Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care

Details Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care

2009-08-17

arxiv.org/abs/0908.2313v1

Annals of Applied Statistics 2009, Vol. 3, No. 2, 663-690

Statistics

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Published in at http://dx.doi.org/10.1214/08-AOAS207 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/08-AOAS207

In the field of quality of health care measurement, one approach to assessing patient sickness at admission involves a logistic regression of mortality within 30 days of admission on a fairly large number of sickness indicators (on the order of 100) to construct a sickness scale, employing classical variable selection methods to find an ``optimal'' subset of 10--20 indicators. Such ``benefit-only'' methods ignore the considerable differences among the sickness indicators in cost of data collection, an issue that is crucial when admission sickness is used to drive programs (now implemented or under consideration in several countries, including the U.S. and U.K.) that attempt to identify substandard hospitals by comparing observed and expected mortality rates (given admission sickness). When both data-collection cost and accuracy of prediction of 30-day mortality are considered, a large variable-selection problem arises in which costly variables that do not predict well enough should be omitted from the final scale. In this paper (a) we develop a method for solving this problem based on posterior model odds, arising from a prior distribution that (1) accounts for the cost of each variable and (2) results in a set of posterior model probabilities that corresponds to a generalized cost-adjusted version of the Bayesian information criterion (BIC), and (b) we compare this method with a decision-theoretic cost-benefit approach based on maximizing expected utility. We use reversible-jump Markov chain Monte Carlo (RJMCMC) methods to search the model space, and we check the stability of our findings with two variants of the MCMC model composition ($\mathit{MC}^3$) algorithm.

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