A multiple imputation approach to regression analysis for doubly censored data with application to AIDS studies

Sun, Liao, and Pagano (1999) proposed an interesting estimating equation approach to Cox regression with doubly censored data. Here we point out that a modification of their proposal leads to a multiple imputation approach, where the double censoring is reduced to single censoring by imputing for the censored initiating times. For each imputed data set one can take advantage of many existing techniques and software for singly censored data. Under the general framework of multiple imputation, the proposed method is simple to implement and can accommodate modeling issues such as model checking, which has not been adequately discussed previously in the literature for doubly censored data. Here we illustrate our method with an application to a formal goodness-of-fit test and a graphical check for the proportional hazards model for doubly censored data. We reanalyze a well-known AIDS data set.