Cumulative viral load as a predictor of CD4+ T-cell response to antiretroviral therapy using Bayesian statistical models

Introduction: There are Challenges in statistically modelling immune responses to longitudinal HIV viral load exposure as a function of covariates. We define Bayesian Markov Chain Monte Carlo mixed effects models to incorporate priors and examine the effect of different distributional assumptions. We prospectively fit these models to an as-yet-unpublished data from the Tshwane District Hospital HIV treatment clinic in South Africa, to determine if cumulative log viral load, an indicator of long-term viral exposure, is a valid predictor of immune response. Methods: Models are defined, to express ‘slope’, i.e. mean annual increase in CD4 counts, and ‘asymptote’, i.e. the odds of having a CD4 count ≥500 cells/μL during antiretroviral treatment, as a function of covariates and random-effects. We compare the effect of using informative versus non-informative prior distributions on model parameters. Models with cubic splines or Skew-normal distributions are also compared using the conditional Deviance Information Criterion. Results: The data of 750 patients are analyzed. Overall, models adjusting for cumulative log viral load provide a significantly better fit than those that do not. An increase in cumulative log viral load is associated with a decrease in CD4 count slope (19.6 cells/μL (95% credible interval: 28.26, 10.93)) and a reduction in the odds of achieving a CD4 counts ≥500 cells/μL (0.42 (95% CI: 0.236, 0.730)) during 5 years of therapy. Using informative priors improves the cumulative log viral load estimate, and a skew-normal distribution for the random-intercept and measurement error results is a better fit compared to using classical Gaussian distributions. Discussion: We demonstrate in an unpublished South African cohort that cumulative log viral load is a strong and significant predictor of both CD4 count slope and asymptote. We argue that Bayesian methods should be used more frequently for such data, given their flexibility to incorporate prior information and non-Gaussian distributions.