Parametric Bayesian modelling of tuberculosis mortality determinants and facility level heterogeneity effect using...

In a normal regression analysis for determinants of tuberculosis (TB) outcomes, assumptions that the sample is homogenous are made. However, the model does not account for the overall effect of unobserved or unmeasured covariates. Frailty may exacerbate the effects of TB on patients and raise their risk of death in Lesotho. This study aims to quantify the amount of heterogeneity that exists at the facility level, and to ascertain the determinants of TB mortality across all the catchment areas in Lesotho.

This was a retrospective cohort of patients on TB treatment registered from January 2015 to December 2020 at twelve (12) health care facilities in the district of Butha Buthe, Lesotho. Data were collected from patient's medical records and analyzed using R and Integrated Nested Laplace Approximation (INLA). Descriptive statistics were presented using frequency tables. Differences between binary outcomes were analyzed using Pearson's X² test. Mixed effect model with five Bayesian regression models of varying distributions were used to assess heterogeneity at facility level. We reported results using the log-logistic regression model with a Gamma frailty term. Kaplan-Meier curves were used to demonstrate time-to-death events.

The total number of patients included in the analysis were 1729 of which 70% were males, and about half of them were employed (54.2%). Being over 60 years (HR: 0.14, Cl: 0.02-0.94) 20-59 years (HR: 0.07, Cl: 0.01-0.41), and TB category 2 (HR 0.27, Cl 0.09-0.80) decreased the risk of dying. Miners had an increased risk of dying from TB (HR:4.13, Cl: 1.05 - 16.43). Assessing heterogeneity by varying the frailty distribution revealed interesting results. For instance, specifying frailty variance structure to follow gamma distribution resulted in estimating minimal 1.01 heterogeneity between catchment areas. The heterogeneity estimated by specifying the Gaussian distribution for the frailty term resulted in nearly 4.5 times more likely to have increased the risk of dying.

The results from both Gamma and Gaussian demonstrate that heterogeneity affected significance of the determinants for TB mortality. The results showed that facility level was significantly likely to increase the risk of dying, indicating differences between catchment areas.