Generalized Method of Moments in Analyzing Recurrent Events for Semiparametric Transformation Models With Informative Censoring

In this article, we consider the semiparametric transformation models with a shared frailty variable for the rate function of recurrent events, where a shared frailty model is imposed to enable a correlation between the recurrent event process and the censoring time. Unlike the commonly used shared-frailty proportional rate models, our models allow for the rate functions associated with any two sets of covariate values not to be proportional over time. The proposed estimating approaches are inspired by Wang and Huang, who decompose the rate function into shape and size components. We start with the inverse-rate weighting approach and subsequently introduce a novel generalized method of moments framework to improve estimation efficiency by combining the estimating procedures derived from the shape and size components, respectively. The proposed methods are robust because they do not require the assumption of a Poisson process for the recurrent events or distributional assumptions for the frailty and censoring times. The large sample properties of the proposed methods are established, and the finite sample properties are examined through the simulation studies. The proposed methods are applied to a real data set.