A numerical strategy to evaluate performance of predictive scores via a copula-based approach

Assessing and comparing the performance of correlated predictive scores are of current interest in precision medicine. Given the limitations of available theoretical approaches for assessing and comparing the predictive accuracy, numerical methods are highly desired which, however, have not been systematically developed due to technical challenges. The main challenges include the lack of a general strategy on effectively simulating many kinds of correlated predictive scores each with some given level of predictive accuracy in either concordance index or the area under a receiver operating characteristic curve area under the curves (AUC). To fill in this important knowledge gap, this paper is to provide a general copula-based numeric framework for assessing and comparing predictive performance of correlated predictive or risk scores. The new algorithms are designed to effectively simulate correlated predictive scores with given levels of predictive accuracy as measured in terms of concordance indices or time-dependent AUC for predicting survival outcomes. The copula-based numerical strategy is convenient for numerically evaluating and comparing multiple measures of predictive accuracy of correlated risk scores and for investigating finite-sample properties of test statistics and confidence intervals as well as assessing for optimism of given performance measures using cross-validation or bootstrap.