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Open Access Highly Accessed Research article

Bias in odds ratios by logistic regression modelling and sample size

Szilard Nemes1*, Junmei Miao Jonasson1, Anna Genell1 and Gunnar Steineck12

Author Affiliations

1 Division of Clinical Cancer Epidemiology, Department of Oncology, Sahlgrenska Academy, University of Gothenburg, Sweden

2 Division of Clinical Cancer Epidemiology, Department of Oncology and Pathology, Karolinska Institutet, Sweden

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BMC Medical Research Methodology 2009, 9:56  doi:10.1186/1471-2288-9-56

Published: 27 July 2009

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.