Estimation of log-odds ratio from group testing data using Firth correction

Area of Science:

• Biostatistics
• Epidemiology
• Medical Statistics

Background:

• Estimating disease prevalence and group-specific log-odds ratios is crucial for public health.
• Group testing offers a cost-effective approach for disease surveillance, especially for rare conditions.
• Standard estimation methods can be biased, particularly in low-prevalence scenarios.

Purpose of the Study:

• To evaluate methods for estimating rare disease prevalence and log-odds ratios using group testing data.
• To assess the impact of Firth correction on the bias of log-odds ratio estimators.
• To compare the precision of group testing versus individual testing for log-odds ratio estimation with imperfect diagnostic tests.

Main Methods:

• Utilized maximum likelihood estimation for log-odds ratio estimation from group testing data.
• Applied Firth correction to the score function to mitigate bias in estimators.
• Simulated scenarios with low disease prevalence and imperfect diagnostic tests.

Main Results:

• Maximum likelihood estimates of the log-odds ratio are severely biased for low-prevalence diseases.
• Firth correction significantly improves the accuracy of the log-odds ratio estimator.
• Group testing provides more precise log-odds ratio estimates than individual testing when diagnostic tests are imperfect.

Conclusions:

• Firth correction is a valuable technique for reducing bias in log-odds ratio estimation from group testing data, especially for rare diseases.
• Group testing, even with imperfect diagnostics, can be more efficient than individual testing for estimating group differences in disease risk.
• These findings have implications for optimizing surveillance strategies for rare diseases.