Chapter 9 196 approaches. Our simulation design was inspired by previous hybrid setups,21,24 as well as motivated by the available setting of a (single-arm) clinical trial with external data from an expanded access program. Data generation We simulate the dichotomous outcome through the following data generating process: Equation 13 where β0 is the intercept, β is a row vector of coefficients and η is a drift term. In our base case setting, we simulate data from N = 800 patients (N0 = 400 in the trial, Ne = 400 in the external data), for K = |X| = 5 different continuous covariates X with βj = 0.1, j = 1,…,5. We set our base case intercept to β0 = 0. Several scenarios are explored to take into account that differences between trial and external outcomes can occur due to differences in covariates and/or a difference in the drift parameter. For the patient characteristics in the current trial, we assume normally distributed covariates with X0 ~ Ɲ(μ0,σ0 2).To account for possible differences in the covariate distribution in the external data, we assume that a proportion (ψ) of the patients in the external data have the same covariate distribution as the trial patients, and that the other external patients (1 − ψ) have data from a different normal distribution, with X0 ~ Ɲ (0,1) and Xe ~ (1 - ψ) Ɲ (μe,σ0 2) + ψƝ (μ 0,σe 2). We vary the value of ψ from 0.5 to 1 in the simulations, to assess the implications of our methods when covariates have different degrees of overlap. To investigate the performance of our method, we consider the following four main scenarios: 1. Scenario 1: Drift. The change in outcome is only caused by drift η. We vary η ∈ [−0.5,0.5]. Both populations have the same covariate distribution, i.e. X0, Xe ~ Ɲ(0,1), but these have no effect on the outcome distributions as β = 0. 2. Scenario 2: Mixture. The change in outcome is only caused (β = 0.1) by a difference in the underlying covariate distributions. The covariates come from a mixture distribution with ψ = 0.5. We assume X0 ~ Ɲ (0,1) and Xe ~ Ɲ(µe,1), where we vary µe ∈ [−0.5,0.5]. There is no drift, η = 0.
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