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Mycobacterium tuberculosis is the causative agent of tuberculosis (TB), and pulmonary TB is the most prevalent form of the disease worldwide. One of the most concrete actions to ensure an effective TB control program is monitoring TB treatment outcomes, particularly duration to cure; but, there is no strong evidence in this respect. Thus, the primary aim of this study was to examine the possible spatial variations of duration to cure and its associated factors in Iran using the Bayesian spatial survival model. All new smear-positive PTB patients have diagnosed from March 2011 to March 2018 were included in the study. Out of 34,744 patients, 27,752 (79.90%) patients cured and 6992 (20.10%) cases were censored. For inferential purposes, the Markov chain Monte Carlo algorithms are applied in a Bayesian framework. According to the Bayesian estimates of the regression parameters in the proposed model, a Bayesian spatial log-logistic model, the variables gender (male vs. female, TR = 1.09), altitude (>750 m vs. ≤750 m, TR = 1.05), bacilli density in initial smear (3+ and 2+ vs. 1-9 Basil & 1+, TR = 1.09 and TR = 1.02, respectively), delayed diagnosis (>3 months vs. <1 month, TR = 1.02), nationality (Iranian vs. other, TR = 1.02), and location (urban vs. rural, TR = 1.02) had a significant influence on prolonging the duration to cure. Indeed, pretreatment weight (TR = 0.99) was substantially associated with shorter duration to cure. In summary, the spatial log-logistic model with convolution prior represented a better performance to analyze the duration to cure of PTB patients. Also, our results provide valuable information on critical determinants of duration to cure. Prolonged duration to cure was observed in provinces with low TB incidence and high average altitude as well. Accordingly, it is essential to pay a special attention to such provinces and monitor them carefully to reduce the duration to cure while maintaining a focus on high-risk provinces in terms of TB prevalence.

While there has been considerable research on the analysis of extreme values and outliers by using heavy-tailed distributions, little is known about the semi-heavy-tailed behaviors of data when there are a few suspicious outliers. To address the situation where data are skewed possessing semi-heavy tails, we introduce two new skewed distribution families of the hyperbolic secant with exciting properties. We extend the semi-heavy-tailedness property of data to a linear regression model. In particular, we investigate the asymptotic properties of the ML estimators of the regression parameters when the error term has a semi-heavy-tailed distribution. We conduct simulation studies comparing the ML estimators of the regression parameters under various assumptions for the distribution of the error term. We also provide three real examples to show the priority of the semi-heavy-tailedness of the error term comparing to heavy-tailedness. Online supplementary materials for this article are available. All the new proposed models in this work are implemented by the shs R package, which can be found on the GitHub webpage., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2020 Informa UK Limited, trading as Taylor & Francis Group.)

Introduction: Survival modeling is a very important tool to detect risk factors and provide a basis for health care planning. However, cancer data may have properties leading to distorted results with routine methods. Therefore, this study aimed to cover specific factors (competing risk, cure fraction and heterogeneity) with a real dataset of Iranian breast cancer patients using a competing risk-cure-frailty model. Materials and methods: For this historical cohort study, information for 550 Iranian breast cancer patients who underwent surgery for tumor removal from 2001 to 2007 and were followed up to March 2017, was analyzed using R 3.2 software. Results: In contrast to T-stage and N-stage, hormone receptor status did not have any significant effect on the cure fraction (long-term disease-free survival). However, T-stage, N-stage and hormone receptor status all had a significant effect on short-term disease-free survival so that the hazard of loco-regional relapse or distant metastasis in cases positive for a hormone receptor was only 0.3 times that for their negative hormone receptor counterparts. The likelihood of locoregional relapse in the first quartile of follow up was nearly twice that of other quartiles. The least cumulative incidence of time to locoregional relapse was for cases with a positive hormone receptor, low N stage and low T stage. The effect of frailty term was significant in this study and a model with frailty appeared more appropriate than a model without, based on the Akaike information criterion (AIC); values for the frailty model and one without the frailty parameter were 1370.39 and 1381.46, respectively. Conclusions: The data from this study indicate ae necessity to consider competing risk, cure fraction and heterogeneity in survival modeling. The competing risk-cure-frailty model can cover complex situations with survival data., (Creative Commons Attribution License)