Recurrent events arise frequently in a wide range of areas in science and technology. While fully specified models are appealing when interest lies in prediction, extrapolation, etc., robust methods based on marginal features of the process are often appealing if the aim is to make simple comparisons. Robust methods for the analysis of recurrent events have been developed based on Poisson estimating functions (Andersen and Gill, 1982; Lawless and Nadeau, 1995). We review these methods and then discuss an alternative approach suitable for settings in which recurrent events occur over multiple periods and treatment comparisons are of primary interest. The approach is motivated by a "working" mixed Poisson model in which suitable conditioning can eliminate the subject-specific effects. A robust variance is derived for the resulting pseudo-score statistic. The relative efficiency of the conditional analyses versus a marginal analysis is examined, and the robustness of the new test to mixed renewal processes and truncated mixed Poisson processes is demonstrated through simulations. The method is illustrated by application to data from an asthma trial. This is joint work with Wei Wei (University of Michigan) and Grace Yi (University of Waterloo).
Group for Research in Decision Analysis