In order to investigate the power of our approach, we assumed the standard liability threshold model in which a continuous normal distribution of liability underlies risk of disease. Under this model, individuals who are affected have a liability exceeding a certain threshold, the value of which being determined by the prevalence of the disease in the population. In the situation where a SNP (or an allelic score of SNPs) affects a biological intermediate which then in turn affects likelihood of disease, power to detect association between the SNP and disease is determined by (a) the proportion of variance in the biological intermediate explained by the allelic score (denoted by σG 2), (b) the strength of the causal relationship between the intermediate and the disease (denoted by β) which together with σG 2 determines the proportion of liability in the disease that is explained by the SNP (denoted by σL 2), (c) the disease prevalence, (d) the sample size of the case-control study in which the test is performed, and (e) the type I error level.
