Dataset Information

Bias in odds ratios by logistic regression modelling and sample size.

ABSTRACT:

Background

In epidemiological studies researchers use logistic regression as an analytical tool to study the association of a binary outcome to a set of possible exposures.

Methods

Using a simulation study we illustrate how the analytically derived bias of odds ratios modelling in logistic regression varies as a function of the sample size.

Results

Logistic regression overestimates odds ratios in studies with small to moderate samples size. The small sample size induced bias is a systematic one, bias away from null. Regression coefficient estimates shifts away from zero, odds ratios from one.

Conclusion

If several small studies are pooled without consideration of the bias introduced by the inherent mathematical properties of the logistic regression model, researchers may be mislead to erroneous interpretation of the results.

SUBMITTER: Nemes S

PROVIDER: S-EPMC2724427 | biostudies-literature | 2009 Jul

REPOSITORIES: biostudies-literature

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Publications

Bias in odds ratios by logistic regression modelling and sample size.

Nemes Szilard S Jonasson Junmei Miao JM Genell Anna A Steineck Gunnar G

BMC medical research methodology 20090727

<h4>Background</h4>In epidemiological studies researchers use logistic regression as an analytical tool to study the association of a binary outcome to a set of possible exposures.<h4>Methods</h4>Using a simulation study we illustrate how the analytically derived bias of odds ratios modelling in logistic regression varies as a function of the sample size.<h4>Results</h4>Logistic regression overestimates odds ratios in studies with small to moderate samples size. The small sample size induced bia ...[more]

PMID: 19635144

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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.

Project description:BackgroundConfounding bias is a common concern in epidemiological research. Its presence is often determined by comparing exposure effects between univariable- and multivariable regression models, using an arbitrary threshold of a 10% difference to indicate confounding bias. However, many clinical researchers are not aware that the use of this change-in-estimate criterion may lead to wrong conclusions when applied to logistic regression coefficients. This is due to a statistical phenomenon called noncollapsibility, which manifests itself in logistic regression models. This paper aims to clarify the role of noncollapsibility in logistic regression and to provide guidance in determining the presence of confounding bias.MethodsA Monte Carlo simulation study was designed to uncover patterns of confounding bias and noncollapsibility effects in logistic regression. An empirical data example was used to illustrate the inability of the change-in-estimate criterion to distinguish confounding bias from noncollapsibility effects.ResultsThe simulation study showed that, depending on the sign and magnitude of the confounding bias and the noncollapsibility effect, the difference between the effect estimates from univariable- and multivariable regression models may underestimate or overestimate the magnitude of the confounding bias. Because of the noncollapsibility effect, multivariable regression analysis and inverse probability weighting provided different but valid estimates of the confounder-adjusted exposure effect. In our data example, confounding bias was underestimated by the change in estimate due to the presence of a noncollapsibility effect.ConclusionIn logistic regression, the difference between the univariable- and multivariable effect estimate might not only reflect confounding bias but also a noncollapsibility effect. Ideally, the set of confounders is determined at the study design phase and based on subject matter knowledge. To quantify confounding bias, one could compare the unadjusted exposure effect estimate and the estimate from an inverse probability weighted model.

Dataset Information

Bias in odds ratios by logistic regression modelling and sample size.

Background

Methods

Results

Conclusion

Publications

Bias in odds ratios by logistic regression modelling and sample size.

Similar Datasets

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