Univariate and pair-wise RPM analyses were performed for the 127 nicotinic receptor SNPs that passed quality control for the combined COGEND data. Because we were analyzing a binary trait, the explained variance, VE, was defined by VE=1−∑NipiqiNpq where N is the total sample size, p is the proportion of cases, and q is the proportion of controls, with the corresponding subscripted variables defined similarly for the resulting RPM model groups. We note that this is always less than or equal to the variance accounted for by the full model (i.e. all cells kept separate). Thus, the merging of cells by the RPM method provides some protection from over-fitting and the corresponding inflation of estimated explained variance. Sampling variability and sparseness can be expected to result in “noise” in the estimates of explained phenotypic variance. A test of the RPM using real genotypes with simulated phenotypes (Culverhouse et al. 2009) suggests that pair-wise results accounting for less than 0.5% of the trait variance may have an increased risk of being false positives. Because of this, we restricted our 2-SNP signals of interest to those explaining more than 1.0% of the trait variance.
