The forgoing is based on linear regression, which is the usual approach for quantitative traits. For binary traits the standard analysis is logistic regression, used both for estimating the coefficients in the polygenic score and for testing the association of the score in a replication sample. For small effects the log-odds are approximately linear in the predictors, so we may continue to work in a linear regression framework for estimating power and accuracy. That is, the binary trait is coded as 0/1 and treated as the response in ordinary linear regression. The variance of in equation 2 is now the binomial variance where is the proportion of study subjects with . In a prospective sample, is the population proportion of the trait, whereas in a case/control sample (to be discussed further below), it is the sampling proportion of cases.
