Model-free scoring system for risk prediction with application to hepatocellular carcinoma study

There is an increasing need to construct a risk-prediction scoring system for survival data and identify important risk factors (e.g., biomarkers) for patient screening and treatment recommendation. However, most existing methodologies either rely on strong model assumptions (e.g., proportional hazards) or only handle binary outcomes. In this article, we propose a flexible method that simultaneously selects important risk factors and identifies the optimal linear combination of risk factors by maximizing a pseudo-likelihood function based on the time-dependent area under the receiver operating characteristic curve. Our method is particularly useful for risk evaluation and recommendation of optimal subsequent treatments. We show that the proposed method has desirable theoretical properties, including asymptotic normality and the oracle property after variable selection. Numerical performance is evaluated on several simulation data sets and an application to hepatocellular carcinoma data.