An improved estimator of the logarithmic odds ratio for small sample sizes using a Bayesian approach

Area of Science:

• Biostatistics
• Statistical Inference
• Comparative Studies

Background:

• The logarithmic odds ratio is crucial for comparing binary outcomes between two independent groups.
• Existing methods often estimate group proportions first, introducing potential errors before calculating the logarithmic odds ratio.
• Researchers prioritize the logarithmic odds ratio over individual group proportions.

Purpose of the Study:

• To develop a Bayesian estimator that directly estimates the logarithmic odds ratio.
• To overcome limitations of existing methods that rely on estimating intermediate proportions.
• To improve the accuracy of logarithmic odds ratio estimation.

Main Methods:

• A novel Bayesian approach is proposed for direct logarithmic odds ratio estimation.
• This method bypasses the need to estimate individual group proportions.
• The estimator focuses on a single parameter: the logarithmic odds ratio itself.

Main Results:

• The proposed Bayesian estimator directly targets the logarithmic odds ratio.
• By estimating only one parameter, it avoids compounded errors from proportion estimation.
• Numerical calculations and applications demonstrate the validity and potential accuracy of the new estimator.

Conclusions:

• The proposed Bayesian estimator offers a more direct and potentially more accurate method for estimating the logarithmic odds ratio.
• This approach may yield estimates closer to the true population logarithmic odds ratio compared to existing methods.
• The validated estimator provides a valuable tool for analyzing binary data in comparative studies.