemize} -\item \textbf{bootstrap resampling} setting the argument \texttt{method.inference} to -\texttt{"bootstrap"}. In large enough samples, this approach gives valid -p-values and confidence intervals. -\end{itemize} - +\Warning In presence of ties, it is recommanded to use another +definition for the proportion in favorable of treatment/control as +their null distribution depends on the data generative mechanism and +the threshold of clinical relevance. The \texttt{confint} method will use a +value of 0.5 for the null hypothesis: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -BT.boot <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), - data = veteran, trace = 0, method.inference = "bootstrap", - seed = 10) -summary(BT.boot) +confint(BT, statistic = "favorable") \end{lstlisting} \begin{verbatim} - Generalized pairwise comparisons with 1 endpoint - - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 - - confidence level: 0.95 - - inference : bootstrap resampling with 1000 samples - CI computed using the percentile method; p-value by test inversion - - treatment groups: 2 (treatment) vs. 1 (control) - - censored pairs : probabilistic score based on the survival curves - - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta - time 20 100 37.78 46.54 15.68 0 -0.0877 - CI [2.5% ; 97.5%] p.value - [-0.2721;0.1034] 0.38362 + estimate se lower.ci upper.ci null p.value +time_t20 0.3777905 0.04902199 0.2874747 0.477467 0.5 0.01673643 \end{verbatim} -\begin{itemize} -\item \textbf{asymptotic distribution} setting the argument \texttt{method.inference} to -\texttt{"u-statistic"}. In large enough samples, this approach gives valid -p-values and confidence intervals \citep{ozenne2021asymptotic}. -\end{itemize} +But this value does not correspond to the location of the null +distribution: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -BT.ustat <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), - data = veteran, trace = 0, method.inference = "u-statistic") -summary(BT.ustat) +BT.perm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = FALSE, + method.inference = "permutation", seed = 10) +confint(BT.perm, statistic = "favorable") \end{lstlisting} \begin{verbatim} - Generalized pairwise comparisons with 1 endpoint + estimate se lower.ci upper.ci null p.value +time_t20 0.3777905 0.04770182 NA NA 0.4205855 0.3556444 +\end{verbatim} - - statistic : net benefit (delta: endpoint specific, Delta: global) - - null hypothesis : Delta == 0 - - confidence level: 0.95 - - inference : H-projection of order 1 after atanh transformation - - treatment groups: 2 (treatment) vs. 1 (control) - - censored pairs : probabilistic score based on the survival curves - - results - endpoint threshold total(%) favorable(%) unfavorable(%) neutral(%) uninf(%) Delta - time 20 100 37.78 46.54 15.68 0 -0.0877 - CI [2.5% ; 97.5%] p.value - [-0.2735;0.1045] 0.37162 + +which, in this example, is around 0.42. Therefore the null hypotheses +tested by \texttt{confint} is generally not meaningful and the p-value should +generally be disregarded. For statistical testing we therefore +recommand defining the proportion in favor of treatment as +\(\Prob[Y\geq X + \tau] + 0.5\Prob[|Y- X| < \tau]\) which matches the +definition of the Wilcoxon-Mann-Whitney parameter. To do so, one +should set the argument \texttt{add.halfNeutral} to \texttt{TRUE} when calling +\texttt{BuyseTest}: +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +BT.half <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = FALSE, add.halfNeutral = TRUE) +confint(BT.half, statistic = "favorable") +\end{lstlisting} + +\begin{verbatim} + estimate se lower.ci upper.ci null p.value +time_t20 0.4561708 0.04880921 0.3632263 0.5522714 0.5 0.3716632 \end{verbatim} -The first two approaches require simulating a large number of samples -and applying the GPC to each of these samples. The \texttt{seed} argument is -used to generate a seed for each sample. The number of samples is set -using the arugment \texttt{n.resampling} and it should large enough to limit -the Monte Carlo error when estimating the p-value. Typically should be -at least 10000 to get, roughtly, 2-digit precision, as examplified -below: + +Note that the win ratio is also often defined that way, i.e. as +\(\frac{\Prob[Y\geq X + \tau] + 0.5\Prob[|Y- X| < \tau]}{\Prob[X\geq Y + +\tau] + 0.5\Prob[|Y- X| < \tau]}\), leading to: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -set.seed(10) -sapply(1:10, function(i){mean(rbinom(1e4, size = 1, prob = 0.05))}) +confint(BT.half, statistic = "winRatio") \end{lstlisting} \begin{verbatim} -[1] 0.0511 0.0491 0.0489 0.0454 0.0516 0.0522 0.0468 0.0483 0.0491 0.0508 + estimate se lower.ci upper.ci null p.value +time_t20 0.8388127 0.1650208 0.5704361 1.233454 1 0.3716211 \end{verbatim} -Indeed, here we get a reasonnable approximation of \texttt{0.05} (if we round -and only keep 2 digits). Note that to get 3 digits precision we would -need more samples. The last method does not rely on resampling but on -the computation of the influence function of the -estimator. Fortunately, when using the Gehan's scoring rule, this does -not really involve any extra-calculations and this is therefore very -fast to perform. When using the Peron's scoring rule, more serious -extra-calculations are involved so the computation time is expected to -increase by a factor 5 to 10 compared to the point estimate alone -(i.e. \texttt{method.inference} equal to \texttt{"none"}). -\bigskip +Testing a Net Benefit of 0, a Win Ratio of 1, and a +Wilcoxon-Mann-Whitney parameter of 0.5 corresponds to the same +hypothesis and therefore the same p-value should be obtained. The +(small) discrepancy in p-values observed in this example (0.371617 +vs. 0.3716211 vs. 0.3716632) are due to large sample +approximation. Such discrepancies will not arise when using +permutation tests, e.g.: +\lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} +\begin{lstlisting} +BT.halfperm <- BuyseTest(trt ~ tte(time, threshold = 20, status = "status"), + data = veteran, trace = FALSE, add.halfNeutral = TRUE, + method.inference = "permutation", seed = 10) +Mstat <- rbind(netBenefit = confint(BT.halfperm, statistic = "netBenefit"), + winRatio = confint(BT.halfperm, statistic = "winRatio"), + favorable = confint(BT.halfperm, statistic = "favorable")) +Mstat +\end{lstlisting} + +\begin{verbatim} + estimate se lower.ci upper.ci null p.value +netBenefit -0.08765836 0.09535235 NA NA 0.0 0.3526474 +winRatio 0.83881270 0.19924455 NA NA 1.0 0.3526474 +favorable 0.45617082 0.04767618 NA NA 0.5 0.3526474 +\end{verbatim} -Note: it is possible to relax the exchangeability assumption using a -studentized permutation. A studentized bootstrap is also possible to -improve on the better small samples properties of the bootstrap -confidence intervals. Both rely on the asymptotic approach to estimate -standard errors and are more numerically intensive. + +This approach has two drawbacks though: no (reliable) confidence +intervals and greater computation time. \clearpage \subsection{Is multiple testing a concern with GPC?} -\label{sec:org127d9b8} +\label{sec:orgec880ac} Yes, as with any other statistical method. Having a pre-defined statistical plan (i.e. written before looking at the data) specifying the hierarchy of endpoints, their threshold of clinical relevance is -recommanded. - -\bigskip - -This being said, there are mainly two way to conclude about results -from running multiple GPC: +recommanded. When planning multiple GPC, summarize the results can be +done via one of two principles: \begin{itemize} \item \textbf{intersection union principle}: one rejects the (global) null hypothesis if there is evidence for an effect in all the GPC @@ -1103,7 +1306,7 @@ \subsection{Is multiple testing a concern with GPC?} priority \texttt{time\_t20}) or a benefit over both endpoint (second priority \texttt{karno}). Setting the argument \texttt{cumulative} to \texttt{FALSE} when considering non-hierarchical GPC analyses enables to efficiently -adjust endpoint specific GPC for multiple comparisons: +adjust endpoint-specific GPC for multiple comparisons: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} BuyseMultComp(BT.nH, cumulative = FALSE, endpoint = 1:2) @@ -1123,17 +1326,17 @@ \subsection{Is multiple testing a concern with GPC?} One can also consider the global endpoint of two different GPC analyses: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} -BuyseMultComp(list(hierchical = BT.H, Obrien = BT.nH), cluster = "id") +BuyseMultComp(list(hierarchical = BT.H, Obrien = BT.nH), cluster = "id") \end{lstlisting} \begin{verbatim} - Univariate tests: - estimate se lower.ci upper.ci null p.value lower.band upper.band -hierchical -0.10092285 0.09971277 -0.2901336 0.09588144 0 0.3147770 -0.3014645 0.1081696 -Obrien -0.05949414 0.08700807 -0.2266953 0.11111326 0 0.4951361 -0.2368800 0.1217304 - adj.p.value -hierchical 0.3831444 -Obrien 0.5851872 + estimate se lower.ci upper.ci null p.value lower.band +hierarchical -0.10092285 0.09971277 -0.2901336 0.09588144 0 0.3147770 -0.3014645 +Obrien -0.05949414 0.08700807 -0.2266953 0.11111326 0 0.4951361 -0.2368800 + upper.band adj.p.value +hierarchical 0.1081696 0.3831444 +Obrien 0.1217304 0.5851872 \end{verbatim} @@ -1150,16 +1353,16 @@ \subsection{Is multiple testing a concern with GPC?} \begin{verbatim} time estimate lower.ci upper.ci p.value lower.band upper.band adj.p.value -1 0.00000 -0.08752774 -0.27851884 0.11012263 0.3858177 -0.32450860 0.1597923 0.7746620 -2 55.55556 -0.08095829 -0.25229456 0.09530004 0.3682107 -0.29401340 0.1397613 0.7528122 -3 111.11111 -0.03170177 -0.17629003 0.11422560 0.6712414 -0.21223939 0.1509285 0.9810295 -4 166.66667 0.01896964 -0.10713643 0.14447503 0.7688360 -0.13892698 0.1759257 0.9969925 -5 222.22222 0.03315614 -0.07506821 0.14060850 0.5486177 -0.10250127 0.1676028 0.9257172 -6 277.77778 0.04217485 -0.04914025 0.13279075 0.3653982 -0.07236883 0.1556205 0.7492675 -7 333.33333 0.04112991 -0.03631838 0.11808708 0.2979105 -0.05604663 0.1375345 0.6544816 -8 388.88889 0.04075638 -0.02402114 0.10519310 0.2174545 -0.04053858 0.1215153 0.5206881 -9 444.44444 0.04097871 -0.01844156 0.10011054 0.1764199 -0.03359858 0.1151022 0.4429140 -10 500.00000 0.03517173 -0.01915553 0.08929191 0.2044340 -0.03301187 0.1030295 0.4967546 +1 0.00000 -0.08752774 -0.27851884 0.11012263 0.3858177 -0.32448885 0.1597708 0.7745625 +2 55.55556 -0.08095829 -0.25229456 0.09530004 0.3682107 -0.29399544 0.1397420 0.7528122 +3 111.11111 -0.03170177 -0.17629003 0.11422560 0.6712414 -0.21222383 0.1509125 0.9810274 +4 166.66667 0.01896964 -0.10713643 0.14447503 0.7688360 -0.13891317 0.1759120 0.9969926 +5 222.22222 0.03315614 -0.07506821 0.14060850 0.5486177 -0.10248934 0.1675911 0.9257172 +6 277.77778 0.04217485 -0.04914025 0.13279075 0.3653982 -0.07235871 0.1556106 0.7492675 +7 333.33333 0.04112991 -0.03631838 0.11808708 0.2979105 -0.05603803 0.1375260 0.6545176 +8 388.88889 0.04075638 -0.02402114 0.10519310 0.2174545 -0.04053138 0.1215082 0.5203739 +9 444.44444 0.04097871 -0.01844156 0.10011054 0.1764199 -0.03359197 0.1150957 0.4429140 +10 500.00000 0.03517173 -0.01915553 0.08929191 0.2044340 -0.03300583 0.1030235 0.4967546 \end{verbatim} Here by setting the argument \texttt{band} to \texttt{TRUE} (and \texttt{adj.p.value} to @@ -1250,12 +1453,12 @@ \subsection{Is multiple testing a concern with GPC?} \includegraphics[width=\textwidth]{./figures/gg-sensitivity2.pdf} \end{center} -Note that the autoplot function cannot be used when more than 2 -thresholds are varied at the same time. +The autoplot function can only be used when 1 or 2 thresholds are +varied at the same time. \clearpage \section{Getting additional inside: looking at the pair level} -\label{sec:org1471139} +\label{sec:orgb9971db} So far we have looked at the overall score and probabilities. But it is also possible to extract the score relative to each pair, as well @@ -1264,7 +1467,7 @@ \section{Getting additional inside: looking at the pair level} each individual on the evaluation of the treatment. \subsection{Extracting the contribution of each pair to the statistic} -\label{sec:org28a33a5} +\label{sec:org46249c8} The net benefit or the win ratio statistics can be expressed as a sum of a score over all pairs of patients. The argument \texttt{keep.pairScore} enables to export the score relative to each pair in the output of @@ -1286,18 +1489,18 @@ \subsection{Extracting the contribution of each pair to the statistic} \end{lstlisting} \begin{verbatim} - index.1 index.2 favorable unfavorable neutral uninf weight - 1: 1 70 1 0 0 0 1 - 2: 2 70 1 0 0 0 1 - 3: 3 70 1 0 0 0 1 - 4: 4 70 1 0 0 0 1 - 5: 5 70 1 0 0 0 1 - --- -4688: 65 137 0 1 0 0 1 -4689: 66 137 0 1 0 0 1 -4690: 67 137 0 1 0 0 1 -4691: 68 137 0 1 0 0 1 -4692: 69 137 0 1 0 0 1 + index.Pl index.Exp favorable unfavorable neutral uninf weight + 1: 1 70 1 0 0 0 1 + 2: 2 70 1 0 0 0 1 + 3: 3 70 1 0 0 0 1 + 4: 4 70 1 0 0 0 1 + 5: 5 70 1 0 0 0 1 + --- +4688: 65 137 0 1 0 0 1 +4689: 66 137 0 1 0 0 1 +4690: 67 137 0 1 0 0 1 +4691: 68 137 0 1 0 0 1 +4692: 69 137 0 1 0 0 1 \end{verbatim} Each line corresponds to different comparison between a pair from the @@ -1315,8 +1518,8 @@ \subsection{Extracting the contribution of each pair to the statistic} \begin{verbatim} id trt celltype time status karno diagtime age prior -70 70 2 squamous 999 1 90 12 54 10 -1 1 1 squamous 72 1 60 7 69 0 +70 70 Exp squamous 999 1 90 12 54 10 +1 1 Pl squamous 72 1 60 7 69 0 \end{verbatim} @@ -1353,7 +1556,7 @@ \subsection{Extracting the contribution of each pair to the statistic} the method \texttt{getPairScore}. \subsection{Extracting the survival probabilities} -\label{sec:org77f2bdc} +\label{sec:orgbdc7b57} When using \texttt{scoring.rule} equals \texttt{"Peron"}, survival probabilities at event time, and event times +/- threshold in the control and treatment arms are used to score the pair. Setting \texttt{keep.survival} to \texttt{TRUE} and @@ -1398,7 +1601,7 @@ \subsection{Extracting the survival probabilities} \end{verbatim} \subsubsection{Computation of the score with only one censored event} -\label{sec:org9d8c009} +\label{sec:orgdfdde36} Let's look at pair 91: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} @@ -1407,10 +1610,10 @@ \subsubsection{Computation of the score with only one censored event} \end{lstlisting} \begin{verbatim} - index.1 index.2 indexWithinStrata.1 indexWithinStrata.2 favorable unfavorable neutral -1: 22 71 22 2 0 0.6950827 0.3049173 - uninf weight -1: 0 1 + index.Pl index.Exp indexWithinStrata.Pl indexWithinStrata.Exp favorable unfavorable +1: 22 71 22 2 0 0.6950827 + neutral uninf weight +1: 0.3049173 0 1 \end{verbatim} @@ -1422,8 +1625,8 @@ \subsubsection{Computation of the score with only one censored event} \begin{verbatim} id trt celltype time status karno diagtime age prior -22 22 1 smallcell 97 0 60 5 67 0 -71 71 2 squamous 112 1 80 6 60 0 +22 22 Pl smallcell 97 0 60 5 67 0 +71 71 Exp squamous 112 1 80 6 60 0 \end{verbatim} @@ -1513,7 +1716,7 @@ \subsubsection{Computation of the score with only one censored event} \end{verbatim} \subsubsection{Computation of the score with two censored events} -\label{sec:org0f9d698} +\label{sec:org46cdc2c} When both observations are censored, the formula for computing the probability in favor of treatment or control involves an @@ -1544,10 +1747,10 @@ \subsubsection{Computation of the score with two censored events} \end{lstlisting} \begin{verbatim} - index.1 index.2 indexWithinStrata.1 indexWithinStrata.2 favorable unfavorable neutral -1: 10 72 10 3 0.5058685 0.3770426 0.1170889 - uninf weight -1: 0 1 + index.Pl index.Exp indexWithinStrata.Pl indexWithinStrata.Exp favorable unfavorable +1: 10 72 10 3 0.5058685 0.3770426 + neutral uninf weight +1: 0.1170889 0 1 \end{verbatim} @@ -1559,8 +1762,8 @@ \subsubsection{Computation of the score with two censored events} \begin{verbatim} id trt celltype time status karno diagtime age prior -10 10 1 squamous 100 0 70 6 70 0 -72 72 2 squamous 87 0 80 3 48 0 +10 10 Pl squamous 100 0 70 6 70 0 +72 72 Exp squamous 87 0 80 3 48 0 \end{verbatim} @@ -1617,7 +1820,7 @@ \subsubsection{Computation of the score with two censored events} \clearpage \section{Dealing with missing values or/and right censoring} -\label{sec:orgdced178} +\label{sec:orgea37c7b} In presence of censoring or missing values, it is often not be possible to classify all pairs without a model for the censoring @@ -1714,7 +1917,7 @@ \section{Dealing with missing values or/and right censoring} \end{itemize} \subsection{Gehan's scoring rule} -\label{sec:org37ce495} +\label{sec:orgab3430b} In the example, Gehan's scoring rule: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} @@ -1735,7 +1938,7 @@ \subsection{Gehan's scoring rule} closer to 0 than the truth. \subsection{Peron's scoring rule} -\label{sec:org5b6cec2} +\label{sec:org65ef454} In the example, Peron's scoring rule: \lstset{language=r,label= ,caption= ,captionpos=b,numbers=none} \begin{lstlisting} @@ -1882,7 +2085,7 @@ \subsection{Peron's scoring rule} for defining \texttt{BuyseTTEM.survreg} can be helpful. \subsection{Correction via inverse probability-of-censoring weights (IPCW)} -\label{sec:org10f15f7} +\label{sec:org59f1c28} With IPCW, the weights of the non-informative pairs is redistributed to the informative pairs. This is only a good strategy when there are @@ -1951,7 +2154,7 @@ \subsection{Correction via inverse probability-of-censoring weights (IPCW)} i.e. the inverse probability of being informative. \subsection{Correction at the pair level} -\label{sec:orgbb3782f} +\label{sec:orgc44affe} Another possible correction is to distribute the non-informative weight of a pair to the average favorable/unfavorable/neutral @@ -2011,7 +2214,7 @@ \subsection{Correction at the pair level} \end{verbatim} \subsection{Note on the use of the corrections} -\label{sec:org55404f5} +\label{sec:org0df886b} As mentioned in \cite{peron2021correcting}, the corrections (at the pair level or IPCW) are assumes that uninformative pairs would on average @@ -2058,8 +2261,8 @@ \subsection{Note on the use of the corrections} \end{lstlisting} \begin{verbatim} -Advarselsbesked: -I .BuyseTest(envir = envirBT, iid = outArgs$iid, method.inference = "none", : +Warning message: +In .BuyseTest(envir = envirBT, iid = outArgs$iid, method.inference = "none", : Some of the survival curves for endpoint(s) "timeC" are unknown beyond a survival of 0.25. The correction of uninformative pairs assume that uninformative pairs would on average behave like informative pairs. This can be a strong assumption and have substantial impact when the tail of the survival curve is unknown. @@ -2086,7 +2289,7 @@ \subsection{Note on the use of the corrections} \clearpage \section{Simulating data using \texttt{simBuyseTest}} -\label{sec:orgee99471} +\label{sec:org2d21f06} You can simulate data with the \texttt{simBuyseTest} function. For instance the following code simulates data for 5 individuals in the treatment arm and 5 individuals in the control arm: @@ -2146,7 +2349,7 @@ \section{Simulating data using \texttt{simBuyseTest}} \clearpage \section{Power calculation using \texttt{powerBuyseTest}} -\label{sec:org4265aae} +\label{sec:org9ee7f63} The function \texttt{powerBuyseTest} can be used to perform power calculation, i.e., estimate the probability of rejecting a null @@ -2219,7 +2422,7 @@ \section{Power calculation using \texttt{powerBuyseTest}} Simulation study with Generalized pairwise comparison with 1000 samples - - statistic : net benefit (null hypothesis Delta=0) + - net benefit statistic (null hypothesis Delta=0) endpoint threshold n.T n.C mean.estimate sd.estimate mean.se rejection.rate Y 1e-12 5 5 0.2484 0.359 0.3395 0.069 10 10 0.2471 0.2551 0.2464 0.137 @@ -2265,11 +2468,11 @@ \section{Power calculation using \texttt{powerBuyseTest}} This procedure is inspired from the procedure presented by \cite{brunner2018rank} in section 3.8.2.2. In short, several 'large' datasets are generated and analyzed using GPC to approximate the -statistic of interest (\(\delta\)) and its asymptotic variance +statistic of interest (\(\Delta\)) and its asymptotic variance (\(\sigma^2\)). The sample size needed to achieve the requested power (\(1-\beta\)) and the requested type 1 error (\(\alpha\)) is then deduce, give a dataset, according to the equation \(N = \sigma^2 -\frac{\left(u_{1-\alpha/2}+u_{1-\beta}\right)^2}{\delta^2}\) where +\frac{\left(u_{1-\alpha/2}+u_{1-\beta}\right)^2}{\Delta^2}\) where \(u_x\) denotes the x-quantile of the normal distribution. The estimated sample size is then the average calculated sample size across dataset. The argument \texttt{max.sample.size} specifies the number of @@ -2285,10 +2488,13 @@ \section{Power calculation using \texttt{powerBuyseTest}} \end{lstlisting} \begin{verbatim} - Simulation study with Generalized pairwise comparison - with 1000 samples + Sample size calculation with Generalized pairwise comparison + for a power of 0.8 and type 1 error rate of 0.05 + + - estimated sample size (mean [min;max]): 89 [60;145] controls + 89 [60;145] treated - - statistic : net benefit (null hypothesis Delta=0) + - net benefit statistic (null hypothesis Delta=0) endpoint threshold n.T n.C mean.estimate sd.estimate mean.se rejection.rate Y 1e-12 89 89 0.2452 0.0854 0.0834 0.806 @@ -2304,7 +2510,7 @@ \section{Power calculation using \texttt{powerBuyseTest}} \clearpage \section{Modifying default options} -\label{sec:org94fef85} +\label{sec:orgdc6f3fa} The \texttt{BuyseTest.options} method enable to get and set the default options of the \texttt{BuyseTest} function. For instance, the default option for trace is: @@ -2355,7 +2561,7 @@ \section{Modifying default options} \clearpage \section*{References} -\label{sec:orgf87f212} +\label{sec:orgbe6c6b4} \begingroup \renewcommand{\section}[2]{} diff --git a/tests/testthat/test-BuyseTest-previousBug.R b/tests/testthat/test-BuyseTest-previousBug.R index f60614c..bad7648 100644 --- a/tests/testthat/test-BuyseTest-previousBug.R +++ b/tests/testthat/test-BuyseTest-previousBug.R @@ -3,9 +3,9 @@ ## Author: Brice Ozenne ## Created: apr 17 2018 (16:46) ## Version: -## Last-Updated: jul 3 2023 (15:56) +## Last-Updated: Jul 4 2023 (09:32) ## By: Brice Ozenne -## Update #: 218 +## Update #: 221 ##---------------------------------------------------------------------- ## ### Commentary: @@ -511,7 +511,7 @@ test_that("backtransformation after permutation",{ gpc_ex1 <- BuyseTest(trt~cont(time), data=veteran, seed = 10, n.resampling = 100, method.inference = "permutation") - test <- suppressWarnings(confint(gpc_ex1, statistic='winratio') ) + test <- suppressWarnings(confint(gpc_ex1, statistic='winratio', conf.level = 0.95) ) expect_true(test$estimate < test$upper.ci) expect_true(test$estimate > test$lower.ci) }) diff --git a/tests/testthat/test-BuyseTest-resampling.R b/tests/testthat/test-BuyseTest-resampling.R index 600e6ec..8f1c081 100644 --- a/tests/testthat/test-BuyseTest-resampling.R +++ b/tests/testthat/test-BuyseTest-resampling.R @@ -3,9 +3,9 @@ ## author: Brice ## created: maj 12 2017 (14:34) ## Version: -## last-updated: jun 30 2023 (10:01) +## last-updated: Jul 4 2023 (09:31) ## By: Brice Ozenne -## Update #: 199 +## Update #: 202 #---------------------------------------------------------------------- ## ### Commentary: Check @@ -501,13 +501,14 @@ test_that("compare with t-test (two.sided)", { ## same variance for studentized bootstrap and asymptotic expect_true(all(abs(diff(M.res[c("studboot","studboot.trans","ustat","ustat.trans"),"se"])<1e-6))) ## lower.ci smaller than upper ci - expect_true(all(M.res[,"lower.ci"]

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