Joint modelling of left- and interval-censored viral load for couples in Mozambique

Mathematical and statistical models have been essential tools in exploring the dynamics of viral load measures, understanding of the pathogenesis of HIV-1 infection and in assessment of the potency of antiretroviral therapies. However, this can be challenging due to the potential intra-couple correlation as well as the presence of multiple measurements collected from the same study site or cluster. A second complication arises due to censoring of the individual viral load measurements. The aim of this paper is to investigate the association between age and viral load of woman and man within a couple, while accounting for the presence of antiretroviral biomarkers in blood. An additional question of interest is how weakly or strongly are viral load of woman and man correlated, and how does this correlation depend on covariates as well. Joint marginal and random-effects models assuming constant and non-constant correlation were fitted using maximum likelihood while accounting for the left- and interval-censoring nature of the two viral loads. Findings show a weak positive correlation between the viral loads of women and men. Next, interaction between age and antiretroviral biomarker's presence is only significant in the mean viral load for women, showing that the effect of age on a women's viral load varies by the antiretroviral biomarker's status. No age effect on the mean viral load for men is observed. These findings reinforce the need of interventions that stimulate adherence to antiretroviral therapy treatment once one or both partners are HIV infected as well as to monitor their viral load as they get older, especially the female partner.