Computation of multifactorial receiver operator and predictive accuracy characteristics

The computation of the so-called receiver operator characteristics (i.e. functions that assign the maximum specificity to each value of sensitivity) is simple when the characteristics are based on univariate data. On the contrary, multivariate characteristics are difficult to compute, as the complexity of their calculation increases exponentially with the dimension of the data. This paper describes an algorithm for computation of multivariate receiver operator characteristics and derived functions (namely positive and negative predictive characteristics). The algorithm is based on several concepts that increase its computational efficiency. The most important of them is a pre-sorting of the data in each dimension and the division of each dimension into groups in which the positive and negative cases are 100% stratified. The paper also presents a risk stratification study that utilised this algorithm. The study was aimed at identifying those survivors of acute myocardial infarction who are at risk of early death. A cohort of 539 patients was stratified based on time-domain (three variables) and spectral turbulence (six variables) indices of signal-averaged electrocardiogram. The computing times of the algorithm in this study are presented in the text, and the efficiency of the computation is discussed in detail.