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.