Abstract: Patients who undergo hematopoietic stem cell transplantation (HSCT) often experience multiple bacterial infections during the early post-transplant period. In this article, we consider a semiparametric regression model that correlates patient-and transplant-related risk factors with inter-infection gap times. Existing regression methods for recurrent gap times are not directly applicable to studies of post-transplant infections because the initiating event (i.e., the transplant) is different to the recurrent events of interest (i.e., post-transplant infections). As a result, the time between a transplant and the first infection and that between consecutive infections have distinct biological meanings and, hence, follow different distributions. Moreover, risk factors may have different effects on these two types of gap times. Therefore, we propose a semiparametric estimation procedure that lets us simultaneously evaluate the covariate effects on the time between a transplant and the first infection and on the gap times between consecutive infections. The proposed estimator accounts for dependent censoring induced by within-subject correlation between recurrent gap times and length bias in the last censored gap time due to intercept sampling. We study the finite sample properties through simulations and apply the proposed method to post-HSCT bacterial infection data collected at the University of Minnesota.

Key words and phrases: Accelerated failure time model, gap times, recurrent events, semiparametric method, weighted risk-set method.