testIndepTimeMark {sievePH}

Kolmogorov-Smirnov-Type Test of Conditional Independence between the Time-to-Event and a Multivariate Mark Given Treatment

Description

A nonparametric Komogorov-Smirnov-type test of the null hypothesis that the time-to-event T and a possibly multivariate mark V are conditionally independent given treatment Z as described in Juraska and Gilbert (2013). The conditional independence is a necessary assumption for parameter identifiability in the time-independent density ratio model. A bootstrap algorithm is used to compute the p-value.

Usage

testIndepTimeMark(data, iter = 1000)

Arguments

data

a data frame restricted to subjects in a given treatment group with the following columns (in this order): the observed right-censored time to the event of interest, the event indicator (1 if event, 0 if right-censored), and the mark variable (one column for each component, if multivariate)

iter

the number of bootstrap iterations (1000 by default) used for computing the p-value

Details

The test statistic is the supremum of the difference between the estimated conditional joint cumulative distribution function (cdf) of (T,V) given Z and the product of the estimated conditional cdfs of T and V given Z. The joint cdf is estimated by the nonparametric maximum likelihood estimator developed by Huang and Louis (1998). The marginal cdf of T is estimated as one minus the Kaplan-Meier estimator for the conditional survival function of T, and the cdf of V is estimated as the empirical cdf of the observed values of V. A bootstrap algorithm is used to compute the p-value.

Value

Returns the bootstrap p-value from the test of conditional independence between T and V given Z.

References

Juraska, M. and Gilbert, P. B. (2013), Mark-specific hazard ratio model with multivariate continuous marks: an application to vaccine efficacy. Biometrics 69(2):328–337.

Huang, Y. and Louis, T. (1998), Nonparametric estimation of the joint distribution of survival time and mark variables. Biometrika 85, 785–798.

Examples

n <- 500
tx <- rep(0:1, each=n/2)
tm <- c(rexp(n/2, 0.2), rexp(n/2, 0.2 * exp(-0.4)))
cens <- runif(n, 0, 15)
eventTime <- pmin(tm, cens, 3)
eventInd <- as.numeric(tm <= pmin(cens, 3))
mark1 <- ifelse(eventInd==1, c(rbeta(n/2, 2, 5), rbeta(n/2, 2, 2)), NA)
mark2 <- ifelse(eventInd==1, c(rbeta(n/2, 1, 3), rbeta(n/2, 5, 1)), NA)

# perform the test for a univariate mark in the placebo group
testIndepTimeMark(data.frame(eventTime, eventInd, mark1)[tx==0, ], iter=20)

# perform the test for a bivariate mark in the placebo group
testIndepTimeMark(data.frame(eventTime, eventInd, mark1, mark2)[tx==0, ], iter=20)