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

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Summary

This study introduces a new method using Welch statistics for confidence intervals to assess osteotomy stability after surgery. This approach confirmed non-inferiority for magnesium screws compared to titanium screws in bunion surgery.

Keywords:
Welch statisticdistal metatarsal articular anglehallux valgusmagnesium‐based implantnon‐inferiority

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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.