To induce population stratification, we randomly assigned 80% of samples from HIV samples and 20% of SCZ samples as cases, and remaining samples as controls. We then used case-control labels to run four association tests: fixed-threshold approach (T1 and T5 versions of the CMC test58), WSS59, and VT test61. We quantified the evidence of population stratification by considering the most significant p-value (of 15,122 genes) and the proportion of p-values < 0.05, and < 0.01. As seen in the null distribution (Figure 2), it is expected that, due to low counts, p-values will have a deficiency of statistically significant signals. Before correction for population stratification, however, our metrics indicate an excess of statistically significant signals. For example, for T5, the most significant p-value was <0.000001, and the proportions of p-values were 0.0595 at level 0.05, and 0.0136 at level 0.01. Results were similar for the other statistical tests, and for other proportions of HIV samples assigned as cases (we experimented with 90%, 80%, and 70%, as well as 30%, 20%, and 10%). We note that when the proportion of HIV
