Performance metrics for models designed to predict treatment effect

ABSTRACTBackgroundMeasuring the performance of models that predict individualized treatment effect is challenging because the outcomes of two alternative treatments are inherently unobservable in one patient. The C-for-benefit was proposed to measure discriminative ability. However, measures of calibration and overall performance are still lacking. We aimed to propose metrics of calibration and overall performance for models predicting treatment effect.MethodsSimilar to the previously proposed C-for-benefit, we defined observed pairwise treatment effect as the difference between outcomes in pairs of matched patients with different treatment assignment. We redefined the E-statistics, the cross-entropy, and the Brier score into metrics for measuring a model’s ability to predict treatment effect. In a simulation study, the metric values of deliberately “perturbed models” were compared to those of the data-generating model, i.e., “optimal model”. To illustrate these performance metrics, different modeling approaches for predicting treatment effect are applied to the data of the Diabetes Prevention Program: 1) a risk modelling approach with restricted cubic splines; 2) an effect modelling approach including penalized treatment interactions; and 3) the causal forest.ResultsAs desired, performance metric values of “perturbed models” were consistently worse than those of the “optimal model” (Eavg-for-benefit≥0.070 versus 0.001, E90-for-benefit≥0.115 versus 0.003, cross-entropy-for-benefit≥0.757 versus 0.733, Brier-for-benefit≥0.215 versus 0.212). Calibration, discriminative ability, and overall performance of three different models were similar in the case study. The proposed metrics were implemented in a publicly available R-package “HTEPredictionMetrics”.ConclusionThe proposed metrics are useful to assess the calibration and overall performance of models predicting treatment effect.