Robust modelling of the relationship between CD4 and viral load for complex AIDS data

CD4 and viral load play important roles in HIV/AIDS studies, and the study of their relationship has received much attention with well-known results. However, AIDS datasets are often highly complex in the sense that they typically contain outliers, measurement errors, and missing data. These data complications can greatly affect statistical analysis results, but much of the literature fail to address these issues in data analysis. In this paper, we re-visit the important relationship between CD4 and viral load and propose methods which simultaneously address outliers, measurement errors, and missing data. We find that the strength of the relationship may be severely mis-estimated if measurement errors and outliers are ignored. The proposed methods are general and can be used in other settings, where jointly modelling several different types of longitudinal data is required in the presence of data complications.