A Frequentist Approach Using Weighted Estimating Equations for Survival Analysis of Randomized Controlled Trial With External Control Arm

Clinical trials using a hybrid control, which integrates a randomized control with external control data, may be one solution to facilitate clinical development where traditional randomized controlled trials are challenging. Despite its attractive features, systematic differences between controls can introduce bias in treatment effect estimation and inflate Type I error. Although propensity score methods may be used to address systematic differences from measured covariate imbalance, potential differences from unmeasured or unknown factors may still arise despite careful consideration. In such cases, dynamic borrowing methods have been proposed to account for potential differences between randomized and external control data and discount the contribution of external control data when needed. Conventional methods, however, often rely on Bayesian approaches, requiring proper specification of the likelihood. This is particularly challenging for survival analysis using proportional hazards model due to specification of the baseline hazard function. To address these challenges, we propose to utilize the weighted partial likelihood score equation where external control patients are weighted by the inverse probability of the propensity score and an additional discounting weight, adjusting the contribution of external control data according to its similarity to randomized control data. A new variance estimator based on stacked estimating equations is proposed to incorporate the uncertainty in estimating discounting weights. Operating characteristics of the proposed method are studied via extensive simulation. The proposed method yields reduced bias in treatment effect estimation and Type I error while improving statistical power in either scenarios where measured or unmeasured confounders exist.