Parametric Bayesian Modelling of Tuberculosis Mortality determinants and Facility level heterogeneity effect using Gamma and Gaussian shared frailty techniques

Background: In a normal regression analysis for determinants of TB outcomes, assumptions that the sample is homogenous is made. This model does not account for the overall effect of unobserved or unmeasured covariates. This study aims to quantify the amount of heterogeneity that exists at community level, and to ascertain the determinants of TB mortality across all the catchment areas in Lesotho. Methods: This was a retrospective record review of patients on TB treatment registered between January 2015 to December 2020 at 12 health care facilities in the district of Butha Buthe, Lesotho. Data collected from patient medical and statistical analysis was performed using R and INLA statistical software. Descriptive statistics were presented using frequency tables. Differences between binary outcomes were analysed using Person's X2 test. Mixed effect model with five Bayesian regression models of varying distributions were used to assess heterogeneity at facility level. Kaplan-Meier curves were used to demonstrate time-to-death events. Results: The total number of patients included in the analysis were 1729 of which 70% were males. And half of them were employed (54.2%). Being over 60 years (HR: 0.02, Cl: 0.01-0.04) and having a community health worker as a treatment contact person (HR: 0.36, Cl: 0.19-0.71) decreased the risk of dying. Miners had 1.73 times increased risk of dying (HR: 1.73, Cl: 1.07-2.78). The frailty variance was observed to be very minimal (<0.001), but significant indicating heterogeneity between catchment areas. Although similar hazard ratios and confidence intervals of covariates are seen between Gamma and Gaussian frailty log-logistic models, the credibility intervals for the Gamma model are consistently narrower. Conclusion: The results from both Gamma and Gaussian demonstrate that heterogeneity affected significance of the determinants for TB mortality. The results showed community level to significantly affect the risk of dying indicating differences between catchment areas.