The problem of analysing the relationship between change and initial value in oral health research

The relationship between initial disease status and subsequent change following treatment has attracted great interest in dental research. However, medical statisticians have repeatedly warned against correlating/regressing change with baseline because of two methodological concerns known as mathematical coupling and regression to the mean. In general, mathematical coupling occurs when one variable directly or indirectly contains the whole or part of another, and the two variables are then analyzed by using correlation or regression. Consequently, the statistical procedure of testing the null hypothesis - that the coefficient of correlation or the slope of regression is zero - may become inappropriate. Regression to the mean occurs with any variable that fluctuates within an individual or a population, either owing to measurement error and/or to physiological variation. The aim of this article was to clarify the conceptual confusion around mathematical coupling and regression to the mean within the statistical literature, and to correct a popular misconception about the correct analysis of the relationship between change and initial value. As examples that use inappropriate methods to analyze the relationship between change and baseline are still found in leading dental journals, this article seeks to help oral health researchers understand these problems and explain how to overcome them.