Additive quantile mixed effects modelling with application to longitudinal CD4 count data

Abstract

Quantile regression offers an invaluable tool to discern effects that would be missed by other conventional regression models, which are solely based on modeling conditional mean. Quantile regression for mixed-effects models has become practical for longitudinal data analysis due to the recent computational advances and the ready availability of efficient linear programming algorithms. Recently, quantile regression has also been extended to additive mixed-effects models, providing an efficient and flexible framework for nonparametric as well as parametric longitudinal forms of data analysis focused on features of the outcome beyond its central tendency. This study applies the additive quantile mixed model to analyze the longitudinal CD4 count of HIV-infected patients enrolled in a follow-up study at the Centre of the AIDS Programme of Research in South Africa. The objective of the study is to justify how the procedure developed can obtain robust nonlinear and linear effects at different conditional distribution locations. With respect to time and baseline BMI effect, the study shows a significant nonlinear effect on CD4 count across all fitted quantiles. Furthermore, across all fitted quantiles, the effect of the parametric covariates of baseline viral load, place of residence, and the number of sexual partners was found to be major significant factors on the progression of patients’ CD4 count who had been initiated on the Highly Active Antiretroviral Therapy study.