The Importance of the Frailty Effect In Survival Models: For Multidrug-resistant Tuberculosis Data

Background: Frailty models have been proposed to analyse survival data, considering unobserved covariates (frailty effects). In a shared frailty model, frailties are common (or shared) amongst groups of individuals and are randomly distributed across groups. Objective: In this paper, the authors compared the semi-parametric model to shared frailty models by studying the time-to-death of patients with multidrug-resistant tuberculosis (MDR-TB). Methods: Secondary data from 1 542 multidrug-resistant tuberculosis patients were used in this study. STATA software was used to analyse frailty models via the streg command. Results: Of 1 542 patients diagnosed with MDR-TB, 245 (15.9%) died during the study period; 77 (5.0%) had treatment failure; 334 (21.7%) defaulted; 213 (13.8%) completed treatment; 651 (42.2%) were cured of MRD-TB; and 22 (1.4%) were transferred out. The results showed that 797 (51.7%) were females, and the majority were aged 18 – 30 and 31 – 40 years (35.5% and 35.7% respectively). Most of the patients (71.3%) were HIV-positive. The results also showed that most patients (95.7%) had no previous MDR-TB episodes, and 792 (51.4%) had no co-morbidities. The estimate of the variance for the frailty term in the Weibull gamma shared frailty model was 2.83, which is relatively large and therefore suggests the existence of heterogeneity. Conclusion: The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to the hazards and survival functions observed in a population.