Application of a joint multivariate probit model for mixed outcomes of CD4 cell count and tuberculosis using a Bayesian latent variable approach in KwaZulu-Natal

HIV and tuberculosis (TB) remain closely linked public health threats in sub-Saharan Africa, with South Africa bearing the highest burden of both diseases. In KwaZulu-Natal, where HIV prevalence peaks among individuals aged 15–49, HIV-induced immunosuppression significantly increases TB risk. Despite their biological interplay, HIV and TB are often analysed separately. This study jointly modelled CD4 cell count and TB diagnosis using a Bayesian latent variable approach to examine their interdependence among HIV-positive individuals. Data were drawn from 7,776 HIV-positive individuals aged 15–49 participating in two population-based cross-sectional surveys (2014–2016) under the HIPSS project. A Bayesian multivariate latent variable model jointly estimated CD4 cell count (continuous) and TB diagnosis (binary) using a probit link. Model fitting was conducted in R using the brms package with Hamiltonian Monte Carlo sampling. The analysis revealed a moderate negative correlation (−0.38) between predicted CD4 cell counts and TB probabilities, supporting the inverse biological relationship between immune suppression and TB risk. Antiretroviral therapy (ARV) use was significantly associated with improved immune status and reduced TB risk. Other key factors, such as male sex, lower educational attainment, and high viral load, were linked to both increased TB susceptibility and lower CD4 cell counts. These findings demonstrate the utility of joint Bayesian modelling in capturing the interdependence of comorbid outcomes and highlight the clinical and policy relevance of integrated HIV–TB programming. They support targeted screening, early treatment initiation, and resource prioritisation for at-risk populations in high-burden settings like KwaZulu-Natal.