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.

Motivating study and statistical approaches Crohn's disease (CD) is a chronic debilitating condition characterized by periods of inflammatory activity in the bowel that causes symptoms such as abdominal pain, diarrhea, andweight loss. Pharmacologic treatment for CD includes medications such as steroids, immunomodulating drugs, and biological therapy. Despite these available medications, many people with CD are escalated to surgical interventions from small to extensive resections of the bowel or colon (Gomollón et al., 2016). Previous studies have estimated that up to 50% of patients with CD undergo surgery within 10 years after diagnosis; however, surgical rates have decreased over time, possibly due to the introduction of modern treatments such as thiopurines and anti-TNF (Lakatos et al., 2012; Ramadas et al., 2010). The aim of this study is to determine whether clinical and demographic characteristics observed at the time of diagnosis can be used to predict the occurrence of major abdominal surgery within 5 years, with the goal of personalized disease management.