We let X=(X1, …, Xn) be the n × 1 vector of genotype data. We code each genotype as 0, 1, or 2, corresponding to the number of minor alleles present at that locus. For n individuals, we let Y=(Y1, …, Yn) be the n × 1 vector of the case–control status, which is coded 0 for control subjects and 1 for case subjects. Further, Ȳ denotes the proportion of cases. The score statistic for testing for an additive effect of a diallelic locus on phenotype is given as Ux=(Y−Ȳ)X. Under the null hypothesis of no association between genotype and disease, the score test U2x/Var(UX) is asymptotically distributed as χ2 with 1 degree of freedom. To account for relatedness of cases we used the kinship coefficients matrix when computing the variance of the score statistic.14 Imputation is dealt with by accounting for loss of information due to genotype uncertainty. A detailed derivation of the score test is given in the Appendix.
