University of California, Los Angeles
The R-squared statistic, or coefficient of determination, is commonly used to measure the predictive power of a linear model. It is interpreted as the fraction of variation in the response explained by the predictors. Despite its popularity, a direct equivalent measure is not available for nonlinear regression models and for right-censored time-to-event data. In this talk, I will show that in addition to a measure of explained variation, another measure of explained prediction error is required to assess the predictive power of a nonlinear model. The measures are well defined even for a mis-specified model. I will discuss how to extend these measures to right censored time-to-event data and illustrate the methodology using simulated and real data examples.