Nonparametric estimation of linear personalized diagnostics rules via efficient grid algorithm

Many diseases are heterogeneous, comprised of multiple disease subgroups. It is of great interest but highly unlikely to find a single biomarker that can accurately detect such heterogeneous diseases across different subgroups. In this article, we propose to estimate a personalized diagnostic rule (PDR) to tailor more effective biomarkers to each individual according to a linear combination of his or her profiles. A standard grid search algorithm can be used to estimate the optimal linear PDR that maximizes the area under the receiver operating characteristics curve (AUC) among all the linear PDRs, but it is time-consuming especially when the number of variables is large. Alternatively, we developed an efficient grid rotation algorithm that provides a nearly suboptimal solution and studied its variation to find the optimal solution. We implemented the cross-validated forward variable selection method to find a subset of useful variables while avoid overfitting. Extensive simulations show that our proposed method reduces bias and variance. Analysis of a gastric cancer biomarker study and censored survival outcome data illustrates the practical utility of our proposed method. The proposed method is implemented in the open-source R package persDx.