Augmenting treatment arms with external data through propensity-score weighted power-priors with an application in expanded access 197 9♥ Within these two scenarios, we also assess the following four settings: 1. Setting 1: Equal sample sizes. N0 = Ne = 400 2. Setting 2: Larger external data. N0 = / Ne = 400 3. Setting 3: Larger current trial data. N0 = 2 x Ne = 400 4. Setting 4: Increase in the number of covariates, with 10 instead of 5 covariates Additionally, we look at how sensitive our method is to (mis)-specification. Therefore, we also consider: 1. Scenario 3: No Mixture. The change in outcome is only caused by a difference in underlying covariate distributions. Unlike Scenario 2, there are no latent classes. 2. Scenario 4: Superfluous covariates. This setting mimics setting 1, but now some of the parameters βj are forced to zero to simulate the inclusion of ’superfluous covariates’ (i.e. C3 in Figure 2). Our parameter of primary interest is the baseline trial rate, β0. Both in our simulation and in our expanded access use case, this is the response rate in a single-arm trial. Methods and performance measure The methods that we compare in our simulation study belong to the following three classes: ’naive methods’ such as (i) Ignore: leaving out external data and (ii) Pooling: directly combining current trial and external data,’dynamic borrowing methods’ such as (iii) the modified power prior, and ’hybrid methods’ such as (iv) the stratification + power-prior method suggested by Wang et al.21,24 whilst borrowing at most 10% and 20% (of the current trial) of patients from the external data source. Our proposed method forms an addition to the hybrid methods. Performance will be assessed by measuring: Equation 14 and the type I error rate. To assess the type I error rate, we checked how frequently the objective response rate from the trial (through β0 = 0) was within the equal-tailed 95% posterior credible interval of our estimand.
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