Is reduction of pocket probing depth correlated with the baseline value or is it "mathematical coupling"?

Previous studies using correlation or regression analysis have showed that treatment effects measured by the change in clinical parameters are often associated with baseline values of the same parameters. These studies, however, have a methodological weakness. Correlation/regression between baseline measures and the derived change variable invalidates the statistical procedures of testing the null hypothesis: that the coefficient of correlation/regression is zero. This is due to the phenomenon of mathematical coupling. To investigate the impact that this has on the observed correlation/regression coefficient when in reality this is zero, we used random simulations of hypothetical data to model the treatment of periodontal pockets. Results showed a strong probability of obtaining statistically significant correlation/regression coefficients. To separate this artificial effect of mathematical coupling from the true underlying biological relationship, one must apply appropriate analytical strategies to re-evaluate previous evidence within the periodontal literature.