Influencing factors of death in patients with MDR-TB based on Bayesian Cox regression model

Objectives: Multidrug-resistant tuberculosis (MDR-TB) has a high mortality and is always one of the major challenges in global TB prevention and control. Analyzing the factors that may impact the adverse outcomes of MDR-TB patients is helpful for improving the systematic management and optimizing the treatment strategies for MDR-TB patients. For follow-up data, the Cox proportional hazards regression model is an important multifactor analysis method. However, the method has significant limitations in its application, such as the fact that it is difficult to deal with the impacts of small sample sizes and other practical issues on the model. Therefore, Bayesian and conventional Cox regression models were both used in this study to analyze the influencing factors of death in MDR-TB patients during the anti-TB therapy, and compare the differences between these 2 methods in their application.

Methods: Data were obtained from 388 MDR-TB patients treated at Lanzhou Pulmonary Hospital from November 1, 2017 to March 31, 2021. Survival analysis was employed to analyze the death of MDR-TB patients during the therapy and its influencing factors. Conventional and Bayesian Cox regression models were established to estimate the hazard ratios (HR) and their 95% confidence interval (95% CI) for the factors affecting the death of MDR-TB patients. The reliability of parameter estimation in these 2 models was assessed by comparing the parameter standard deviation and 95% CI of each variable. The smaller parameter standard deviation and narrower 95% CI range indicated the more reliable parameter estimation.

Results: The median survival time (1st quartile, 3rd quartile) of the 388 MDR-TB patients included in the study was 10.18 (4.26, 18.13) months, with the longest survival time of 31.90 months. Among these patients, a total of 12 individuals died of MDR-TB and the mortality was 3.1%. The median survival time (1st quartile, 3rd quartile) for the deceased patients was 4.78(2.63, 6.93) months. The majority of deceased patients, accounting for 50%, experienced death within the first 5 months of anti-TB therapy, with the last mortality case occurring within the 13th month of therapy. The results of the conventional Cox regression model showed that the risk of death in MDR-TB patients with comorbidities was approximately 6.96 times higher than that of patients without complications (HR=6.96, 95% CI 2.00 to 24.24, P=0.002) and patients who received regular follow-up had a decrease in the risk of death by approximately 81% compared to those who did not receive regular follow-up (HR=0.19, 95% CI 0.05 to 0.77, P=0.020). In the results of Bayesian Cox regression model, the iterative history plot and Blue/Green/Red (BGR) plot for each parameter showed the good model convergence, and parameter estimation indicated that the risk of death in patients with a positive first sputum culture was lower than that of patients with a negative first sputum culture (HR=0.33, 95% CI 0.08 to 0.87). Additionally, compared to patients without complications, those with comorbidities had an approximately 6.80-fold increase in the risk of death (HR=7.80, 95% CI 1.90 to 21.91). Patients who received regular follow-up had a 90% reduction in the risk of death compared to those who did not receive regular follow-up (HR=0.10, 95% CI 0.01 to 0.30). The comparison between these 2 models showed that the parameter standard deviations and corresponding 95% CI ranges of other variables in the Bayesian Cox model were significantly smaller than those in the conventional model, except for parameter standard deviations of receiving regular follow-up (Bayesian model was 0.77; conventional model was 0.72) and pulmonary cavities (Bayesian model was 0.73; conventional model was 0.73).

Conclusions: The first year of anti-TB therapy is a high-risk period for mortality in MDR-TB patients. Complications are the main risk factors of death in MDR-TB patients, while patients who received regular follow-up and had positive first sputum culture presented a lower risk of death. For data with a small sample size and low incidence of outcome, the Bayesian Cox regression model provides more reliable parameter estimation than the conventional Cox model.