Background: Bayesian Mixture cure rate frailty model is a model used in survival analysis by controlling frailty when the fraction of cured individuals exists. The present study was performed as the first systematic review in survival analysis with cure fraction. The aim of this systematic review was to study and evaluate the related studies on Bayesian Mixture cure rate frailty model. Also, this model was used to demonstrate its importance and applicability in determining the variables affecting the survival of patients with gastric cancer. Methods: This systematic review was done based on the PRISMA guideline by considering related searching keywords in PubMed, Scopus, Science Direct, Web of Science, and Google Scholar. Also, Bayesian Mixture cure rate frailty model was used to analyze gastric cancer data. Results: In the beginning, 882 studies related to survival analysis of cure rate model were found. Finally, by reading the full-text, only 4 related studies were found based on the inclusion and exclusion criteria. In these studies, semi-parametric models and parametric model with Weibull distribution were used for time-to-event data. Also, based on the results of the model, significant and affective variables on the survival of patients with gastric cancer were found. Conclusion: According to the results of this study, in the cure model, choice of proper distribution for the frailty variable and baseline distribution can influence the results. It was also found that place of residence, chemotherapy, morphology, and metastasis are effective variables on survival of patients with gastric cancer.

Aim: We used Mixture cure mode to separately investigate the risk factors for long-term and short-term survival of colorectal cancer patients. Background: Colorectal cancer (CRC) is the second most common cancer worldwide. In cancer studies, patients’ survival is the most important indicator of patients’ status. Classical methods in analyzing the survival data usually apply Cox proportional hazard regression. Methods: The study was performed on 1121 patients diagnosed with colorectal cancer. Mixture cure model with Weibull distribution and logit link function was fitted to data. Results: Odds of long-term survival for rectum cancer patients were lower than for colon cancer patients (OR=0. 29(0. 09, 0. 9)). Also, patients with the advanced stage of the disease had lower odds of long-term survival compared to early-stage patients (OR=0. 24(0. 06, 0. 86)). In the short-term, the hazard of death for people with normal BMI was lower than the underweight group (HR=0. 4(0. 21, 0. 76)). The short-term hazard of death for rectum cancer was about half of the short-term hazard for colon cancer (HR=0. 49(0. 29, 0. 81)). Further, people with moderately (HR=2. 11(1. 26, 3. 55)) and poorly (HR=4. 04(2. 03, 8. 03)) differentiated tumor grade had a higher short-term hazard of death compared to people with well-differentiated grade. Conclusion: Predictive variables of colorectal cancer survival showed different effects in short-and long-terms. Site topography was a prognosis for both long-term and short-term survival; BMI and tumor grade were short-term predictors of survival while stage was a long-term predictor of survival.

Background & Aim: Esophageal cancer is one of the main common causes of death. The high prevalence of esophageal cancer in northern Iran is an important public health problem. The main aim of this paper was to assess the factors affecting survival of patients with esophageal cancer in neighbor provinces around the Caspian Sea using Weibull Mixture cure model and Mixture cure model based on a non-proportional hazard.Methods & Materials: This prospective study was designed to gather data of esophageal cancer from the Babol cancer registry, Iran, registered during 1990 to 1991. The study cases were also followed for a period of 15 years up to 2006. Mixture cure model via non-proportional hazard modeling was used to calculate cure fraction and investigate the factors responsible for the cure probability of patients. Estimates were obtained by maximization of the likelihood via SAS proc NLMIXED.Results: The median survival time was about 9 months and survival probability in 1, 3, and 5 years following diagnosis were 23%, 15% and 13%, respectively. The family history affected the cured fraction independently of its effect on the early outcome. In addition, it had significant effect on the probability of uncured state in the both models.Conclusion: The results demonstrated the great potential in cure modeling survival data via nonproportional hazard model compared to Weibull Mixture cure model.

Background: Cervical cancer is the fourth most common cancer among women and the seventh most common worldwide. Objectives: The present study aimed at investigating the usability of cure models in analyzing patients’ survival. Besides, the factors affecting the long-term and short-term survival of the patients were determined, usingWeibull, log-logistic, and log-normal models. Methods: The sample population of the study included 109 female patients with cervical cancer referred to Motahhari Hospital of Urmia (West Azerbaijan province) from 2004 to 2015. The cure survival analysis was used to determine the patients’ survival. Results: The mean and standard deviation age at diagnosis was 50. 1 11. 7 years. The patients’ age, age at marriage, and the disease relapse were significant in the single-variable model on the long-term survival function of the patients. Moreover, the findings showed that cured Log Logistic Parametric Model was more suitable for analyzing survival data in West Azerbaijan Province, Iran. The relapse variable was significant for all the parametric models. Conclusions: Given the divided sample population into immune and susceptible groups, the Mixture cure models can be used to analyze the long-term and short-term survival of the patients with cervical cancer. Moreover, these models can be used to recognize the factors affecting both groups simultaneously.

Background & Objective: Esophageal cancer (EC) has been identified as one of the most common cancers in the northeastern regions of Iran. In our study, parametric non-Mixture cure rate model was applied to evaluate the effects of risk factors on the long-term survival of patients with EC in East Azerbaijan, Northeastern Iran. Materials & Methods: This retrospective cohort study of 127 patients with EC registered at Iran National Cancer Registry office in the period 2009-2010. These patients were followed up for 5 years in East Azerbaijan, Iran until 2015. The best parametric cure rate model was identified and the risk factors of survival in patients with EC were measured by Akaike Information Criteria and parametric non-Mixture cure rate model, respectively. Results: The survival time of EC patients ranged 0. 10-69. 03 months. Male sex (Odds Ratio (OR) =0. 08, 95% confidence interval (CI: 0. 02-0. 32, P<0. 001), patients who underwent esophagectomy surgery (OR=6. 11, 95%CI: 1. 46-25. 55, P=0. 013) had a significant effect on the survival and the cure fraction of EC patients. Population cure rate was 0. 11 (95%CI: 0. 07-0. 19) and cure fraction was estimated 4. 9%. Conclusion: The Weibull non-Mixture cure rate model was the most appropriate statistical tool to identify potential risk factors that affect both survival and cure fraction of EC patients. It is a recommended tool for analyzing the long-term survival of patients with EC.