Estimation for an accelerated failure time model with intermediate states as auxiliary information

The accelerated failure time (AFT) model is a common method for estimating the effect of a covariate directly on a patient's survival time. In some cases, death is the final (absorbing) state of a progressive multi-state process, however when the survival time for a subject is censored, traditional AFT models ignore the intermediate information from the subject's most recent disease state despite its relevance to the mortality process. We propose a method to estimate an AFT model for survival time to the absorbing state that uses the additional data on intermediate state transition times as auxiliary information when a patient is right censored. The method extends the Gehan AFT estimating equation by conditioning on each patient's censoring time and their disease state at their censoring time. With simulation studies, we demonstrate that the estimator is empirically unbiased, and can improve efficiency over commonly used estimators that ignore the intermediate states.