Confidence Intervals for Comparing Two Independent Folded Normals: A Case Study in Bunion Surgery

Area of Science:

• Orthopedic surgery
• Biostatistics

Background:

• Osteotomy stability is crucial and assessed by angle changes post-surgery.
• Absolute angle change follows a folded normal distribution.
• Evaluating non-inferiority of fixation screws requires robust statistical methods.

Purpose of the Study:

• To propose Welch statistic-based confidence intervals (CIs) for comparing two folded normal distributions.
• To evaluate the non-inferiority of novel fixation screws against standard ones using these CIs.
• To assess the stability of osteotomies in orthopedic procedures.

Main Methods:

• Simulations were conducted to investigate the coverage probabilities of derived CIs.
• Welch statistic was used as the basis for CI calculations.
• Asymptotic, non-parametric bootstrap, and parametric bootstrap CIs were compared.

Main Results:

• Welch statistic-based CIs demonstrated coverage probabilities close to nominal levels.
• T-statistic-based CIs showed limitations with unequal sample sizes.
• Methods based on chi-square distributions were inappropriate for comparing folded normals.

Conclusions:

• Welch statistic-based CIs are recommended for evaluating non-inferiority in osteotomy stability trials.
• Magnesium-based screws were found to be non-inferior to titanium-based screws in bunion surgery.
• The proposed statistical method provides a reliable approach for clinical endpoint assessment.