Concepts for the construction of confidence intervals for measuring stability after hallux vulgus surgery: theoretical development and application.
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Date
2021
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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.
Description
Masters Degree. University of KwaZulu-Natal, Pietermaritzburg.