Investigation of type 1 error (100,000 replicates) under the normal model showed that all individual and joint tests considered here maintained the nominal error rates at the 0.05, 0.005, and 0.0005 levels when MAF was at least 0.1 and there were ≥ 20 individuals within each genotype group (Tables S1 and S2). However, as MAF or the smallest genotype group size decreased, the LRT method demonstrated inflated type 1 error (Tables S1 and S2). Departure from normality also resulted in LRT having inflated type 1 error, as previously discussed in Cao et al.17