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

Abstract

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