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. 2009 Jul 27:9:56.
doi: 10.1186/1471-2288-9-56.

Bias in odds ratios by logistic regression modelling and sample size

Szilard Nemes  1 , Junmei Miao Jonasson, Anna Genell, Gunnar Steineck
Affiliations

Bias in odds ratios by logistic regression modelling and sample size

Szilard Nemes et al. BMC Med Res Methodol. .

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.

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Figures

Figure 1
Figure 1
Coefficient estimates and its sample size dependent systematic bias in logistic regression estimates. The deviance from the true population value (2 respectively -0.9 in this case) represents the analytically induced bias in regression estimates.
Figure 2
Figure 2
Sampling distribution of logistic regression coefficient estimates at different sample sizes.
Figure 3
Figure 3
Increasing sample size not only reduces the analytically induced bias in regression estimates but protects against extreme value estimates.
See this image and copyright information in PMC

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