Robust tests for treatment comparisons based on recurrent event responses

Robust nonparametric tests are considered for use in longitudinal studies in which the response of interest is a recurrent event. The tests are robust in the sense that they do not rely on distributional assumptions regarding the processes generating the events. The methods we describe are presented in the context of a clinical trial with attention initially directed at the two-sample problem in which a single experimental treatment is compared to a control. We investigate a family of generalized pseudo-score statistics (Lawless and Nadeau, 1995, Technometrics 37, 158-168) in which weight functions may be chosen to generate tests sensitive to various types of departure from the null hypothesis that the mean functions for the treatment and control groups are identical. All tests we consider are evaluated by simulation with respect to the type I error rate and power under a variety of practical scenarios. An application involving data from a kidney transplant study illustrates these procedures. For trials with multiple treatment arms, we generalize these approaches and indicate test statistics appropriate for unstructured alternatives and tests based on linear contrasts of the treatment-specific mean functions. Extensions of this methodology for stratified designs are also indicated.