title: 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. 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. Asymptotically correct critical values are obtained through a simple simulation procedure. The testing procedures are shown to perform well in numerical studies, and are illustrated with an AIDS clinical trial example. 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.
authors.affiliation: Department of Biostatistics, University of Washington and Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA. pgilbert@scharp.org
authors.forename: Peter B
authors.initials: PB
authors.lastname: Gilbert
authors.forename: Ian W
authors.initials: IW
authors.lastname: McKeague
authors.forename: Yanqing
authors.initials: Y
authors.lastname: Sun
mesh_terms: D044966:Anti-Retroviral Agents / Q000494:pharmacology / Q000627:therapeutic use; D002986:Clinical Trials as Topic; D024882:Drug Resistance, Viral; D006678:HIV / Q000187:drug effects / Q000276:immunology; D015658:HIV Infections / Q000188:drug therapy / Q000821:virology; D006801:Humans; D015994:Incidence; D009010:Monte Carlo Method; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods*; D018709:Statistics, Nonparametric; D016019:Survival Analysis; D017211:Treatment Failure
chemical_list: D044966:Anti-Retroviral Agents