Development and evaluation of multi-marker risk scores for clinical prognosis

Heart failure research suggests that multiple biomarkers could be combined with relevant clinical information to more accurately quantify individual risk and guide patient-specific treatment strategies. Therefore, statistical methodology is required to determine multi-marker risk scores that yield improved prognostic performance. Development of a prognostic score that combines biomarkers with clinical variables requires specification of an appropriate statistical model and is most frequently achieved using standard regression methods such as Cox regression. We demonstrate that care is needed in model specification and that maximal use of marker information requires consideration of potential non-linear effects and interactions. The derived multi-marker score can be evaluated using time-dependent receiver operating characteristic methods, or risk reclassification methods adapted for survival outcomes. We compare the performance of alternative model accuracy methods using simulations, both to evaluate power and to quantify the potential loss in accuracy associated with use of a sub-optimal regression model to develop the multi-marker score. We illustrate development and evaluation strategies using data from the Penn Heart Failure Study. Based on our results, we recommend that analysts carefully examine the functional form for component markers and consider plausible forms for effect modification to maximize the prognostic potential of a model-derived multi-marker score.