Joint functional mapping of quantitative trait loci for HIV-1 and CD4⁺ dynamics

Plasma HIV-1 RNA levels and CD4+ T cell counts in patients are associated with their progression rates to AIDS. After initiation of highly active antiretroviral therapy, these two variables display time-dependent dynamic changes with particular patterns well described by mathematical functions. In this article, we present a unifying statistical model for simultaneously characterizing specific quantitative trait loci in hosts that govern two different dynamic processes of HIV-1 loads and CD4+ T cell counts. The proposed model integrates clinically meaningful mathematical equations into a general framework for functional mapping of dynamic traits based on single nucleotide polymorphisms genotyped from candidate genes or the entire human genome. An EM-simplex hybrid algorithm was derived to estimate the frequencies of QTL alleles and marker-QTL linkage disequilibria with the EM closed form as well as dynamic genetic effects of QTL specified by curve parameters and the parameters modeling the covariance structure. The new model allows for the formulation of various hypothesis tests to explore how a QTL pleiotropically affects HIV-1 and CD4+ dynamics and what is the relative contribution of pleiotropic effects and close association to the correlations between these two processes. The usefulness of the proposed model is demonstrated by the statistical analysis of real data containing longitudinal HIV-1 and CD4+ dynamics, and its statistical properties are examined through simulation studies. Finally, the extensions of the model and their clinical implications are discussed.