version 0.1.0

DESCRIPTION

@@ -0,0 +1,29 @@
+Package: OVL.CI
+Type: Package
+Title: Inference on the Overlap Coefficient: The Binormal Approach and
+        Alternatives
+Version: 0.1.0
+Authors@R: c(
+  person("Alba M. Franco-Pereira", role = c("aut", "cre","cph"), email = "albfranc@ucm.es"),
+  person("Christos T. Nakas", role = "aut"),
+  person("Benjamin Reiser", role = "aut"),
+  person("M.Carmen Pardo", role = "aut"))
+Maintainer: Alba M. Franco-Pereira <albfranc@ucm.es>
+Description: Provides functions to construct confidence intervals for the Overlap Coefficient (OVL). OVL measures the similarity between two distributions through the overlapping area of their distribution functions. Given its intuitive description and ease of visual representation by the straightforward depiction of the amount of overlap between the two corresponding histograms based on samples of measurements from each one of the two distributions, the development of accurate methods for confidence interval construction can be useful for applied researchers. Implements methods based on the work of Franco-Pereira, A.M., Nakas, C.T., Reiser, B., and Pardo, M.C. (2021) <doi:10.1177/09622802211046386>.
+License: GPL-2
+Encoding: UTF-8
+Language: en-US
+LazyData: true
+RoxygenNote: 7.2.3
+Imports: ks
+Depends: R (>= 2.10)
+Suggests: testthat (>= 3.0.0)
+Config/testthat/edition: 3
+NeedsCompilation: no
+Packaged: 2023-11-12 16:53:32 UTC; Alba
+Author: Alba M. Franco-Pereira [aut, cre, cph],
+  Christos T. Nakas [aut],
+  Benjamin Reiser [aut],
+  M.Carmen Pardo [aut]
+Repository: CRAN
+Date/Publication: 2023-11-13 17:43:18 UTC

MD5

@@ -0,0 +1,65 @@
+e4693a75c15136c611c1c141dc544d27 *DESCRIPTION
+fa12e29c608d52123c6b8d3dbf2f0823 *NAMESPACE
+0c2e62b0d72e6a0551283341ec8a0998 *NEWS.md
+8e38ab4379e0b3e525fb37e36d7e8cb8 *R/OVL.BCAN.R
+381d2e9d1989d745e3c44d7415b3d110 *R/OVL.BCPB.R
+99a9cc7f52b84e30ab6f75b96392bf1d *R/OVL.BCbias.R
+af3a24f1975bde18c645613bff6e2a87 *R/OVL.D.R
+aae02bd310cdefccd88d8d8b2aad629c *R/OVL.DBC.R
+e5b5d6a00e1986340dd91b8f7cbc5799 *R/OVL.DBCL.R
+7d776aacb5cef1b4dc5c03bfbc0ec441 *R/OVL.K.R
+d718047b1b7c30ebcbd4a18a3bc2b25b *R/OVL.KPB.R
+ca6609cddf4d0d8dfd1be6873f7f6d16 *R/OVL.LogitBCAN.R
+72b766dd7353168b1a46db8c789398a9 *R/OVL.LogitD.R
+d55a6eac1870ccaf358abe9199e85b84 *R/OVL.LogitDBC.R
+0a7d2a01e4cc72eb970d2f9a97be52eb *R/OVL.LogitDBCL.R
+43f95b5e963626a41368533b1d86f955 *R/OVL.LogitK.R
+600560b92662f3dd3c08f0e22f4f4be0 *R/U.R
+bae069d1f9e27687f69605e4b9469c5f *R/data.R
+bf00caa715d2be358808e020bec3259f *R/kernel.e.R
+31e00a594097b38e50263b5b2bbca4a5 *R/kernel.e.density.R
+5a01a85c875c9485ebf6597673d89de2 *R/kernel.g.R
+7cb6c5614f809a95054df4c3bb18e7d9 *R/kernel.g.density.R
+7d13dcf59de07e02ad5fd84fadeedd49 *R/likbox.R
+26c1b4419cd79a7464fc1249798b4bfd *R/ssdd.R
+7eee0a7f3cc81096a899072a976722c8 *data/test_data.rda
+bcae6dd9b935842231abb4c2a30bf247 *man/OVL.BCAN.Rd
+23927fdb3bc565c2734593dbb21fd756 *man/OVL.BCPB.Rd
+f938f01d1bf949989432c297e7c2e63d *man/OVL.BCbias.Rd
+d9d882ccf74c3fbd928a493144c26be1 *man/OVL.D.Rd
+ddb795ed876c20476f2882ce609174b9 *man/OVL.DBC.Rd
+936bdd965e87ddf342778bc95100a773 *man/OVL.DBCL.Rd
+3f1ad66c0b7bedb9b8f407c774c17af7 *man/OVL.K.Rd
+25e89329e070345c8771ff100e062ccb *man/OVL.KPB.Rd
+451732f5736a56208e541564ce033754 *man/OVL.LogitBCAN.Rd
+30d80ea73c4a4abf479eae4ab192467f *man/OVL.LogitD.Rd
+ed7806ac24b0bce557645c91d0aa477c *man/OVL.LogitDBC.Rd
+fb1e4fb3fce74d8d0bdf5865073aebde *man/OVL.LogitDBCL.Rd
+c5908017923831a971cec4762937c432 *man/OVL.LogitK.Rd
+ac5470b9fa1fe99564a8857f17d15e02 *man/U.Rd
+030665cbc18d4f4b32112112e84b90fa *man/kernel.e.Rd
+e63927e2d63eed634f1c710f3491dfd6 *man/kernel.e.density.Rd
+6984b7bd0743dc5185b53a9e6db56199 *man/kernel.g.Rd
+a0b6cf653cafd967b0c91d841302b40e *man/kernel.g.density.Rd
+437c5765eea839ba54502d38f179e8c0 *man/likbox.Rd
+4745b5a43310ba3971dcc21447f3d1ef *man/ssdd.Rd
+a93d956b35b257c99ab0653d43fd1045 *man/test_data.Rd
+1541877e3ad3597dcd343d1887d34a95 *tests/testthat.R
+311d5d83a972c47d7efe76ede8e1746f *tests/testthat/test_LogitBCAN.R
+7d1db2627ef2c902d0733227b2b0901d *tests/testthat/test_LogitD.R
+e1de623750c15a2fd603c3a50643099a *tests/testthat/test_LogitDBC.R
+c85719a247861cac7bf714714e35f948 *tests/testthat/test_LogitDBCL.R
+01865427b372c3e1081b2e82cc256187 *tests/testthat/test_LogitK.R
+dc31b6b901f04bc2bc7bce47a815d7c1 *tests/testthat/test_OVL.BCAN.R
+c8a983e6ebbb68ec03843999dd60e0ea *tests/testthat/test_OVL.BCPB.R
+648684e3db976dc53621a8068603bcef *tests/testthat/test_OVL.BCbias.R
+288e757336e564a8db02a3038f0f7f10 *tests/testthat/test_OVL.D.R
+475b7cefff82c567645a7fcda97bb2b8 *tests/testthat/test_OVL.DBC.R
+3f7d7674a3186d84780e69efd6e2940c *tests/testthat/test_OVL.DBCL.R
+a497531acd068a8a3aa4d75058ccba1e *tests/testthat/test_OVL.K.R
+65edfaf662539d7e9adc0b6b516edd9b *tests/testthat/test_OVL.KPB.R
+93f7df1a44feb75a781e4015a5b0249c *tests/testthat/test_U.R
+159686dca949c862929151b725b28917 *tests/testthat/test_kernel.e&kernel.e.R
+d8dff68dd26194571dfa88ab46f3a9fe *tests/testthat/test_kernel.e.density&test_kernel.g.density.R
+1798206d2c8fa86a88cc572fd8241772 *tests/testthat/test_likbox.R
+478a717537523956a3d1efffaa078195 *tests/testthat/test_ssdd.R

NAMESPACE

@@ -0,0 +1,29 @@
+# Generated by roxygen2: do not edit by hand
+
+export(OVL.BCAN)
+export(OVL.BCPB)
+export(OVL.BCbias)
+export(OVL.D)
+export(OVL.DBC)
+export(OVL.DBCL)
+export(OVL.K)
+export(OVL.KPB)
+export(OVL.LogitBCAN)
+export(OVL.LogitD)
+export(OVL.LogitDBC)
+export(OVL.LogitDBCL)
+export(OVL.LogitK)
+export(U)
+export(kernel.e)
+export(kernel.e.density)
+export(kernel.g)
+export(kernel.g.density)
+export(likbox)
+export(ssdd)
+importFrom(stats,dnorm)
+importFrom(stats,optim)
+importFrom(stats,pnorm)
+importFrom(stats,qnorm)
+importFrom(stats,quantile)
+importFrom(stats,sd)
+importFrom(stats,var)

NEWS.md

@@ -0,0 +1,3 @@
+# OVL.CI 0.1.0
+
+* Added a `NEWS.md` file to track changes to the package.

R/OVL.BCAN.R

@@ -0,0 +1,85 @@
+#' @title OVL.BCAN
+#' @description Parametric approach using a bootstrap-based approach to estimate the variance
+#' @param x controls
+#' @param y cases
+#' @param alpha confidence level
+#' @param B bootstrap size
+#' @param h_ini initial value in the optimization problem
+#' @return confidence interval
+#' @export OVL.BCAN
+#' @importFrom stats dnorm optim pnorm qnorm quantile sd var
+#' @examples
+#' controls = rnorm(50,6,1)
+#' cases = rnorm(100,6.5,0.5)
+#' OVL.BCAN (controls,cases)
+OVL.BCAN<-function(x,y,alpha=0.05,B=100,h_ini=-0.6){
+  x_aux<-x
+  y_aux<-y
+  all_values<-c(x_aux,y_aux)
+  if (any(all_values<=0)){
+    x<-x_aux+abs(min(all_values))+(max(all_values)-min(all_values))/2
+    y<-y_aux+abs(min(all_values))+(max(all_values)-min(all_values))/2
+  } else {
+    x<-x_aux
+    y<-y_aux
+  }
+  xo<-x
+  yo<-y
+  hhat<-optim(h_ini,likbox,data=c(xo,yo),n=length(xo),method="BFGS")$par
+  if (abs(hhat)<1e-5){
+    x<-log(xo)
+    y<-log(yo)
+  } else {
+    x<-((xo^hhat)-1)/hhat
+    y<-((yo^hhat)-1)/hhat
+  }
+  if(ssdd(x)<ssdd(y)){
+    muestra1<-x
+    muestra2<-y
+  } else {
+    muestra1<-y
+    muestra2<-x
+  }
+  mu1_hat<-mean(muestra1)
+  mu2_hat<-mean(muestra2)
+  sigma1_hat<-ssdd(muestra1)
+  sigma2_hat<-ssdd(muestra2)
+  x1<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)-sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+  x2<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)+sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+  OVL<-1+pnorm((x1-mu1_hat)/sigma1_hat)-pnorm((x1-mu2_hat)/sigma2_hat)-pnorm((x2-mu1_hat)/sigma1_hat)+pnorm((x2-mu2_hat)/sigma2_hat)
+  OVL_ib<-numeric(B)
+  for (b in 1:B){
+    xo_ib<-sample(xo,replace=TRUE,size=length(x))
+    yo_ib<-sample(yo,replace=TRUE,size=length(y))
+    hhat<-optim(h_ini,likbox,data=c(xo_ib,yo_ib),n=length(xo_ib),method="BFGS")$par
+    if (abs(hhat)<1e-5){
+      x<-log(xo_ib)
+      y<-log(yo_ib)
+    } else {
+      x<-((xo_ib^hhat)-1)/hhat
+      y<-((yo_ib^hhat)-1)/hhat
+    }
+    if(ssdd(x)<ssdd(y)){
+      muestra1<-x
+      muestra2<-y
+    } else {
+      muestra1<-y
+      muestra2<-x
+    }
+    mu1_hat<-mean(muestra1)
+    mu2_hat<-mean(muestra2)
+    sigma1_hat<-ssdd(muestra1)
+    sigma2_hat<-ssdd(muestra2)
+    x1<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)-sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+    x2<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)+sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+    OVL_ib[b]<-1+pnorm((x1-mu1_hat)/sigma1_hat)-pnorm((x1-mu2_hat)/sigma2_hat)-pnorm((x2-mu1_hat)/sigma1_hat)+pnorm((x2-mu2_hat)/sigma2_hat)
+  }
+  var_OVL<-var(OVL_ib,na.rm=TRUE)
+  IC1<-OVL-qnorm(1-alpha/2)*sqrt(var_OVL)
+  IC1_aux<-IC1
+  if(IC1<0){IC1<-0}else{IC1<-IC1_aux}
+  IC2<-OVL+qnorm(1-alpha/2)*sqrt(var_OVL)
+  IC2_aux<-IC2
+  if(IC2>1){IC2<-1}else{IC2<-IC2_aux}
+  return(list(IC1,IC2))
+}

R/OVL.BCPB.R

@@ -0,0 +1,81 @@
+#' @title OVL.BCPB
+#' @description Parametric approach using a bootstrap percentil approach to estimate the variance
+#' @param x controls
+#' @param y cases
+#' @param alpha confidence level
+#' @param B bootstrap size
+#' @param h_ini initial value in the optimization problem
+#' @return confidence interval
+#' @export OVL.BCPB
+#' @importFrom stats dnorm optim pnorm qnorm quantile sd var
+#' @examples
+#' controls = rnorm(50,6,1)
+#' cases = rnorm(100,6.5,0.5)
+#' OVL.BCPB (controls,cases)
+OVL.BCPB<-function(x,y,alpha=0.05,B=100,h_ini=-0.6){
+x_aux<-x
+y_aux<-y
+all_values<-c(x_aux,y_aux)
+if (any(all_values<=0)){
+  x<-x_aux+abs(min(all_values))+(max(all_values)-min(all_values))/2
+  y<-y_aux+abs(min(all_values))+(max(all_values)-min(all_values))/2
+} else {
+  x<-x_aux
+  y<-y_aux
+}
+xo<-x
+yo<-y
+hhat<-optim(h_ini,likbox,data=c(xo,yo),n=length(xo),method="BFGS")$par
+if (abs(hhat)<1e-5){
+    x<-log(xo)
+    y<-log(yo)
+} else {
+    x<-((xo^hhat)-1)/hhat
+    y<-((yo^hhat)-1)/hhat
+}
+if(ssdd(x)<ssdd(y)){
+muestra1<-x
+muestra2<-y
+} else {
+muestra1<-y
+muestra2<-x
+}
+mu1_hat<-mean(muestra1)
+mu2_hat<-mean(muestra2)
+sigma1_hat<-ssdd(muestra1)
+sigma2_hat<-ssdd(muestra2)
+x1<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)-sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+x2<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)+sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+OVL<-1+pnorm((x1-mu1_hat)/sigma1_hat)-pnorm((x1-mu2_hat)/sigma2_hat)-pnorm((x2-mu1_hat)/sigma1_hat)+pnorm((x2-mu2_hat)/sigma2_hat)
+OVL_ib<-numeric(B)
+for (b in 1:B){
+xo_ib<-sample(xo,replace=TRUE)
+yo_ib<-sample(yo,replace=TRUE)
+hhat<-optim(h_ini,likbox,data=c(xo_ib,yo_ib),n=length(xo_ib),method="BFGS")$par
+if (abs(hhat)<1e-5){
+    x<-log(xo_ib)
+    y<-log(yo_ib)
+} else {
+    x<-((xo_ib^hhat)-1)/hhat
+    y<-((yo_ib^hhat)-1)/hhat
+}
+if(ssdd(x)<ssdd(y)){
+muestra1<-x
+muestra2<-y
+} else {
+muestra1<-y
+muestra2<-x
+}
+mu1_hat<-mean(muestra1)
+mu2_hat<-mean(muestra2)
+sigma1_hat<-ssdd(muestra1)
+sigma2_hat<-ssdd(muestra2)
+
+x1<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)-sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+x2<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)+sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+OVL_ib[b]<-1+pnorm((x1-mu1_hat)/sigma1_hat)-pnorm((x1-mu2_hat)/sigma2_hat)-pnorm((x2-mu1_hat)/sigma1_hat)+pnorm((x2-mu2_hat)/sigma2_hat)
+}
+IC1<-quantile(OVL_ib,alpha/2,na.rm=TRUE)
+IC2<-quantile(OVL_ib,1-alpha/2,na.rm=TRUE)
+return(list(IC1,IC2))
+}

R/OVL.BCbias.R

@@ -0,0 +1,84 @@
+#' @title OVL.BCbias
+#' @description Parametric approach using a bootstrap bias-corrected approach
+#' @param x controls
+#' @param y cases
+#' @param alpha confidence level
+#' @param B bootstrap size
+#' @param h_ini initial value in the optimization problem
+#' @return confidence interval
+#' @export OVL.BCbias
+#' @importFrom stats dnorm optim pnorm qnorm quantile sd var
+#' @examples
+#' controls = rnorm(50,6,1)
+#' cases = rnorm(100,6.5,0.5)
+#' OVL.BCAN (controls,cases)
+OVL.BCbias<-function(x,y,alpha=0.05,B=100,h_ini=-0.6){
+x_aux<-x
+y_aux<-y
+all_values<-c(x_aux,y_aux)
+if (any(all_values<=0)){
+  x<-x_aux+abs(min(all_values))+(max(all_values)-min(all_values))/2
+  y<-y_aux+abs(min(all_values))+(max(all_values)-min(all_values))/2
+} else {
+  x<-x_aux
+  y<-y_aux
+  }
+xo<-x
+yo<-y
+hhat<-optim(h_ini,likbox,data=c(xo,yo),n=length(xo),method="BFGS")$par
+if (abs(hhat)<1e-5){
+    x<-log(xo)
+    y<-log(yo)
+} else {
+    x<-((xo^hhat)-1)/hhat
+    y<-((yo^hhat)-1)/hhat
+}
+if(ssdd(x)<ssdd(y)){
+muestra1<-x
+muestra2<-y
+} else {
+muestra1<-y
+muestra2<-x
+}
+mu1_hat<-mean(muestra1)
+mu2_hat<-mean(muestra2)
+sigma1_hat<-ssdd(muestra1)
+sigma2_hat<-ssdd(muestra2)
+x1<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)-sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+x2<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)+sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+OVL<-1+pnorm((x1-mu1_hat)/sigma1_hat)-pnorm((x1-mu2_hat)/sigma2_hat)-pnorm((x2-mu1_hat)/sigma1_hat)+pnorm((x2-mu2_hat)/sigma2_hat)
+OVL_ib<-numeric(B)
+for (b in 1:B){
+xo_ib<-sample(xo,replace=TRUE)
+yo_ib<-sample(yo,replace=TRUE)
+hhat<-optim(h_ini,likbox,data=c(xo_ib,yo_ib),n=length(xo_ib),method="BFGS")$par
+if (abs(hhat)<1e-5){
+    x<-log(xo_ib)
+    y<-log(yo_ib)
+} else {
+    x<-((xo_ib^hhat)-1)/hhat
+    y<-((yo_ib^hhat)-1)/hhat
+}
+if(ssdd(x)<ssdd(y)){
+muestra1<-x
+muestra2<-y
+} else {
+muestra1<-y
+muestra2<-x
+}
+mu1_hat<-mean(muestra1)
+mu2_hat<-mean(muestra2)
+sigma1_hat<-ssdd(muestra1)
+sigma2_hat<-ssdd(muestra2)
+x1<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)-sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+x2<-((mu1_hat*sigma2_hat^2-mu2_hat*sigma1_hat^2)+sigma1_hat*sigma2_hat*sqrt((mu1_hat-mu2_hat)^2+(sigma1_hat^2-sigma2_hat^2)*log(sigma1_hat^2/sigma2_hat^2)))/(sigma2_hat^2-sigma1_hat^2)
+OVL_ib[b]<-1+pnorm((x1-mu1_hat)/sigma1_hat)-pnorm((x1-mu2_hat)/sigma2_hat)-pnorm((x2-mu1_hat)/sigma1_hat)+pnorm((x2-mu2_hat)/sigma2_hat)
+}
+z0<-qnorm(mean(OVL_ib<=OVL,na.rm=TRUE))
+alpha1<-pnorm(2*z0+qnorm(alpha/2))
+alpha2<-pnorm(2*z0+qnorm(1-alpha/2))
+IC1<-quantile(OVL_ib,alpha1,na.rm=TRUE)
+IC2<-quantile(OVL_ib,alpha2,na.rm=TRUE)
+return(list(IC1,IC2))
+}
+