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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