A comparison of group prediction approaches in longitudinal discriminant analysis

Longitudinal discriminant analysis (LoDA) can be used to classify patients into prognostic groups based on their clinical history, which often involves longitudinal measurements of various clinically relevant markers. Patients' longitudinal data is first modelled using multivariate generalised linear mixed models, allowing markers of different types (e.g. continuous, binary, counts) to be modelled simultaneously. We describe three approaches to calculating a patient's posterior group membership probabilities which have been outlined in previous studies, based on the marginal distribution of the longitudinal markers, conditional distribution and distribution of the random effects. Here we compare the three approaches, first using data from the Mayo Primary Biliary Cirrhosis study and then by way of simulation study to explore in which situations each of the three approaches is expected to give the best prediction. We demonstrate situations in which the marginal or random-effects approach perform well, but find that the conditional approach offers little extra information to the random-effects and marginal approaches.