Population-based reversible jump Markov chain Monte Carlo methods for Bayesian variable selection and evaluation under cost limit restrictions

• Published in: Applied statistics Vol. 58; no. 3; pp. 383 - 403
• Main Authors: Fouskakis, D., Ntzoufras, I., Draper, D.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.07.2009; Blackwell Publishing Ltd; Blackwell Publishing; Wiley-Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series C
• Subjects: Accuracy; Algorithms; Applications; Bayesian analysis; Bayesian model comparison; Clinical outcomes; Cost benefit analysis; Cost restriction-benefit analysis; Data collection; Distribution theory; Estimation; Exact sciences and technology; Feature selection; Health care delivery; Health care evaluation; Health care expenditures; Health expenditure; Hospital admissions; Hospital management; Hospitals; Markov analysis; Markov chains; Markov processes; Markovian processes; Mathematics; Medical records; Medical sciences; Modeling; Monte Carlo simulation; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric models; Patients; Pneumonia; Population; Population-based Markov chain Monte Carlo algorithms; Predictive modeling; Probabilities; Probability and statistics; Probability theory and stochastic processes; Quality of care; R&D; Research & development; Restrictions; Reversible jump Markov chain Monte Carlo methods; Sciences and techniques of general use; Simulated tempering; Statistical methods; Statistics; Studies; Total costs; Variable costs; Variables; Biometrics; Rank statistic; Statistical distribution; Error estimation; Bayesian model comparison; Median; Probability distribution; Population-based Markov chain Monte Carlo algorithms; Stochastic method; Convergence; Markov chain; Parametric method; Health care evaluation; Medical science; Cost restriction―benefit analysis; Reversible jump; Marginal distribution; Selection method; Approximation theory; Sampling; Posterior distribution; Variable selection; Bayes estimation; Monte Carlo method; Factor model; Reversible jump Markov chain Monte Carlo methods; Simulated tempering; Care; Search algorithm; Case study; Statistical method; Selection problem; Numerical analysis; Posterior probability; Quality control; Environment; Application
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/j.1467-9876.2008.00658.x

The measurement and improvement of the quality of health care are important areas of current research and development. A judgement of appropriateness of medical outcomes in hospital quality-of-care studies must depend on an assessment of patient sickness at admission to hospital. Indicators of patient sickness often must be abstracted from medical records, and some variables are more expensive to measure than others. Quality-of-care studies are frequently undertaken in an environment of cost restriction; thus any scale measuring patient sickness must simultaneously respect two optimality criteria: high predictive accuracy and low cost. Here we examine a variable selection strategy for construction of a scale of sickness in which predictive accuracy is optimized subject to a bound on cost. Conventional model search algorithms (such as those based on standard reversible jump Markov chain Monte Carlo (RJMCMC) sampling) in our setting will often fail, because of the existence of multiple modes of the criterion function with movement paths that are forbidden because of the cost restriction. We develop a population-based trans-dimensional RJMCMC (population RJMCMC) algorithm, in which ideas from the population-based MCMC and simulated tempering algorithms are combined. Comparing our method with standard RJMCMC sampling, we find that the population-based RJMCMC algorithm moves successfully and more efficiently between distant neighbourhoods of 'good' models, achieves convergence faster and has smaller Monte Carlo standard errors for a given amount of central processor unit time. In a case-study of n=2532 pneumonia patients on whom p=83 sickness indicators were measured, with marginal costs varying from smallest to largest across the predictor variables by a factor of 20, the final model chosen by population RJMCMC sampling, on the basis of both highest posterior probability and specifying the median probability model, was clinically sensible for pneumonia patients and achieved good predictive ability while capping data collection costs.