| Title: | The Cross-Match Test |
|---|---|
| Description: | Performs the cross-match test that is an exact, distribution free test of equality of 2 high dimensional multivariate distributions. The input is a distance matrix and the labels of the two groups to be compared, the output is the number of cross-matches and a p-value. See Rosenbaum (2005) <doi:10.1111/j.1467-9868.2005.00513.x>. |
| Authors: | Ruth Heller [aut, cph], Dylan Small [aut, cph], Paul Rosenbaum [aut, cph], Marieke Stolte [cre] |
| Maintainer: | Marieke Stolte <[email protected]> |
| License: | GPL-2 |
| Version: | 1.4-0 |
| Built: | 2024-12-21 06:50:00 UTC |
| Source: | CRAN |
The exact null distribution of the number of crossmatches for bigN>=4 cases,
n>=2 from one type and N-n>=2 from another type.
crossmatchdist(bigN, n)crossmatchdist(bigN, n)
bigN |
The total number of observations |
n |
The number of cases from one type |
bigN is even. Let a1 be the number of cross-matches pairs. Then a2=(n-a1)/2 and
a0=bigN/2-(n+a1)/2 are the number of pairs both of one type and the other type
respectively.
dist |
A matrix with rows |
Ruth Heller
Rosenbaum, P.R. (2005), An exact distribution-free test comparing two multivariate distributions based on adjacency, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 4, 515-530.
crossmatchdist(18,9)crossmatchdist(18,9)
A test for comparing two multivariate distributions by using the distance between the observations.
crossmatchtest(z, D)crossmatchtest(z, D)
z |
A binary vector corresponding to observations class labels. |
D |
A distance matrix of dimensions NxN, where N is the total number of observations. |
Observations are divided into pairs to minimize the total distance within pairs, using a polynomial time algorithm made available in R by Lu, B., Greevy, R., Xu, X., and Beck, C in the R package "nbpMatching". The cross-match test takes as the test statistic the number of times a subject from one group was paired with a subject from another group, rejecting the hypothesis of equal distribution for small values of the statistic; see Rosenbaum (2005) for details.
A list with the following
a1 |
The number of cross-matches |
Ea1 |
The expected number of cross-matches under the null |
Va1 |
The variance of number of cross-matches under the null |
dev |
The observed difference from expectation under null in SE units |
pval |
The p-value based on exact null distribution (NA for datasets with 340 observations or more) |
approxpval |
The approximate p-value based on normal approximation |
Ruth Heller
Rosenbaum, P.R. (2005), An exact distribution-free test comparing two multivariate distributions based on adjacency, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67, 4, 515-530.
## The example in Section 2 of the article (see References) #The data consists of 2 outcomes measured on 9 treated cases and 9 controls: dat <- rbind(c(0.47,0.39,0.47,0.78,1,1,0.54,1,0.38,1,0.27,0.63,0.22,0,-1,-0.42,-1,-1), c(0.03,0.11,0.16,-0.1,-0.05,0.16,0.12,0.4,0.04,0.71,0.01,0.21,-0.18, -0.08,-0.35,0.26,-0.6,-1.0)) z <- c(rep(0,9),rep(1,9)) X <- t(dat) ## Rank based Mahalanobis distance between each pair: X <- as.matrix(X) n <- dim(X)[1] k <- dim(X)[2] for (j in 1:k) X[,j] <- rank(X[,j]) cv <- cov(X) vuntied <- var(1:n) rat <- sqrt(vuntied/diag(cv)) cv <- diag(rat) %*% cv %*% diag(rat) out <- matrix(NA,n,n) library(MASS) icov <- ginv(cv) for (i in 1:n) out[i,] <- mahalanobis(X,X[i,],icov,inverted=TRUE) dis <- out ## The cross-match test: crossmatchtest(z,dis)## The example in Section 2 of the article (see References) #The data consists of 2 outcomes measured on 9 treated cases and 9 controls: dat <- rbind(c(0.47,0.39,0.47,0.78,1,1,0.54,1,0.38,1,0.27,0.63,0.22,0,-1,-0.42,-1,-1), c(0.03,0.11,0.16,-0.1,-0.05,0.16,0.12,0.4,0.04,0.71,0.01,0.21,-0.18, -0.08,-0.35,0.26,-0.6,-1.0)) z <- c(rep(0,9),rep(1,9)) X <- t(dat) ## Rank based Mahalanobis distance between each pair: X <- as.matrix(X) n <- dim(X)[1] k <- dim(X)[2] for (j in 1:k) X[,j] <- rank(X[,j]) cv <- cov(X) vuntied <- var(1:n) rat <- sqrt(vuntied/diag(cv)) cv <- diag(rat) %*% cv %*% diag(rat) out <- matrix(NA,n,n) library(MASS) icov <- ginv(cv) for (i in 1:n) out[i,] <- mahalanobis(X,X[i,],icov,inverted=TRUE) dis <- out ## The cross-match test: crossmatchtest(z,dis)