Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions

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.

A NOVEL AND SIMPLE RULE OF THUMB FOR MULTIPLICITY CONTROL IN EQUIVALENCE TESTING USING TWO ONE-SIDED TESTS

Equivalence testing is growing in use in scientific research outside of its traditional role in the drug approval process. Largely due to its ease of use and recommendation from the United States Food and Drug Administration guidance, the most common statistical method for testing (bio)equivalence is the two one-sided tests procedure (TOST). Like classical point-null hypothesis testing, TOST is subject to multiplicity concerns as more comparisons are made. In this manuscript, a condition that bounds the family-wise error rate (FWER) using TOST is given. This condition then leads to a simple solution for controlling the FWER. Specifically, we demonstrate that if all pairwise comparisons of k independent groups are being evaluated for equivalence, then simply scaling the nominal Type I error rate down by (k - 1) is sufficient to maintain the family-wise error rate at the desired value or less. The resulting rule is much less conservative than the equally simple Bonferroni correction. An example of equivalence testing in a non drug-development setting is given.