title: Mathematical coupling can undermine the statistical assessment of clinical research: illustration from the treatment of guided tissue regeneration.
abstract: OBJECTIVE
  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 Oldham's 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, Oldham's method is recommended.
authors.affiliation: Department of Periodontology, Leeds Dental Institute, University of Leeds, Clarendon Way, LS2 9LU, Leeds, UK.
authors.forename: Yu-Kang
authors.initials: YK
authors.lastname: Tu
authors.forename: Ian H
authors.initials: IH
authors.lastname: Maddick
authors.forename: Gareth S
authors.initials: GS
authors.lastname: Griffiths
authors.forename: Mark S
authors.initials: MS
authors.lastname: Gilthorpe
mesh_terms: D016301:Alveolar Bone Loss / Q000601:surgery; D002986:Clinical Trials as Topic / Q000379:methods*; D003627:Data Interpretation, Statistical; D018865:Dental Research / Q000379:methods*; D017823:Furcation Defects / Q000601:surgery; D005889:Gingival Recession / Q000601:surgery; D016557:Guided Tissue Regeneration, Periodontal; D006801:Humans; D008433:Mathematics; D017063:Outcome Assessment, Health Care / Q000379:methods*; D017622:Periodontal Attachment Loss / Q000175:diagnosis; D010512:Periodontal Index; D010514:Periodontal Pocket / Q000175:diagnosis; D012044:Regression Analysis; D012107:Research Design