Mathematical coupling can undermine the statistical assessment of clinical research: illustration from the treatment of guided tissue regeneration

Objectives. Previous periodontal literature has shown that there is a strong relationship between treatment effects, such as guided tissue regeneration (GTR), and baseline disease severity. However, relating change to baseline values using correlation or regression is methodologically flawed due to mathematical coupling, where the statistical procedure of testing the null hypothesis—that the coefficient of correlation or slope of regression is equal to zero—becomes erroneous. The aim of this study is to investigate if baseline disease severity is genuinely associated with the treatment outcome of intrabony defects using GTR after adjustment for mathematical coupling. In particular, we seek to demonstrate the potential effect that mathematical coupling has in distorting the results from the statistical analyses of trials of dental treatment, using data from the periodontal literature on GTR. The erroneous results arising from the use of simple correlation and regression techniques to analyse this association will be demonstrated, also the methodological flaw where the statistical procedure tests the null hypothesis—that the coefficient of correlation or the slope of regression is equal to zero. Methods. Three main periodontal journals were electronically and manually searched to extract the data for the clinical outcomes of pocket probing depth (PPD) and lifetime cumulative attachment loss (LCAL) in the studies using GTR. The relationship between clinical outcomes and baseline measurements were reanalysed using Oldhamʹs method and the variance ratio test. Results. The results of these analyses were compared with those from the papers where the authors used the standard approach of correlation or regression. This shows that mathematical coupling caused spurious correlations between baseline disease severity and treatment effect. Ten out of 12 studies for PPD and nine out of 14 for LCAL initially claimed a significant positive relationship; after using either of the more appropriate statistical methods of adjustment, only three correlations in each group of studies remained significant. Conclusions: Previous evidence suggesting an association between baseline disease severity and treatment effect for GTR is challenged and therefore needs to be critically reviewed. All future clinical research should avoid using mathematically coupled data in correlation or regression analysis. In seeking to examine the bivariate association between baseline and subsequent change, Oldhamʹs method is recommended.