Robust Estimation of Mean Functions and Treatment Effects for Recurrent Events Under Event-Dependent Censoring and Termination: Application to Skeletal Complications in Cancer Metastatic to Bone

In clinical trials featuring recurrent clinical events, the definition and estimation of treatment effects involves a number of interesting issues, especially when loss to follow-up may be event-related and when terminal events such as death preclude the occurrence of further events. This paper discusses a clinical trial of breast cancer patients with bone metastases where the recurrent events are skeletal complications, and where patients may die during the trial. We argue that treatment effects should be based on marginal rate and mean functions. When recurrent event data are subject to event-dependent censoring, however, ordinary marginal methods may yield inconsistent estimates. Incorporating correctly specified inverse probability of censoring weights into analyses can protect against dependent censoring and yield consistent estimates of marginal features. An alternative approach is to obtain estimates of rate and mean functions from models that involve some conditioning to render censoring conditionally independent. We consider three methods of estimating mean functions of recurrent event processes and examine the bias and efficiency of unweighted and inverse probability weighted versions of the methods with and without a terminating event. We compare the methods via simulation and use them to analyse the data from the breast cancer trial.