Application of an adjusted χ2 statistic to site-specific data in observational dental studies

Background: When a binary response is observed on teeth from each subject belonging to 2 or more exposure groups, application of the usual Pearson chi(2) 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 chi(2) 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. Method: We investigate the conditions under which the adjusted chi(2) statistic is valid and examine the performance of the adjusted chi(2) statistic when these conditions are violated. Results: Our simulation study shows that the adjusted chi(2) 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). Conclusion: The discussion is illustrated using an observational study of caries on the roots of teeth.