Risk prediction using genome-wide association studies

Abstract

Over the last few years, many new genetic associations have been identified by genome-wide association studies (GWAS). There are potentially many uses of these identified variants: a better understanding of disease etiology, personalized medicine, new leads for studying underlying biology, and risk prediction. Recently, there has been some skepticism regarding the prospects of risk prediction using GWAS, primarily motivated by the fact that individual effect sizes of variants associated with the phenotype are mostly small. However, there have also been arguments that many disease-associated variants have not yet been identified; hence, prospects for risk prediction may improve if more variants are included. From a risk prediction perspective, it is reasonable to average a larger number of predictors, of which some may have (limited) predictive power, and some actually may be noise. The idea being that when added together, the combined small signals results in a signal that is stronger than the noise from the unrelated predictors. We examine various aspects of the construction of models for the estimation of disease probability. We compare different methods to construct such models, to examine how implementation of cross-validation may influence results, and to examine which single nucleotide polymorphisms (SNPs) are most useful for prediction. We carry out our investigation on GWAS of the Welcome Trust Case Control Consortium. For Crohn's disease, we confirm our results on another GWAS. Our results suggest that utilizing a larger number of SNPs than those which reach genome-wide significance, for example using the lasso, improves the construction of risk prediction models.

Figure 1

Log-likelihood for the WTCCC Crohn’s disease data using three different ways to carry out the pre-selection of significant SNPs in relation to the cross-validation. The training data log-likelihood was rescaled by a factor of 1878/2808 to be on the same scale as the test data log-likelihood.

Figure 2

Log-likelihood and AUC for the WTCCC Crohn’s disease data for prediction models for test and training data. The training data log-likelihood was rescaled by a factor of 1878/2808 to be on the same scale as the test data log-likelihood. Note that not all SNPs considered have nonzero coefficients, see Table 1. The log-likelihood for stepwise GLM using AIC (GLM-AIC) is −1287.7. The insert figure at the left bottom vertically expands the curves for the models with 100 SNPs or less.

Figure 3

Which SNPs are and are not used with nonzero coefficients for the lasso model and other prediction models for the WTCCC Crohn’s disease data. The SNPs are ordered on the horizontal axis by significance. The vertical stripes suggest that frequently the same SNPs are selected.

Figure 4

ROC curves for the WTCCC Crohn’s disease data for prediction for lasso models considering different numbers of SNPs. The AUCs for these models are displayed in Table 1.

Figure 5

Smoothed estimates of the probability of being a case as a function of the predicted probability of being a case with 95% confidence intervals for the WTCCC Crohn’s disease data. The steeper curves for the training data suggest some overfitting, while the test data appears better calibrated.

Figure 6

Comparison of test data AUC for the NIDDK and WTCCC data. The model for the NIDDK data is trained on the complete WTCCC data, the model for the test part of the WTCCC data is trained on the training part of the WTCCC data.