Concepts for the construction of confidence intervals for measuring stability after hallux vulgus surgery: theoretical development and application.

Abstract

The absolute change in the corrected angle measured immediately after surgery and after bone healing is a clinically relevant endpoint to judge an osteotomy's stability. The primary objective of this research is to illustrate the non-inferiority of a novel screw used for fixation of the osteotomy compared with a standard screw. If the difference in the angles after surgery and after bone healing can be assumed to be normally distributed, the absolute change follows the folded normal distribution. The most natural approach to present the clinical study results is using a confidence interval to compare two folded normal distributions. We construct a confidence interval to compare two independent folded normal distributions using the ratio of two chi-square random variables, the difference of two chi-square distribution, and the bootstrap method. We illustrate the approaches from a study on hallux valgus osteotomy. The proposed confidence intervals permit an investigation of the noninferiority for the two treatment groups in clinical trials with end points following a folded normal distribution. The application to real data results indicates that the confidence interval for the ratio of two chi-squares random variable and bootstrap is straightforward and easy to calculate. Bootstrapping was asymptotically more accurate than the standard interval obtained from samples that assume normality. Also, it was an appropriate way to ascertain the stability of the results. Judging by δ of the bootstrap method, we establish non-inferiority for the new surgical method. In conclusion, the approaches are promising, and we recommend them for use to compare other practical data that require the use of the folded normal distribution.