A structural equation modelling approach to the analysis of change.

Analysis of change is probably the most commonly adopted study design in medical and dental research when comparing the efficacy of two or more treatment modalities. The most commonly used methods for testing the difference in treatment efficacy are the two-sample t-test and the analysis of covariance (ANCOVA). It has been suggested that ancova should be used in the analysis of change for data from randomized controlled trials (RCTs) as a result of its greater statistical power. However, it is less well known that although both methods will give rise to similar results in the analysis of change for RCTs, there are different assumptions behind these methods in terms of the relationship between baseline value and the subsequent change, and the results may therefore differ if baseline values are not balanced between groups. This article uses structural equation modelling as a conceptual framework to explain the assumptions behind these methods, and two examples are used to show when the two methods yield similar results and why, in some non-randomized studies, the two methods might give substantially different results, known as 'Lord's paradox' in the statistical literature. For the appropriate interpretation of non-randomized studies, the assumptions underlying these methods therefore need to be taken into consideration.