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

The absolute change in the angle measured immediately after surgery and after bone healing is a clinically relevant endpoint to judge the stability of an osteotomy. Assuming that the difference in angles is normally distributed, the absolute difference follows a folded normal distribution. The confidence interval (CI) for the absolute angle change of a novel fixation screw compared to a standard fixation screw may be used for evaluating non-inferiority. We suggest that the Welch statistic may serve as the basis for CI calculations of the difference between two folded normals. The coverage probabilities of derived CIs are investigated by simulations. We illustrate the approaches with data from a randomized controlled trial and an observational study on bunion surgery, in which magnesium-based and titanium-based fixation screws were compared. In the simulation studies, asymptotic and both non-parametric and parametric bootstrap CIs based on the Welch statistic were close to nominal coverage levels. In case of different sample sizes between groups, the t-statistic-based CIs were not always meeting the nominal coverage levels. Methods based on chi-square distributions were not deemed appropriate for comparing two folded normals. The re-analysis of the bunion trial permitted the conclusion of non-inferiority for the primary endpoint, the absolute difference between baseline and six months follow-up for the distal metatarsal articular angle, between magnesium-based and titanium-based fixation screws. We recommend the use of CIs based on the Welch statistic to evaluate non-inferiority in trials where the stability of angles after osteotomy is to be compared.