Abstract
In majority of clinical studies, the patients are monitored for a longer period of time, during which many tests and examinations are gradually repeated. This creates a longitudinal dataset of diverse biomedical markers.
Consider, for example, the well known PBC (primary biliary cholangitis) dataset gathered by the Mayo Clinic between 1974 and 1984. Data for this randomized placebo controlled trial of the drug D-penicillamine contain precise concentration values of albumin, bilirubin, etc. in a blood sample.
Moreover, several binary indicators (presence of hepatomegaly, etc.), ordinal outcomes (seriousness of edema) or even count variables (platelet count) are also recorded. As the time progresses, each of these closely related markers evolves in relation with the overall health of the patient.
Our task is to identify groups of patients that share the same evolution pattern in order to construct a classification rule for newly observed patients. First, we restrict ourselves to the patients still alive and followed after 2.5 years of the study (n = 260) to imitate a real situation when data from several time points are already available, while the survival itself remains unknown and a prognosis for each patient is yet to be assessed.
Generalized linear mixed-effects models (GLMM) of suitable families for diverse markers of interest are joined together through joint distribution of random effects to address and capture possible relationships among the markers. Viewed in a Bayesian setting, we elegantly overcome the problem of unobserved group allocations, latent parameters and missing data by adopting model-based clustering (MBC) and Bayesian data augmentation (BDA) principles.
Carefully constructed Markov chain enhances removal of redundant groups to identify the apriori unknown number of groups. Finally, the patients are divided into the two discovered groups of contrasting patterns, which also differ in the survival potential as the data past 2.5 years suggest.
Hence, a prognosis for a newly observed patient can be established by classification into one of the discovered groups.