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Combining experimental and observational follow-up datasets has received alot of attention lately. In a time-to-event setting, recent work has usedmedicare claims to extend the follow-up period for participants in a prostatecancer clinical trial. This allows the estimation of the long-term effect thatcannot be estimated by clinical trial data alone. In this paper, we study theestimation of long-term effect when participants in a clinical trial are linkedto an observational follow-up dataset with incomplete data. Such data linkagesare often incomplete for various reasons. We formulate incomplete linkages as amissing data problem with careful considerations of the relationship betweenthe linkage status and the missing data mechanism. We use the popular Coxproportional hazard model as a working model to define the long-term effect. Wepropose a conditional linking at random (CLAR) assumption and an inverseprobability of linkage weighting (IPLW) partial likelihood estimator. We showthat our IPLW partial likelihood estimator is consistent and asymptoticallynormal. We further extend our approach to incorporate time-dependentcovariates. Simulations results confirm the validity of our method, and wefurther apply our methods to the SWOG study.

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