Semiparametric temporal process regression of survival-out-of-hospital

The recurrent/terminal event data structure has undergone considerable methodological development in the last 10–15 years. An example of the data structure that has arisen with increasing frequency involves the recurrent event being hospitalization and the terminal event being death. We consider the response Survival-Out-of-Hospital, defined as a temporal process (indicator function) taking the value 1 when the subject is currently alive and not hospitalized, and 0 otherwise. Survival-Out-of-Hospital is a useful alternative strategy for the analysis of hospitalization/survival in the chronic disease setting, with the response variate representing a refinement to survival time through the incorporation of an objective quality-of-life component. The semiparametric model we consider assumes multiplicative covariate effects and leaves unspecified the baseline probability of being alive-and-out-of-hospital. Using zero-mean estimating equations, the proposed regression parameter estimator can be computed without estimating the unspecified baseline probability process, although baseline probabilities can subsequently be estimated for any time point within the support of the censoring distribution. We demonstrate that the regression parameter estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. Simulation studies are performed to show that our estimating procedures have satisfactory finite sample performances. The proposed methods are applied to the Dialysis Outcomes and Practice Patterns Study (DOPPS), an international end-stage renal disease study.