datasets will generally not include all relevant confounding variables. Therefore, we calculated a second PC from randomly selected subsets of the confounding variable, ranging from 10% (10 variables) to 100% (100 variables) at intervals of 1% in order to model the effectiveness of the method under different assumptions about the proportion of confounding data that is measured. We fixed other model parameters across all simulation iterations, as shown in Figure 1. We extracted estimates of the effect of PRS on the target phenotype from the following models: Model A1. Target Phenotype ~ PRSModel A2. Target Phenotype ~ PRS + EnvironmentModel A3. Target Phenotype ~ PRS + Environment + Incomplete Phenotypic PCModel A4. Target Phenotype ~ PRS + Environment + Complete Phenotypic PC We repeated this procedure 1250 times for each combination of parameters. New simulated data was generated at each iteration of the simulation. Estimates were plotted using the ggplot2 (Wickham, 2009) package in R. Note that in this simulation we refer to the collider variable as an environment. In the application of this method to real data, we use the more general term “collider variable” to identify the covariate that may induce collider bias.
