A multi-locus predictiveness curve and its summary assessment for genetic risk prediction

With the advance of high-throughput genotyping and sequencing technologies, it becomes feasible to comprehensive evaluate the role of massive genetic predictors in disease prediction. There exists, therefore, a critical need for developing appropriate statistical measurements to access the combined effects of these genetic variants in disease prediction. Predictiveness curve is commonly used as a graphical tool to measure the predictive ability of a risk prediction model on a single continuous biomarker. Yet, for most complex diseases, risk prediciton models are formed on multiple genetic variants. We therefore propose a multi-marker predictiveness curve and provide a non-parametric method to construct the curve for case-control studies. We further introduce a global predictiveness U and a partial predictiveness U to summarize prediction curve across the whole population and sub-population of clinical interest, respectively. We also demonstrate the connections of predictiveness curve with ROC curve and Lorenz curve. Through simulation, we compared the performance of the predictiveness U to other three summary indices: R square, Total Gain, and Average Entropy, and showed that Predictiveness U outperformed the other three indexes in terms of unbiasedness and robustness. Moreover, we simulated a series of rare-variants disease model, found partial predictiveness U performed better than global predictiveness U. Finally, we conducted a real data analysis, using predictiveness curve and predictiveness U to evaluate a risk prediction model for Nicotine Dependence.