Analyzing longitudinal data to characterize the accuracy of markers used to select treatment

With the increasing availability of detailed clinical information, there is optimism that treatment choices can be selectively directed to those individuals most likely to benefit. While standard clinical trials can establish whether a treatment appears to be effective on average, subsequent work is needed to determine whether there are identifiable subgroups of subjects for whom treatment is either particularly beneficial or harmful. Molecular assays and modern imaging technology now allow numerous candidate measures to be used as potential determinants of treatment choice. In this manuscript, we focus on novel measures of decision accuracy that reflect the treatment marker objective. Specifically, we define longitudinal individual-level potential outcomes (principal strata) that characterize patient outcomes under treated and untreated states. We propose generalizations of sensitivity and specificity that measure the accuracy with which a marker can distinguish those subjects who are expected to have a more favorable outcome under a specific treatment choice from those subjects who are expected to have a more favorable outcome under alternative treatment options. For quantitative markers, we propose principal receiver operating characteristic curves that display the full range of potential sensitivity and specificity. We use simulations to demonstrate the properties of proposed estimators, and we illustrate the methods using candidate neuroimaging and electrodiagnostic markers that could be used to select patients for carpal tunnel surgery.