Semiparametric Trend Analysis for Stratified Recurrent Gap Times under Weak Comparability Constraint

Abstract Recurrent event data are frequently encountered in many longitudinal studies where each individual may experience more than one event. [1] proposed a comparability constraint to estimate the time trend for the gap times, where the gap time pairs that satisfy the constraint have the same conditional distribution. However, the comparable paired gap times are also independent. Therefore, the comparable gap time pairs will be subject to a stronger constraint than needed for the estimation. Thus their procedure is subject to information loss. Under the accelerated failure time model, we propose a new comparability constraint that can overcome the drawback mentioned above. The gap time pairs being selected by the proposed comparability constraint will still have the same distribution, but they do not need to be independent of each other. We prove that the new estimator will still be unbiased. However, the variance will be smaller than [1]’s estimator. Thus our method is superior to [1]. Numerical studies also confirm the theoretical findings. We apply the proposed method to the HIV Prevention Trial Network 052 study.