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Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio

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      Cross-sectional studies with binary outcomes analyzed by logistic regression are frequent in the epidemiological literature. However, the odds ratio can importantly overestimate the prevalence ratio, the measure of choice in these studies. Also, controlling for confounding is not equivalent for the two measures. In this paper we explore alternatives for modeling data of such studies with techniques that directly estimate the prevalence ratio.


      We compared Cox regression with constant time at risk, Poisson regression and log-binomial regression against the standard Mantel-Haenszel estimators. Models with robust variance estimators in Cox and Poisson regressions and variance corrected by the scale parameter in Poisson regression were also evaluated.


      Three outcomes, from a cross-sectional study carried out in Pelotas, Brazil, with different levels of prevalence were explored: weight-for-age deficit (4%), asthma (31%) and mother in a paid job (52%). Unadjusted Cox/Poisson regression and Poisson regression with scale parameter adjusted by deviance performed worst in terms of interval estimates. Poisson regression with scale parameter adjusted by χ 2 showed variable performance depending on the outcome prevalence. Cox/Poisson regression with robust variance, and log-binomial regression performed equally well when the model was correctly specified.


      Cox or Poisson regression with robust variance and log-binomial regression provide correct estimates and are a better alternative for the analysis of cross-sectional studies with binary outcomes than logistic regression, since the prevalence ratio is more interpretable and easier to communicate to non-specialists than the odds ratio. However, precautions are needed to avoid estimation problems in specific situations.

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      Most cited references 34

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      Covariance analysis of censored survival data.

       N Breslow (1974)
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        Prevalence odds ratio or prevalence ratio in the analysis of cross sectional data: what is to be done?

        To review the appropriateness of the prevalence odds ratio (POR) and the prevalence ratio (PR) as effect measures in the analysis of cross sectional data and to evaluate different models for the multivariate estimation of the PR. A system of linear differential equations corresponding to a dynamic model of a cohort with a chronic disease was developed. At any point in time, a cross sectional analysis of the people then in the cohort provided a prevalence based measure of the effect of exposure on disease. This formed the basis for exploring the relations between the POR, the PR, and the incidence rate ratio (IRR). Examples illustrate relations for various IRRs, prevalences, and differential exodus rates. Multivariate point and interval estimation of the PR by logistic regression is illustrated and compared with the results from proportional hazards regression (PH) and generalised linear modelling (GLM). The POR is difficult to interpret without making restrictive assumptions and the POR and PR may lead to different conclusions with regard to confounding and effect modification. The PR is always conservative relative to the IRR and, if PR > 1, the POR is always > PR. In a fixed cohort and with an adverse exposure, the POR is always > or = IRR, but in a dynamic cohort with sufficient underlying follow up the POR may overestimate or underestimate the IRR, depending on the duration of follow up. Logistic regression models provide point and interval estimates of the PR (and POR) but may be intractable in the presence of many covariates. Proportional hazards and generalised linear models provide statistical methods directed specifically at the PR, but the interval estimation in the case of PH is conservative and the GLM procedure may require constrained estimation. The PR is conservative, consistent, and interpretable relative to the IRR and should be used in preference to the POR. Multivariate estimation of the PR should be executed by means of generalised linear models or, conservatively, by proportional hazards regression.
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          Prevalence proportion ratios: estimation and hypothesis testing.

          Recent communications have argued that often it may not be appropriate to analyse cross-sectional studies of prevalent outcomes with logistic regression models. The purpose of this communication is to compare three methods that have been proposed for application to cross sectional studies: (1) a multiplicative generalized linear model, which we will call the log-binomial model, (2) a method based on logistic regression and robust estimation of standard errors, which we will call the GEE-logistic model, and (3) a Cox regression model. Five sets of simulations representing fourteen separate simulation conditions were used to test the performance of the methods. All three models produced point estimates close to the true parameter, i.e. the estimators of the parameter associated with exposure had negligible bias. The Cox regression produced standard errors that were too large, especially when the prevalence of the disease was high, whereas the log-binomial model and the GEE-logistic model had the correct type I error probabilities. It was shown by example that the GEE-logistic model could produce prevalences greater than one, whereas it was proven that this could not happen with the log-binomial model. The log-binomial model should be preferred.

            Author and article information

            [1 ]Programa de Pós-graduação em Epidemiologia, Universidade Federal de Pelotas, Brazil
            BMC Med Res Methodol
            BMC Medical Research Methodology
            BioMed Central (London )
            20 October 2003
            : 3
            : 21
            Copyright © 2003 Barros and Hirakata; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL.
            Research Article


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