We estimated posterior probabilities for each of the top loci identified from the meta-analysis to quantify disorder-specific effects (Han and Eskin, 2012). This estimation, known as the m-value, relies on two assumptions, 1) effects are either present or absent in studies, and 2) if they are present, they are similarly sized across studies. Assume Xi is the observed effect size of study i, and Ti is a random variable with value 1 if study i has an effect and 0 if not, then the m-value can be estimated using Bayes’ theorem: mi=P(Ti=1|X)=P(X|Ti=1)P(Ti=1)P(X|Ti=0)P(Ti=0)+P(X|Ti=1)P(Ti=1) which can then be used to predict whether an effect exists in a given study (>.9) or not (<.1) under the binary effects assumption.
