Augmenting treatment arms with external data through propensity-score weighted power-priors with an application in expanded access 207 9♥ DISCUSSION We developed a method to integrate the propensity score with variable power prior methodology. Our motivation stems from the increasing interest to incorporate external real-world evidence, and in particular expanded access data, into current trial data. Our novel ProPP method flexibly accounts for differences in outcomes and covariates between these two data sources in a twostage design. Differences due to observed covariates are first incorporated through the propensity score. Remaining confounding is subsequently attenuated via the MPP in a dynamic borrowing setting. To our knowledge, we are the first to present the causal implications of the propensity score-integrated methods, and our modeling choices are guided by this causal interpretation. Our work explores the idea of augmenting treatment arms with current expanded access data. Overall, we observed that our method performs better than or on par with existing methods in a simulation study. In simulation our method provides higher precision (lower RMSE) compared with both ’naive’ methods and ’hybrid’ methods, at the cost of light-to-moderate inflation of type I error rate. The additional two-stage safeguarding does not lead to a significant loss when there is no difference in outcomes due to underlying differences in covariates. This finding is in line with previous research exploring hybrid two-stage designs.14,43 Additionally, our method can be shown to behave similarly to the standard MPP when covariates are equal across data sets and, unlike the MPP, naturally accounts for differences in sample sizes between data sets. Compared with previous methods,21,24,36 our method needs no pre-elicitation of a fixed power parameter or a fixed amount of external patients to be borrowed, nor does it require decisions on trimming, distance measures, or the number of strata. On the other hand, it does entail a choice of prior specification. This degree of flexibility of the ProPP leads to an increase in precision, but it comes at the cost of lacking an ’outcome-free’ design principle as the Bayesian estimation of the power prior takes into account the posterior probabilities, whereas fixed power prior weights do not. When contrasts in outcomes are in part caused by contrasts in covariates, all propensity score-integrated methods outperform ’naive’ methods - a conclusion backed by a recent review.25 Nonetheless, we echo prior scholarship that borrowing information entails a trade-off between cost (potential incremental errors in decision-making and type I error rate inflation) and benefits (increased precision, decrease in patient burden).2,6,7 The high unmet need innate to expanded access programs together with the abundance of innovative statistical designs may tip the scale in favor of borrowing. Our method, like all propensity score integrated designs, may be particularly applicable in a setting when a part of the external patients is similar to patients in the current trial. We argue
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