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

Fridge: Focused fine‐tuning of ridge regression for personalized predictions Statistical prediction methods typically require some form of fine‐tuning of tuning parameter(s), with K‐fold cross‐validation as the canonical procedure. For ridge regression, there exist numerous procedures, but common for all, including cross‐validation, 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 ridge—fridge—procedure is introduced with a 2‐part 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 plug‐in estimates of the regression coefficients and error variance parameter. The procedure is extended to logistic ridge regression by using parametric bootstrap. For high‐dimensional data, we propose to use ridge regression with cross‐validation as the plug‐in estimate, and simulations show that fridge gives smaller average prediction error than ridge with cross‐validation 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 package fridge. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistics in Medicine Wiley

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

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0277-6715
eISSN
1097-0258
D.O.I.
10.1002/sim.7576
Publisher site
See Article on Publisher Site

Abstract

Statistical prediction methods typically require some form of fine‐tuning of tuning parameter(s), with K‐fold cross‐validation as the canonical procedure. For ridge regression, there exist numerous procedures, but common for all, including cross‐validation, 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 ridge—fridge—procedure is introduced with a 2‐part 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 plug‐in estimates of the regression coefficients and error variance parameter. The procedure is extended to logistic ridge regression by using parametric bootstrap. For high‐dimensional data, we propose to use ridge regression with cross‐validation as the plug‐in estimate, and simulations show that fridge gives smaller average prediction error than ridge with cross‐validation 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 package fridge.

Journal

Statistics in MedicineWiley

Published: Jan 15, 2018

Keywords: ; ; ; ;

References

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