https://www.jstage.jst.go.jp/article/jea/33/6/33_JE20210089/_article

PMC

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10165217/

Highlights

• In logistic regression models, bias of the odds ratio is possible when using the maximum likelihood method and few study participants at the outcome and covariate levels. This bias is known as sparse data bias, and the estimated odds ratios show impossibly large values because of data sparsity.

• This study reviews several bias-reducing methods in the logistic regression context and compares the performance of these methods using a simulation study.

• Firth’s method and the exact method do not reduce the sparse data bias sufficiently. The Bayesian methods using log F -type priors and g-prior are the preferred choices when fitting logistic models to sparse data.

• Logistic regression analyses based on the maximum likelihood method should be interpreted with caution when the number of events is fewer than 10 and the proportion of study participants with an exposure of interest is below 0.1.

Selected Result