Augmenting treatment arms with external data through propensity-score weighted power-priors with an application in expanded access 201 9♥ 0.0 0.1 0.2 0.3 -0.50 -0.25 0.00 0.25 0.50 μe Type I error rate A Mixture 1. Equal sample size:N0 =Ne 0.024 0.026 0.028 0.030 0.032 0.034 -0.50 -0.25 0.00 0.25 0.50 μe RMSE B Mixture 1. Equal sample size:N0 =Ne 0.0 0.1 0.2 0.3 -0.50 -0.25 0.00 0.25 0.50 μe Type I error rate C Mixture 2. Larger external data:N0 × 5 =Ne 0.02 0.03 0.04 0.05 -0.50 -0.25 0.00 0.25 0.50 μe RMSE D Mixture 2. Larger external data:N0 × 5 =Ne 0.0 0.1 0.2 0.3 -0.50 -0.25 0.00 0.25 0.50 μe Type I error rate E Mixture 3. Larger current data:N0 = 2 ×Ne 0.020 0.022 0.024 0.026 -0.50 -0.25 0.00 0.25 0.50 μe RMSE F Mixture 3. Larger current data:N0 = 2 ×Ne 0.0 0.1 0.2 0.3 -0.50 -0.25 0.00 0.25 0.50 μe Type I error rate G Mixture 3. More covariates: |X| = 10 0.024 0.028 0.032 0.036 -0.50 -0.25 0.00 0.25 0.50 μe RMSE H Mixture 3. More covariates: |X| = 10 Method Ignore Pooling Pro P M P Wang 10% Wang 20% Figure 4: Comparison of different estimation methods in terms of type I error (left) and root mean squared error (RMSE) (right) when the difference in outcomes is in part driven by difference in covariates. There is a latent class structure in covariates. (Setting 2) Sensitivity analysis: no mixture We first explored how the methods would compare when there is no latent class structure in the distribution of the covariates, in the setting ’no mixture’. The results of this sensitivity analysis are depicted in Figure 5. Compared with the mixture setting (Setting 2), we observe a steeper increase in both RMSE and type I error rate due to the absence of the leveling effect caused by the latent class structure. Furthermore, the further the covariate distribution shifts, the less their overlap becomes. In case of a large difference in covariate distributions, the corresponding
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