Sufficient dimension reduction on marginal regression for gaps of recurrent events

A semiparametric linear transformation of gap time is proposed to model recurrent event data with high-dimensional covariates and informative censoring. It is derived from a proportional hazards model for the conditional intensity function of a renewal process. To overcome the difficulty arising from high-dimensional covariates, we develop a modified sliced regression for censored data and use a sufficient dimension reduction procedure to transform them to a lower dimensional space. Simulation studies are performed to confirm and evaluate the theoretical findings, and to compare the proposed method with existing methods in the literature. An example of application on a set of medical data is demonstrated as well. The proposed model together with the dimension reduction method offers an effective alternative for the analysis of recurrent event with high-dimensional covariates and informative censoring.