Testing for conditional independence of survival time from covariate

This study examined the test of independence of survival time from a covariate in a more general setting using empirical process techniques. Previous research has been extended in several ways: (1) allow incompleteness of observation owing to censoring (2) allow the time-dependent covariate (3) allow the non-uniform covariate (4) prove the validity of weighted bootstrap to implement the proposed testing procedure. Certain classes of test statistics that are functionals of a natural empirical process were studied, and the limiting distribution of these statistics was then derived using the functional delta method. The limiting distributions included some linear functionals of zero mean tight Brownian bridges under the null hypothesis, and the tests were consistent against general alternatives. Tests implemented using weighted bootstrap were shown to be valid. The proposals are illustrated via simulation studies and an application to acute leukemia data.