Gilbert, P. B., McKeague, I. W. and Sun, Y. (January 2001)
Tests for Comparing Mark-Specific Hazards
and Cumulative Incidence Functions
Abstract:
It is of interest in some applications
to determine whether there is a relationship
between a hazard rate function (or a cumulative incidence function)
and a mark variable which is only observed at uncensored failure times.
We develop nonparametric tests for this problem when the mark variable is
continuous. Tests are developed for the null hypothesis that
the mark-specific hazard rate is independent of the mark
versus ordered and two-sided alternatives expressed in terms of
mark-specific hazard functions and mark-specific cumulative incidence
functions. No assumptions are made about the nature of dependence
between the risks. The test statistics are based on functionals
of a bivariate test process equal to a weighted average
of differences between a Nelson--Aalen-type estimator of
the mark-specific cumulative hazard function and a nonparametric
estimator of this function under the null hypothesis.
The weight function in the test process can be chosen
so that the test statistics are asymptotically distribution-free.
Since the limiting covariance structure of each test statistic is
complicated, asymptotically correct critical values are obtained
through a simple simulation procedure.
Numerical studies show that the testing procedure has good size
and power characteristics at moderate sample sizes.
We present an application to viral genetics data collected in AIDS Clinical
Trials Group Study 241, which evaluated two antiretroviral treatments
of HIV infection. Specifically, the tests are used to assess
if the instantaneous or absolute risk of treatment failure
depends on the amount of accumulation of drug resistance
mutations in a subject's HIV virus.
This assessment helps guide development of
anti-HIV therapies that surmount the problem of drug resistance.