Blomqvist revisited: how and when to test the relationship between level and longitudinal rate of change

Longitudinal studies are often interested in assessing the relationship between severity (level) and rate of change (slope). Blomqvist describes an estimator of this relationship that has been used in a variety of contexts. This paper reviews and generalizes the Blomqvist method. Most published applications of the Blomqvist method contain substantial bias because they fail to consider and accommodate confounding due to the pooling of multiple age cohorts in a single analysis. We describe this bias, and present an unbiased algorithm consistent with the intentions of Blomqvist. We also explore when it is appropriate to apply the Blomqvist analysis, and what inferences can be made using this statistic. Aetiological inference about premorbid level of function predicting future rate of decline is often desired, but may not be justified when modelling chronic progressive conditions, since differential progression prior to the start of longitudinal follow-up can induce a relationship between level and rate of decline, even in the absence of an aetiologically relevant association. We conclude that aetiological inference by the Blomqvist analysis is not appropriate in most investigations of chronic progressive disease. Using the model to develop descriptive and predictive equations in these circumstances, however, remains appropriate, as does testing simply for clinical heterogeneity in longitudinal rate of decline.