Apnea-hypopnea index as the outcome variable in multiple linear regression analysis: Statistical issues

Background: It is common for apnea-hypopnea index (AHI) to be used as an outcome variable in ordinary least squares linear regression. However, the distribution of AHI is not tested. The assumption of ordinary least squares linear regression may be violated. Methods: The distribution of AHI from a pediatric sleep laboratory was assessed by Kolomgorov-Smirnov test. Transformation of AHI was attempted. In addition, we fitted an ordinary linear regression model (OLSM) and negative binomial regression model (NBRM) of the relationship between body mass index and the rate of apnea and hypopnea events. OLSM and NBRM were evaluated by residuals analysis. Results: AHI from the studied population deviated significantly from normal distribution. Commonly used transformation algorithm could not transform AHI to normal distribution. In addition, OLSM violated the underlying statistical assumptions of homogeneity of variance and normality of error. NBRM, on the other hand, was not restricted by these assumptions. Conclusion: The current study suggested AHI is not likely to be normally distributed and its distribution cannot be transformed to normal. Negative binomial regression of the total number of apnea and hypopnea with an offset of log TST should be used in data analysis.