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Beta-binomial regression and bimodal utilization.

ABSTRACT: OBJECTIVE: To illustrate how the analysis of bimodal U-shaped distributed utilization can be modeled with beta-binomial regression, which is rarely used in health services research. DATA SOURCES/STUDY SETTING: Veterans Affairs (VA) administrative data and Medicare claims in 2001-2004 for 11,123 Medicare-eligible VA primary care users in 2000. STUDY DESIGN: We compared means and distributions of VA reliance (the proportion of all VA/Medicare primary care visits occurring in VA) predicted from beta-binomial, binomial, and ordinary least-squares (OLS) models. PRINCIPAL FINDINGS: Beta-binomial model fits the bimodal distribution of VA reliance better than binomial and OLS models due to the nondependence on normality and the greater flexibility in shape parameters. CONCLUSIONS: Increased awareness of beta-binomial regression may help analysts apply appropriate methods to outcomes with bimodal or U-shaped distributions.

SUBMITTER: Liu CF

PROVIDER: S-EPMC3796113 | biostudies-literature | 2013 Oct

REPOSITORIES: biostudies-literature

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Beta-binomial regression and bimodal utilization.

Liu Chuan-Fen CF Burgess James F JF Manning Willard G WG Maciejewski Matthew L ML

Health services research 20130323 5

<h4>Objective</h4>To illustrate how the analysis of bimodal U-shaped distributed utilization can be modeled with beta-binomial regression, which is rarely used in health services research.<h4>Data sources/study setting</h4>Veterans Affairs (VA) administrative data and Medicare claims in 2001-2004 for 11,123 Medicare-eligible VA primary care users in 2000.<h4>Study design</h4>We compared means and distributions of VA reliance (the proportion of all VA/Medicare primary care visits occurring in VA) ...[more]

PMID: 23521600

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Project description:Background/aimsThis work is motivated by the HEALing Communities Study, which is a post-test only cluster randomized trial in which communities are randomized to two different trial arms. The primary interest is in reducing opioid overdose fatalities, which will be collected as a count outcome at the community level. Communities range in size from thousands to over one million residents, and fatalities are expected to be rare. Traditional marginal modeling approaches in the cluster randomized trial literature include the use of generalized estimating equations with an exchangeable correlation structure when utilizing subject-level data, or analogously quasi-likelihood based on an over-dispersed binomial variance when utilizing community-level data. These approaches account for and estimate the intra-cluster correlation coefficient, which should be provided in the results from a cluster randomized trial. Alternatively, the coefficient of variation or R coefficient could be reported. In this article, we show that negative binomial regression can also be utilized when communities are large and events are rare. The objectives of this article are (1) to show that the negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model and to explain why the estimates may differ; (2) to derive formulas relating the negative binomial overdispersion parameter k with the intra-cluster correlation coefficient, coefficient of variation, and R coefficient; and (3) analyze pre-intervention data from the HEALing Communities Study to demonstrate and contrast models and to show how to report the intra-cluster correlation coefficient, coefficient of variation, and R coefficient when utilizing negative binomial regression.MethodsNegative binomial and over-dispersed binomial regression modeling are contrasted in terms of model setup, regression parameter estimation, and formulation of the overdispersion parameter. Three specific models are used to illustrate concepts and address the third objective.ResultsThe negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model, although estimates may differ. Practical differences arise in regard to how overdispersion, and hence the intra-cluster correlation coefficient is modeled. The negative binomial overdispersion parameter is approximately equal to the ratio of the intra-cluster correlation coefficient and marginal probability, the square of the coefficient of variation, and the R coefficient minus 1. As a result, estimates corresponding to all four of these different types of overdispersion parameterizations can be reported when utilizing negative binomial regression.ConclusionNegative binomial regression provides a valid, practical, alternative approach to the analysis of count data, and corresponding reporting of overdispersion parameters, from community randomized trials in which communities are large and events are rare.

Project description:BackgroundThe odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR.MethodsWe propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial.ResultsIn simulation studies, confidence intervals for the OR were 56-65% as wide (geometric model), 75-79% as wide (Poisson model), and 61-69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression.ConclusionsMore precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions.

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Beta-binomial regression and bimodal utilization.

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Beta-binomial regression and bimodal utilization.

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