Power and Predictive Accuracy of Polygenic Risk Scores

Polygenic scores have recently been used to summarise genetic effects among an ensemble of markers that do not individually achieve significance in a large-scale association study. Markers are selected using an initial training sample and used to construct a score in an independent replication sample by forming the weighted sum of associated alleles within each subject. Association between a trait and this composite score implies that a genetic signal is present among the selected markers, and the score can then be used for prediction of individual trait values. This approach has been used to obtain evidence of a genetic effect when no single markers are significant, to establish a common genetic basis for related disorders, and to construct risk prediction models. In some cases, however, the desired association or prediction has not been achieved. Here, the power and predictive accuracy of a polygenic score are derived from a quantitative genetics model as a function of the sizes of the two samples, explained genetic variance, selection thresholds for including a marker in the score, and methods for weighting effect sizes in the score. Expressions are derived for quantitative and discrete traits, the latter allowing for case/control sampling. A novel approach to estimating the variance explained by a marker panel is also proposed. It is shown that published studies with significant association of polygenic scores have been well powered, whereas those with negative results can be explained by low sample size. It is also shown that useful levels of prediction may only be approached when predictors are estimated from very large samples, up to an order of magnitude greater than currently available. Therefore, polygenic scores currently have more utility for association testing than predicting complex traits, but prediction will become more feasible as sample sizes continue to grow. Author Summary: Recently there has been much interest in combining multiple genetic markers into a single score for predicting disease risk. Even if many of the individual markers have no detected effect, the combined score could be a strong predictor of disease. This has allowed researchers to demonstrate that some diseases have a strong genetic basis, even if few actual genes have been identified, and it has also revealed a common genetic basis for distinct diseases. These analyses have so far been performed opportunistically, with mixed results. Here I derive formulae based on the heritability of disease and size of the study, allowing researchers to plan their analyses from a more informed position. I show that discouraging results in some previous studies were due to the low number of subjects studied, but a modest increase in study size would allow more successful analysis. However, I also show that, for genetics to become useful for predicting individual risk of disease, hundreds of thousands of subjects may be needed to estimate the gene effects. This is larger than most existing studies, but will become more common in the near future, so that gene scores will become more useful for predicting disease than has appeared to date.