To calculate power, however, we would need to specify , which is a parameter with non-intuitive properties, and depends on the prevalence of the disease in the population (K), the proportion of variance in disease liability that is captured by the SNPs at population level, and the proportional of cases in the sample (v). For this reason we define as the variance explained by all SNPs at the population level on the unobserved underlying scale of disease liability, and use a linear transformation to transform to on the liability scale [4], i.e. and with . We then get(11)where N case is the number of cases, N control is the number of controls, and i is the selection intensity which is a function of K [4]. We illustrate in Figure 2 the dependency of the SE of on disease prevalence (K) and proportion of cases in the sample (v) due to the transformation.
