In this work, statistical properties of polygenic score analyses are derived from a quantitative genetics model as a function of the explained genetic variance and sample sizes in discovery and replication samples. A range of options for constructing the score is considered, including estimation of the score from a different trait to the one predicted, selection of markers according to their P-values, and different methods for weighting markers in the score. The power is obtained for testing a polygenic score for association in a replication sample, and the correlation, mean square error, and area under the receiver-operator characteristic curve (AUC) are obtained for a predictor estimated from a finite training sample. These results are used to assess some recent studies and to discuss prospects for the future utility of polygenic score analyses for the prediction of complex traits.
