Some Graphical Displays and Marginal Regression Analyses for Recurrent Failure Times and Time Dependent Covariates

Recurrent event time data are common in medical research; examples include infections in AIDS patients and seizures in epilepsy patients. In this context, as well as in the more usual context of a single failure time variable, time-dependent covariates are frequently of interest. We suggest some rate functions that might be displayed when analyzing recurrent failure time data or when the effect of a categorical time-dependent covariate is of interest. Estimators of these functions are provided along with two-sample test statistics. A new approach to regression modeling of these data is suggested and contrasted with existing methods. Our methods do not require that an explicit model be formulated for the probabilistic association between failure times within an individual. This is in line with the currently popular generalized estimating equation approach to longitudinal data. If the nature of such associations is known or is of particular interest, then alternative methods may be appropriate.