Augmenting treatment arms with external data through propensity-score weighted power-priors with an application in expanded access 209 9♥ devoted to the development of statistical methods to analyze expanded access programs. Our method provides a quantitative toolbox to augment treatment arms with expanded access data in a cautious and prudent way. Limitations and future research We acknowledge several limitations to our study. First, we have chosen a subset of the potentially available methods for integrating propensity score and dynamic borrowing, and we did not consider other relevant comparator methods such as direct covariate adjustment.49 Second, evaluating our method in terms of inflation of type I error rate could be questioned. For the true frequentist requiring strict type I error rate control, we know that given the external data, gains are typically not possible.10 For the true Bayesian, operating characteristics such as type I error rate are less relevant. Furthermore, these methods are a combination of frequentist and Bayesian methodology, as the propensity scores are still estimated from a frequentist logistic regression model. A fully Bayesian design that integrates the estimation of the propensity score remains uncharted territory.30,50 Our restriction of the propensity score weights is a result of this mixed methodology. It should be noted that our limiting of the weights to a maximum of 1, while possibly desirable from the point of view of a regulator, will result in weights that will potentially not be able to capture all of the confounding effects of the variables in the propensity score model. Third, we derived the results from our method in the binomial setting. The binary outcome leads to a closed form posterior which greatly simplifies sampling and shortens computation time. We have not explored other outcome types, but it should be feasible to extend our method to time-to-event or normally distributed outcomes. Our method showed favorable computational performance compared with the method from Wang and others as described in their psrwe package,21 where the propensity-score stratification sometimes failed to produce estimates. Finally, our simulation set-up including latent classes was inspired both by the original simulation set-up of Wang and others,14,21,24 and by our analysis of patient populations in expanded access programs. The latent class setup may however favor hybrid methods in our simulation. The underlying assumptions and plausibility of such specifications should be tested prior to utilizing our suggested approach. Conclusion We developed a novel statistical design to augment the treatment arm of a current trial with external (expanded access) data. We illustrated our method through causal interpretation, simulation, and a real-life application to expanded access data. Our study shows that our
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