Prediction Accuracy Measures for a Nonlinear Model and for Right-Censored Time-to-Event Data

Abstract: This paper studies prediction summary measures for a prediction function under a general setting in which the model is allowed to be misspecified and the prediction function is not required to be the conditional mean response. We show that the R2 measure based on a variance decomposition is insufficient to summarize the predictive power of a nonlinear prediction function. By deriving a prediction error decompo- sition, we introduce an additional measure, L2, to augment the R2 measure. When used together, the two measures provide a complete summary of the predictive power of a prediction function. Furthermore, we extend these measures to right-censored time-to-event data by establishing right-censored data analogs of the variance and prediction error decompositions. We illustrate the usefulness of the proposed mea- sures with simulations and real data examples. Supplementary materials for this article are available online.