-Adjusted p-values for genome-wide regression analysis with non-normally distributed quantitative phenotypes

This paper provides a small-sample adjustment for Bonferonni- corrected p-values in multiple univariate regressions of a quantitative phenotype (such as a social trait) on individual genome markers. The p-value estimator conventionally used in existing genome-wide asso- ciation (GWA) regressions assumes a normally-distributed dependent variable, or relies on a central limit theorem based approximation. We show that the central limit theorem approximation is unreliable for GWA regression Bonferonni-corrected p-values except in very large samples. We note that measured phenotypes (particularly in the case of social traits) often have markedly non-normal distributions. We propose a mixed normal distribution to better ?t observed pheno- typic variables, and derive exact small-sample p-values for the stan- dard GWA regression under this distributional assumption.