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Optimal threshold estimator of a prognostic marker by maximizing a time-dependent expected utility function for a patient-centered stratified medicine

Defining thresholds of prognostic markers is essential for stratified medicine. Such thresholds are mostly estimated from purely statistical measures regardless of patient preferences potentially leading to unacceptable medical decisions. Quality-Adjusted Life-Years are a widely used preferences-based measure of health outcomes. We develop a time-dependent Quality-Adjusted Life-Years-based expected utility function for censored data that should be maximized to estimate an optimal threshold. We performed a simulation study to compare estimated thresholds when using the proposed expected utility approach and purely statistical estimators. Two applications illustrate the usefulness of the proposed methodology which was implemented in the R package ROCt (www.divat.fr). First, by reanalysing data of a randomized clinical trial comparing the efficacy of prednisone vs. placebo in patients with chronic liver cirrhosis, we demonstrate the utility of treating patients with a prothrombin level higher than 89%. Second, we reanalyze the data of an observational cohort of kidney transplant recipients: we conclude to the uselessness of the Kidney Transplant Failure Score to adapt the frequency of clinical visits. Applying such a patient-centered methodology may improve future transfer of novel prognostic scoring systems or markers in clinical practice.