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The quantile probability model


Heyard, Rachel; Held, Leonhard (2019). The quantile probability model. Computational Statistics & Data Analysis, 132:84-99.

Abstract

There is now a large literature on optimal predictive model selection. Bayesian methodology based on the -prior has been developed for the linear model where the median probability model (MPM) has certain optimality features. However, it is unclear if these properties also hold in the generalised linear model (GLM) framework, frequently used in clinical prediction models. In an application to the GUSTO-I trial based on logistic regression where the goal was the development of a clinical prediction model for 30-day mortality, sensitivity of the MPM with respect to commonly used prior choices on the model space and the regression coefficients was encountered. This makes a decision on a final model difficult. Therefore an extension of the MPM has been developed, the quantile probability model (QPM), that uses posterior inclusion probabilities to define a drastically reduced set of candidate models. Predictive model selection criteria are then applied to identify the model with best predictive performance. In the application the QPM turns out to be independent of the prior choices considered and gives better predictive performance than the MPM. In addition, a novel batching method is presented to efficiently estimate the Monte Carlo standard error of the predictive model selection criterion.

Abstract

There is now a large literature on optimal predictive model selection. Bayesian methodology based on the -prior has been developed for the linear model where the median probability model (MPM) has certain optimality features. However, it is unclear if these properties also hold in the generalised linear model (GLM) framework, frequently used in clinical prediction models. In an application to the GUSTO-I trial based on logistic regression where the goal was the development of a clinical prediction model for 30-day mortality, sensitivity of the MPM with respect to commonly used prior choices on the model space and the regression coefficients was encountered. This makes a decision on a final model difficult. Therefore an extension of the MPM has been developed, the quantile probability model (QPM), that uses posterior inclusion probabilities to define a drastically reduced set of candidate models. Predictive model selection criteria are then applied to identify the model with best predictive performance. In the application the QPM turns out to be independent of the prior choices considered and gives better predictive performance than the MPM. In addition, a novel batching method is presented to efficiently estimate the Monte Carlo standard error of the predictive model selection criterion.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Uncontrolled Keywords:Statistics and Probability, Computational Theory and Mathematics, Applied Mathematics, Computational Mathematics
Language:English
Date:1 April 2019
Deposited On:14 Mar 2019 17:37
Last Modified:17 Sep 2019 20:07
Publisher:Elsevier
ISSN:0167-9473
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.csda.2018.08.022

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Embargo till: 2021-04-01