The statistical analysis of multiple binary measurements

Epidemiologic studies often compare several groups of subjects for the presence or absence of a specified biological trait, where each subject in a group contributes two or more observations to the analysis. Examples occur in ophthalmologic studies, where each subject contributes observations on each of two eyes, and dental studies, where observations on each of several teeth may be contributed. Application of the standard Pearson chi-square test to such data is not valid, since the resulting sample observations are not statistically independent. In this paper we show how simple adjustments can be made to the Pearson chi-square statistic that adjust for the within-subject clustering. Application to other types of investigations involving clustered data is also discussed.