A note on interval estimation of the relative difference in data with matched pairs

Area of Science:

• Biostatistics
• Statistical Inference
• Comparative Studies

Background:

• Controlled comparative trials with matched pairs are crucial for evaluating treatment effects.
• Existing asymptotic interval estimators for relative difference may require improvement, especially for smaller sample sizes.

Purpose of the Study:

• To develop and evaluate new asymptotic closed-form interval estimators for the relative difference in matched pair studies.
• To compare the performance of novel estimators against an existing one using Monte Carlo simulations.

Main Methods:

• Development of two new asymptotic interval estimators: one using logarithmic transformation, another based on Fieller's theorem.
• Monte Carlo simulation to assess coverage probability and average interval length of the three estimators.
• Comparison across different sample sizes, including small (n=20) and large (n>=100) numbers of pairs.

Main Results:

• The logarithmic transformation interval estimator performs well even with small sample sizes (n=20), outperforming others in coverage probability and interval length.
• For large sample sizes (n>=100), all three considered asymptotic interval estimators are deemed appropriate and perform similarly.
• The proposed logarithmic transformation estimator offers a robust alternative, particularly when sample sizes are limited.

Conclusions:

• The asymptotic interval estimator utilizing logarithmic transformation is recommended for controlled comparative trials with matched pairs, especially when dealing with smaller sample sizes.
• For larger sample sizes, the choice of estimator among the three considered has minimal impact on study outcomes.
• These findings contribute to more reliable statistical inference in comparative studies involving matched pairs.