In their study of breast and prostate cancers Machiela et al also calculated the AUC for prediction of disease from the polygenic score. Here it is more important for the training sample to be large, ensuring accurate estimation of the score, justifying the 10-fold cross-validation design. Their AUC did not exceed 53% for breast cancer and 56.4% for prostate cancer. Under the same assumptions as above, the analytic AUC is 53.6% for breast cancer if the markers explain the full genetic variance, or 51.8% if they explain half. However if the sample were infinitely large, the AUCs would be 89% and 79% respectively. For prostate cancer, the analytic AUCs are 54.1% if the markers explain the full genetic variance, and 52% if they explain half; for a large sample they would be 90% and 80%. Thus, the low AUCs observed by Machiela et al are compatible with their study design, but they could be considerably higher if a larger training sample were available.
