A bivariate multi-level model, which avoids mathematical coupling in the study of change and initial periodontal attachment level after therapy

Abstract

When relating the change of periodontal attachment level to its baseline value, mathematical coupling has to be taken into account. Oldham’s strategy of testing the differences in variances of two repeated measurements was recently advocated as a possible solution. Here, a simple bivariate three-level (site and subject with a lowest level specifying the multivariate structure) model is introduced where gingival units (sites) were nested in subjects. It allows the easy interpretation of the variance–covariance structure and fixed model estimates, and provides an unbiased estimate of the correlation between the mean and change of periodontal measurements. The properties of this model are exemplified using data of a study on the clinical effects of non-surgical periodontal therapy in adults. Based on the covariance terms, correlation between the change in clinical attachment after therapy and the mean of the pre-operative and post-operative attachment level was very low (about −0.11, p < 0.001) at the site level, and not significant at the subject level. Regarding the attachment level, differential treatment effects may be neglected. With regard to periodontal probing depth, however, patients with larger extent and severity would benefit more from treatment. The present communication provides an easy strategy for the avoidance of mathematical coupling in the study between change and initial value by employing a bivariate multi-level model.