First, we sampled 100 variables from a multivariate normal distribution with mean set to 0. We defined the correlation structure of the multivariate normal distribution by drawing individual values from a uniform distribution for each cell of the symmetric correlation matrix. The range of the uniform distribution varied across simulation iterations to model confounders that are correlated at a range of different levels (0.05 – 0.1, 0.2 – 0.3, 0.5 – 0.6, 0.8 – 0.9). We chose to use a set of 100 confounding variables in order to be able to test the incremental difference in effect size correction that results from decreasing the proportion of confounders in the correction PC. Starting with 100 variables allowed us to test random sets of cofounders ranging from 10 variables (10% of the confounders) to 100 variables (100%) at intervals of 1% in order to determine how PC covariates perform when only a subset of the total confounding data is measured. This provides a more detailed picture of how the method can work in practice. A PRS variable was generated from a standard
