Fridge: Focused fine‐tuning of ridge regression for personalized predictions

摘要

Statistical prediction methods typically require some form of finetuning of tuning parameter(s), withK fold crossvalidation as the canonical procedure. For ridge regression, there exist numerous procedures, but common for all, including crossvalidation, is that one single parameter is chosen for all future predictions. We propose instead to calculate a unique tuning parameter for each individual for which we wish to predict an outcome. This generates an individualized prediction by focusing on the vector of covariates of a specific individual. The focused ridgefridgeprocedure is introduced with a 2part contribution: First we define an oracle tuning parameter minimizing the mean squared prediction error of a specific covariate vector, and then we propose to estimate this tuning parameter by using plugin estimates of the regression coefficients and error variance parameter. The procedure is extended to logistic ridge regression by using parametric bootstrap. For highdimensional data, we propose to use ridge regression with crossvalidation as the plugin estimate, and simulations show that fridge gives smaller average prediction error than ridge with crossvalidation for both simulated and real data. We illustrate the new concept for both linear and logistic regression models in 2 applications of personalized medicine: predicting individual risk and treatment response based on gene expression data. The method is implemented in the R packagefridge .