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      A comparison of two methods for estimating prevalence ratios

      research-article
      1 , , 1 , 2
      BMC Medical Research Methodology
      BioMed Central

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          Abstract

          Background

          It is usually preferable to model and estimate prevalence ratios instead of odds ratios in cross-sectional studies when diseases or injuries are not rare. Problems with existing methods of modeling prevalence ratios include lack of convergence, overestimated standard errors, and extrapolation of simple univariate formulas to multivariable models. We compare two of the newer methods using simulated data and real data from SAS online examples.

          Methods

          The Robust Poisson method, which uses the Poisson distribution and a sandwich variance estimator, is compared to the log-binomial method, which uses the binomial distribution to obtain maximum likelihood estimates, using computer simulations and real data.

          Results

          For very high prevalences and moderate sample size, the Robust Poisson method yields less biased estimates of the prevalence ratios than the log-binomial method. However, for moderate prevalences and moderate sample size, the log-binomial method yields slightly less biased estimates than the Robust Poisson method. In nearly all cases, the log-binomial method yielded slightly higher power and smaller standard errors than the Robust Poisson method.

          Conclusion

          Although the Robust Poisson often gives reasonable estimates of the prevalence ratio and is very easy to use, the log-binomial method results in less bias in most common situations, and because it fits the correct model and obtains maximum likelihood estimates, it generally results in slightly higher power, smaller standard errors, and, unlike the Robust Poisson, it always yields estimated prevalences between zero and one.

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          Most cited references24

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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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            Regression models for prognostic prediction: advantages, problems, and suggested solutions.

            Multiple regression models have wide applicability in predicting the outcome of patients with a variety of diseases. However, many researchers are using such models without validating the necessary assumptions. All too frequently, researchers also "overfit" the data by developing models using too many predictor variables and insufficient sample sizes. Models developed in this way are unlikely to stand the test of validation on a separate patient sample. Without attempting such a validation, the researcher remains unaware that overfitting has occurred. When the ratio of the number of patients suffering endpoints to the number of potential predictors is small (say less than 10), data reduction methods are available that can greatly improve the performance of regression models. Regression models can make more accurate predictions than other methods such as stratification and recursive partitioning, when model assumptions are thoroughly examined; steps are taken (ie, choosing another model or transforming the data) when assumptions are violated; and the method of model formulation does not result in overfitting the data.
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              Odds ratio or relative risk for cross-sectional data?

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                Author and article information

                Journal
                BMC Med Res Methodol
                BMC Medical Research Methodology
                BioMed Central
                1471-2288
                2008
                28 February 2008
                : 8
                : 9
                Affiliations
                [1 ]Division of Surveillance, Hazard Evaluations, and Field Studies, National Institute for Occupational Safety and Health, Mail Stop R15 4676 Columbia Parkway Cincinnati, OH 45226, USA
                [2 ]Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio, USA
                Article
                1471-2288-8-9
                10.1186/1471-2288-8-9
                2292207
                18307814
                71114afb-ca46-487a-862f-424b2891f237
                Copyright © 2008 Petersen and Deddens; licensee BioMed Central Ltd.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 21 September 2007
                : 28 February 2008
                Categories
                Research Article

                Medicine
                Medicine

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