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Prediction Accuracy Measures for a Nonlinear Model and for Right-Censored Time-to-Event Data, By Gang Li, Professor of Biostatistics, Department of Biostatistics, UCLA School of Public Health
April 10, 2020 @ 11:30 am - 12:30 pm
In this talk I will discuss a pair of new prediction summary measures for a nonlinear prediction function with right-censored time-to-event data. The first measure, defined as the proportion of explained variance by a linearly corrected prediction function, quantifies the potential predictive power of the nonlinear prediction function. The second measure, defined as the proportion of explained prediction error by its corrected prediction function, gauges the closeness of the prediction function to its corrected version and serves as a supplementary measure to indicate (by a value less than 1) whether the correction is needed to fulfill its potential predictive power and quantify how much prediction error reduction can be realized with the correction. The two measures together provide a complete summary of the predictive accuracy of the nonlinear prediction function. We motivate these measures by first establishing a variance decomposition and a prediction error decomposition at the population level and then deriving uncensored and censored sample versions of these decompositions. We note that for the least square prediction function under the linear model with no censoring, the first measure reduces to the classical coefficient of determination and the second measure degenerates to 1. We show that the sample measures are consistent estimators of their population counterparts and conduct extensive simulations to investigate their finite sample properties. An R package, PAmeasures, is available to implement these measures for various nonlinear models and survival models. Real data illustrations will be presented.