The effect of sample size on polygenic hazard models for prostate cancer

Abstract We aimed to determine the effect of sample size on performance of polygenic hazard score (PHS) models in predicting the age at onset of prostate cancer. Age and genotypes were obtained for 40,861 men from the PRACTICAL consortium. The dataset included 201,590 SNPs per subject, and was split into training (34,444 samples) and testing (6,417 samples) sets. Two PHS model-building strategies were investigated. Established-SNP model considered 65 SNPs that had been associated with prostate cancer in the literature. A stepwise SNP selection was used to develop Discovery-SNP models. The performance of each PHS model was calculated for random sizes of the training set (1 to 30 thousand). The performance of a representative Established-SNP model was estimated for random sizes of the testing set (0.5 to 6 thousand). Mean HR 98/50 (hazard ratio of top 2% to the average in the test set) of the Established-SNP model increased from 1.73[95%CI: 1.69-1.77] to 2.41[2.40-2.43] when the number of training samples was increased from 1 to 30 thousand. The corresponding HR 98/50 of the Discovery-SNP model increased from 1.05[0.93-1.18] to 2.19[2.16-2.23]. HR 98/50 of a representative Established-SNP model using testing set sample sizes of 0.6 and 6 thousand observations were 1.78[1.70-1.85] and 1.73[1.71-1.76], respectively. We estimate that a study population of 20 to 30 thousand men is required to develop Discovery-SNP PHS models for prostate cancer. The required sample size could be reduced to 10 thousand samples, if a set of SNPs associated with the disease has already been established. Author summary Polygenic hazard scores represent a recent advancement in polygenic prediction to model the age of onset of various diseases, such as Alzheimer’s disease or prostate cancer. These scores accumulate small effect sizes from several tens of genetic variants and can be used to establish an individual’s risk of experiencing an event relative to a control population across time. The largest barrier to the development of polygenic hazard scores is the large number of study subjects needed to develop the underlying models. We sought to understand the effect of varying the total number of samples on the performance of a polygenic hazard score in the context of prostate cancer. We found that the performance of the score did not appreciably change beyond 20 to 30 thousand observations when developing the model from scratch. However, when the discovery of the genetic variants can be borrowed from those already identified in the literature to be associated with the disease, the required number of samples is reduced to 10 thousand with no appreciable detriment in performance. We hope that these results can guide the design of future studies of polygenic scores in other diseases and demonstrate the importance of genome-wide association studies.