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Article
Bayesian analysis for a single 2 x 2 table
Quantitative Health Sciences Publications and Presentations
  • Lobat Hashemi
  • Balgobin Nandram, Worcester Polytechnic Institute
  • Robert J. Goldberg, University of Massachusetts Medical School
UMMS Affiliation
Department of Medicine, Division of Cardiovascular Medicine
Date
6-30-1997
Document Type
Article
Medical Subject Headings
Adult; Aged; *Bayes Theorem; *Binomial Distribution; *Epidemiologic Methods; Female; Health Services Research; Humans; Male; Massachusetts; Middle Aged; Models, Statistical; Myocardial Infarction; Odds Ratio; Risk; Sex Factors; Survival Analysis
Abstract

The simple comparison of two binomial populations is frequently of interest in epidemiology when the domains are large. For small domains, however, there are no exact methods except Fisher's exact test. A basic problem, therefore, is to compare two populations by assessing the difference between the proportions of individuals who possess a characteristic in the first and second populations. When there is prior information, we take the proportions to have independent conjugate beta distributions with known parameters, thereby facilitating a Bayesian analysis. We consider Bayesian inference on functions of the proportions, and the three most common scalar measures used in epidemiology and health services research, namely relative risk, odds ratio and attributable risk. We develop the highest density regions (both exact and approximate) for relative risk, odds ratio and attributable risk. In addition, we consider the Bayes factor for testing whether the model with a common proportion holds rather than one with distinct proportions. Using data from the population-based Worcester Heart Attack Study, we apply our methodology to study gender differences in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics. The Bayes factor, the approximate and exact intervals generally suggest that there are no substantial differences in the pharmacologic management of males and females hospitalized with AMI.

Rights and Permissions
Citation: Stat Med. 1997 Jun 30;16(12):1311-28.
Related Resources
Link to Article in PubMed
Citation Information
Lobat Hashemi, Balgobin Nandram and Robert J. Goldberg. "Bayesian analysis for a single 2 x 2 table" Vol. 16 Iss. 12 (1997) ISSN: 0277-6715 (Linking)
Available at: http://works.bepress.com/robert_goldberg/15/