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Health Services Research & Development

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2012 HSR&D/QUERI National Conference Abstract

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2012 National Meeting

3086 — Beta-Binomial Regression for Bimodal Utilization

Liu CF, Northwest Center for Outcomes Research in Older Adults, VA Puget Sound Healthcare System, Seattle; University of Washington; Burgess JF, Center for Organization, Leadership & Management Research, VA Boston Healthcare System; Boston University; Manning WG, University of Chicago; Maciejewski ML, Center for Health Services Research in Primary Care, Durham VA Medical Center; Duke University Medical Center;

VA outpatient care reliance, defined as the proportion of total (VA+Medicare) visits in VA, has a bimodal distribution that is not appropriately modeled using standard methods. The purpose of this paper is to illustrate the application of rarely used beta-binomial regression in a model of patient choice for primary care and specialty care (from VA or Medicare) in which the outcome is bimodal (i.e., U shape), and to contrast the results from ordinary least squares (OLS), binomial, and beta-binomial regressions.

The sample included 15,520 Medicare-eligible VA primary care users in 2000. VA reliance for primary care or specialty care was constructed from VA administrative and Medicare claims data. We compared residual plots, estimated overall reliance, and distribution of VA reliance for primary care and specialty care across three models: OLS, binomial, and beta-binomial regressions for explaining VA reliance.

The residual plots show that the residuals were not normally distributed for the OLS and binomial models, and mean VA reliance does not reflect the two dominant types of VA reliance for a majority of Medicare-eligible in the two extremes of the distribution. As expected, VA primary care from the OLS model was identical to the unadjusted VA reliance across years (0.73 in 2001; 0.69 in 2002; 0.65 in 2003; 0.64 in 2004), because the OLS model estimated mean. On the other hand, the beta-binomial distribution more closely tracked with the U-shape of the unadjusted distribution than the OLS and binomial regressions. Similar results were observed for reliance on VA specialty care.

The beta-binomial regression is the appropriate model to examine VA reliance with a bimodal distribution.

Increased awareness of beta-binomial regression may help analysts conducting regressions on outcomes with bimodal distributions (like VA reliance) avoid misleading results through the use of appropriate methods.

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