Effectively Selecting a Target Population for a Future Comparative Study

When comparing a new treatment with a control in a randomized clinical study, the treatment effect is generally assessed by evaluating a summary measure over a specific study population. The success of the trial heavily depends on the choice of such a population. In this paper, we show a systematic, effective way to identify a promising population, for which the new treatment is expected to have a desired benefit, using the data from a current study involving similar comparator treatments. Specifically, with the existing data we first create a parametric scoring system using multiple covariates to estimate subject-specific treatment differences. Using this system, we specify a desired level of treatment difference and create a subgroup of patients, defined as those whose estimated scores exceed this threshold. An empirically calibrated group-specific treatment difference curve across a range of threshold values is constructed. The population of patients with any desired level of treatment benefit can then be identified accordingly. To avoid any ``self-serving'' bias, we utilize a cross-training-evaluation method for implementing the above two-step procedure. Lastly, we show how to select the best scoring system among all competing models. The proposals are illustrated with the data from two clinical trials in treating AIDS and cardiovascular diseases. Note that if we are not interested in designing a new study for comparing similar treatments, the new procedure can also be quite useful for the management of future patients who would receive nontrivial benefits to compensate for the risk or cost of the new treatment.

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.