Small sample estimation of log odds ratios from logistic regression and fourfold tables

Area of Science:

• Biostatistics
• Statistical Modeling

Background:

• Small sample sizes can introduce bias in logistic regression coefficients.
• Accurate estimation of the log odds ratio is crucial in small sample studies.

Purpose of the Study:

• To compare bias and mean squared error of two log odds ratio estimators in small samples.
• To evaluate Schaefer's bias correction method in logistic regression.

Main Methods:

• Review of various log odds ratio estimators for fourfold tables.
• Complete enumeration of estimator properties in small sample tables.
• Evaluation of bias and mean squared error for two Haldane estimators.

Main Results:

• Schaefer's method aligns with Haldane's earlier result for single dichotomous variables.
• Haldane's estimator (adding 1/2 to all cells) generally shows lower bias and MSE.
• Adding 1/2 only when zero frequency arises is usually not recommended.

Conclusions:

• Haldane's consistent cell adjustment estimator is generally preferred for small sample log odds ratio estimation.
• The choice of estimator may depend on prior knowledge of outcome probabilities.
• Bias correction in logistic regression requires careful consideration of sample size.