Ensemble clustering of longitudinal bivariate HIV biomarker profiles to group patients by patterns of disease progression

This paper describes an ensemble cluster analysis of bivariate profiles of HIV biomarkers, viral load and CD4 cell counts, which jointly measure disease progression. Data are from a prevalent cohort of HIV positive participants in a clinical trial of vitamin supplementation in Botswana. These individuals were HIV positive upon enrollment, but with unknown times of infection. To categorize groups of participants based on their patterns of progression of HIV infection using both biomarkers, we combine univariate shape-based cluster results for multiple biomarkers through the use of ensemble clustering methods. We first describe univariate clustering for each of the individual biomarker profiles, and make use of shape-respecting distances for clustering the longitudinal profile data. In our data, profiles are subject to either missing or irregular measurements as well as unobserved initiation times of the process of interest. Shape-respecting distances that can handle such data issues, preserve time-ordering, and identify similar profile shapes are useful in identifying patterns of disease progression from longitudinal biomarker data. However, their performance with regard to clustering differs by severity of the data issues mentioned above. We provide an empirical investigation of shape-respecting distances (Fréchet and dynamic time warping (DTW)) on benchmark shape data, and use DTW in cluster analysis of biomarker profile observations. These reveal a primary group of ‘typical progressors,’ as well as a smaller group that shows relatively rapid progression. We then refine the analysis using ensemble clustering for both markers to obtain a single classification. The information from joint evaluation of the two biomarkers combined with ensemble clustering reveals subgroups of patients not identifiable through univariate analyses; noteworthy subgroups are those that appear to represent recently and chronically infected subsets.