title: Application of an adjusted chi2 statistic to site-specific data in observational dental studies.
abstract: BACKGROUND
  When a binary response is observed on teeth from each subject belonging to 2 or more exposure groups, application of the usual Pearson chi2 tests is invalid, since such responses within the same subject are not independent. Consequently, special statistical methods are needed to control for the correlation among teeth (sites) within the same subject. A simple adjustment to the Pearson chi2 statistic has been proposed for comparing proportions in site-specific data. However, the required assumptions for this statistic have not yet been thoroughly addressed. These assumptions are guaranteed to hold in experimental comparisons, but may be violated in some observational studies.
  
  
  METHODS
  We investigate the conditions under which the adjusted chi2 statistic is valid and examine the performance of the adjusted chi2 statistic when these conditions are violated.
  
  
  RESULTS
  Our simulation study shows that the adjusted chi2 statistic generally produces good empirical type I errors under the assumption of a common intracluster correlation coefficient. Even if the intracluster correlations are different, the adjusted statistic performs well when the groups have equal numbers of clusters (subjects).
  
  
  CONCLUSIONS
  The discussion is illustrated using an observational study of caries on the roots of teeth.
authors.affiliation: Clinical Epidemiology, University of Texas Medical School, Houston, Texas 77030, USA. chul.w.ahn@uth.tmc.edu
authors.forename: Chul
authors.initials: C
authors.lastname: Ahn
authors.forename: Sin-Ho
authors.initials: SH
authors.lastname: Jung
authors.forename: Allan
authors.initials: A
authors.lastname: Donner
mesh_terms: D000704:Analysis of Variance; D016009:Chi-Square Distribution; D016000:Cluster Analysis; D018865:Dental Research / Q000379:methods*; D005260:Female; D006801:Humans; D015994:Incidence; D008297:Male; D015203:Reproducibility of Results; D017213:Root Caries / Q000453:epidemiology; D012744:Sex Ratio