Modelling the association between patient characteristics and the change over time in a disease measure using observational cohort data

In observational cohort studies we may wish to examine the associations between fixed patient characteristics and the longitudinal changes from baseline in a repeated outcome measure. Many biological and other outcome measures are known to be subject to measurement error and biological variation. In an initial analysis we may fit a regression model to all outcome measurements, accounting for all the identified sources of variability, and see how the characteristics are linked to the change for typical patients. However, the characteristics may also be linked to different distributions of the underlying outcome value at baseline, which itself may be correlated with the change over time. Therefore, if we wish to examine the change over time for patients of different characteristics but with the same underlying baseline value then the initial approach is confounded by the baseline values. Furthermore, if we attempt to remove this confounding by including the observed baseline measure as a covariate in a model for later measurements, then this may provide an approximate solution but is likely to introduce some bias. We propose a method based on first following the initial approach but then, applying a correction to the parameter estimates. This allows the predicted trajectories to be plotted and valid significance tests of association with characteristics. Our approach is compared with other methods and illustrated through a simulation study and an analysis of the association between HIV-1 subtype and immunological response after starting antiretroviral therapy.