Long-term effect estimation when combining clinical trial and observational follow-up datasets

Combining experimental and observational follow-up datasets has received a lot of attention lately. In a time-to-event setting, recent work has used medicare claims to extend the follow-up period for participants in a prostate cancer clinical trial. This allows the estimation of the long-term effect that cannot be estimated by clinical trial data alone. In this paper, we study the estimation of long-term effect when participants in a clinical trial are linked to an observational follow-up dataset with incomplete data. Such data linkages are often incomplete for various reasons. We formulate incomplete linkages as a missing data problem with careful considerations of the relationship between the linkage status and the missing data mechanism. We use the popular Cox proportional hazard model as a working model to define the long-term effect. We propose a conditional linking at random (CLAR) assumption and an inverse probability of linkage weighting (IPLW) partial likelihood estimator. We show that our IPLW partial likelihood estimator is consistent and asymptotically normal. We further extend our approach to incorporate time-dependent covariates. Simulations results confirm the validity of our method, and we further apply our methods to the SWOG study.