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ppw.R
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ppw.R
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#' Test for difference in left-censored samples
#' @description Performs a nonparametric Paired Prentice-Wilcoxon test of whether the median difference between two columns of paired censored data equals 0 (O'Brien and Fleming, 1987)
#' @param xd The first column of data values plus detection limits
#' @param xc The column of censoring indicators, where 1 (or `TRUE`) indicates a detection limit in the xd column, and 0 (or `FALSE`) indicates a detected value in `xd`.
#' @param yd The second column of data values plus detection limits
#' @param yc The column of censoring indicators, where 1 (or `TRUE`) indicates a detection limit in the yd column, and 0 (or `FALSE`) indicates a detected value in `yd`
#' @param alternative The usual notation for the alternate hypothesis. Default is `“two.sided”`. Options are `“greater”` or `“less”`.
#' @param printstat Logical `TRUE`/`FALSE` option of whether to print the resulting statistics in the console window, or not. Default is `TRUE.`
#'
#' @importFrom survival survfit Surv
#' @importFrom stats na.exclude pnorm
#' @return Paired Prentice-Wilcoxon test results including Z-statistic, n (sample size), p-value and median difference
#' @export
#'
#' @references
#' Helsel, D.R., 2011. Statistics for Censored Environmental Data using Minitab and R, 2nd ed. John Wiley & Sons, USA, N.J.
#'
#' O’Brien, P.C., Fleming, T.R., 1987. A Paired Prentice-Wilcoxon Test for Censored Paired Data. Biometrics 43, 169–180. https://doi.org/10.2307/2531957
#'
#' @seealso [survival::survfit] [survival::Surv]
#'
#' @examples
#' data(PbHeron)
#' ppw.test(PbHeron$Liver,PbHeron$LiverCen,PbHeron$Bone,PbHeron$BoneCen)
#'
ppw.test <- function(xd, xc, yd, yc, alternative="two.sided",printstat=TRUE)
{
xname <- deparse(substitute(xd))
yname <- deparse(substitute(yd))
OBrienFleming=TRUE
## Error checks
if(length(xd) != length(yd))
stop("Lengths of x and y must be the same for paired data.")
keep <- !(is.na(xd) | is.na(yd) | is.na(xc) | is.na(yc))
x <- xd[keep]
y <- yd[keep]
if(any(c(x, y) < 0))
stop("Negative values in x or y")
N <- length(x)
if(OBrienFleming) {
xd <- x
xc <- xc[keep]
yd <- y
yc <- yc[keep]
for(i in seq(N)) {
if(xc[i] && yc[i]) { # Both censored, make same
xyMax <- max(xd[i], yd[i])
xd[i] <- yd[i] <- xyMax
}
else if(xc[i] && xd[i] > yd[i]) { # x censored > y
yd[i] <- xd[i]
yc[i] <- TRUE
}
else if(yc[i] && yd[i] > xd[i]) { # y censored > x
xd[i] <- yd[i]
xc[i] <- TRUE
}
} # Done, no need to check uncensored observations
}
## Test requires stacked data
group = factor(c(rep(xname, length(x)), rep(yname, length(y))),
levels=c(xname, yname))
values <- c(xd, yd)
cenflag <- as.logical(c(xc, yc))
alternative <- pmatch(alternative, c("two.sided", "greater", "less"))
if(is.na(alternative))
stop('Invalid choice for alternative, must match "two.sided", "greater", or "less"')
## Define the test:
PPW.test <- function(values, cenflag, group) {
## data must be in exactly 2 groups of equal size and stacked
## x first, then y (for alternative not two.sided)
## required adjustment to values
adjust <- min(diff(sort(unique(values))))/10.
values <- ifelse(cenflag, values-adjust, values)
adjust <- adjust / length(values)
dupes <- unique(values[!cenflag][duplicated(values[!cenflag])])
in.values <- values
if(length(dupes) > 0) { #there are dupes
for(i in seq(along=dupes)) {
sel <- which(values == dupes[i])
mult <- 0L:(length(sel) - 1L)
in.values[sel] <- dupes[i] + adjust * mult
}
}
## create data frame and add observed value at 0 to compute
## correct probs
df <- data.frame(values=c(0, -in.values), cenflag=c(T, !cenflag))
kmout <- survfit(Surv(values, cenflag) ~ 1, data=df, na.action=na.exclude)
kmout$time <- - kmout$time # convert back to actual values
## compute mean survival for tied values
St <- kmout$surv
if(length(dupes) > 0L) { #there are dupes
for(i in seq(along=dupes)) {
## take advantage of the fact that the output are sorted
sel <- which(values == dupes[i])
mult <- seq(0L, 1L - length(sel))
sel <- which(kmout$time == dupes[i])
St[sel] <- mean(St[sel + mult])
}
}
## Define the link between the observed data and the kaplan meier table
## and compute needed stats.
link <- match(values, kmout$time)
St <- St[link]
Uncen <- values[!cenflag]
UncenSt <- St[!cenflag]
UncenSt <- UncenSt[order(Uncen)]
Uncen <- sort(Uncen)
Score <- 1. - 2*St
## This is not fast, but it works
for(i in which(cenflag)) # fix each each censored score
Score[i] <- 1. - UncenSt[which(Uncen > values[i])][1L]
## Compute d
## Reverse sense of d so that alternatives are in same direction--
## gives different sense of d from the original
Score <- matrix(Score, ncol=2L)
d <- Score[, 2L] - Score[, 1L]
return(list(Z=sum(d)/sqrt(sum(d^2)), Scores=Score, Diffs=d))
} # end of PPW.test
ret1 <- PPW.test(values, cenflag, group)
stat <- ret1$Z
names(stat) <- "Paired Prentice Z"
meth <- "Paired Prentice-Wilcoxon test"
param <- length(group)/2L
names(param) <- "n"
## add finishing touches
if(alternative == 1L) # alternative is two-sided
{ pvalue <- (1. - pnorm(abs(stat))) * 2.
altern <- paste(xname, "not equal to", yname, sep = " ") }
else if(alternative == 2L) # alternative is greater than
{ pvalue <- 1. - pnorm(stat)
altern <- paste(xname, ">", yname, sep = " ") }
else # alternaitve is less than
{ pvalue <- pnorm(stat)
altern <- paste(xname, "<", yname, sep = " ") }
names(pvalue) <- "p value"
mu <- 0
names(mu) <- "difference"
Scoremat <- cbind(ret1$Scores, ret1$Diffs)
colnames(Scoremat) <- c("xScore", "yScore", "d")
## For diagnostic plot, create min and max differences
d1 <- xd - ifelse(yc, 0, yd)
d2 <- ifelse(xc, 0, xd) - yd
mind <- pmin(d1, d2)
maxd <- pmax(d1, d2)
Scoremat <- cbind(Scoremat, minDiff=mind, maxDiff=maxd)
sv.out <- survfit(Surv(Scoremat[,4], Scoremat[,5], type="interval2")~1)
med.diff <- min(sv.out$time [sv.out$surv <= 0.50])
# getting number of signif digits
y.count <- vector(length=length(yd))
for (i in 7:1) {y.count[yd == signif(yd, i)] <- i}
# computing median difference
median.diff <- paste ("Median difference equals", signif(med.diff, max(y.count)))
retval <- list(statistic = stat, parameters = param,
p.value = pvalue, null.value = mu,
alternative = c("two.sided", "greater", "less")[alternative],
method = meth, data.name = paste(xname, "and", yname, sep = " "),
PPWmat=Scoremat)
#oldClass(retval) <- c("htest", "ppw")
# print(retval)
txt <- paste("Paired Prentice Wilcoxon test for (x:", xname, " - ", "y:", yname, ") equals 0", "\n", " alternative: ", altern, "\n", sep = "")
txt2 <- paste("n =", param, " Z =", signif(stat, 4), " p-value =", signif(pvalue, 4))
if(printstat==TRUE){
cat(txt, "\n", txt2, "\n")
cat(" ", median.diff, "\n")
}
return(invisible(retval))
}