Testing the relation between percentage change and baseline value

Testing the relation between percentage change and baseline value has been controversial, but it is not clear why this practice may yield spurious results. In this paper, we first explained why the usual testing of the relation between percentage change and baseline value is inappropriate and then demonstrated how the appropriate null hypothesis could be formulated. We also proposed a simple procedure for testing the appropriate null hypothesis based on the assumption that when there is no relation between percentage change and baseline value, the coefficients of variation for repeated measurements of a random variable should remain unchanged. Two examples were used to demonstrate how the usual testing gave rise to misleading results, whilst results from our simple test were in general consistent with those from simulations. We also undertook simulations to investigate the impact of measurement errors on the performance of the proposed test. Results suggested the type-I error rates increased with the magnitude of measurement errors, whilst the statistical power to detect a genuine relation decreased. The usual approach to testing the relation between percentage change and baseline value tended to yield misleading results and should be avoided.