Background & Aim: The excess hazard rate proposed by Andersen and Vaeth may underestimate the long-term excess hazard rate for cancer survival. Zahl explained the phenomenon by continuous selection of the most robust individuals after diagnosis. He applied correlated inverse Gaussian and gamma frailty models to estimate excess intensity and reached a better estimate of the rate and called it the corrected excess hazard. The compound Poisson distribution has more parameters and therefore owns more flexibility and includes gamma and inverse Gaussian distributions as special cases. Therefore, the aim of this study was to estimate the excess hazard using compound poisson frailty model Methods & Materials: Both shared and correlated frailty (CF) variables based on compound Poisson distribution were used to model unobserved common covariates. A data set of patients diagnosed with localized or regional gastrointestinal tract cancer collected at the Mazandaran province of Iran was studied. As registration systems in Iran are so affected by omission and various errors, a number of five West Coale- Demeny life tables for men and four for women were constructed corresponding to each birth cohort, which was considered as the reference life tables. Thus, population-based mortality rates [h1 (t)] were simply replaced by the appropriate values of the West tables depending on the sex (male or female) and birth cohort of the patient.Results: The CF model with unequal variances could best estimate the long-term excess hazard.Conclusion: This study advocates the CF models can best estimate the long-term excess hazard rates regardless of the distribution of the frailty variable.

In survival data, it is typical for survival times to be clustered or depend on some unobserved covariates. This can be due to geographical clustering, subjects sharing common genes, specific socioeconomic level, or hereditary and racial characteristics, and other predisposition that cannot be measured and observed directly. Adjusting the effects of these unknown factors on the survival functions is necessary for the independence of survival times and the explanatory variables. The aim of this study is to introduce and compare Cox models with parametric and non-parametric shared frailty on brain stroke survival data. The results showed that non-parametric frailty model has better fitting than parametric distributions (AIC=4686 and BIC=4684), especially when the exact parametric distribution is not known. According to the results of best model, following variables were statistical significant,BMI (HR=0. 97, P=0. 045),Age (HR=1. 04, P<0. 001),HDL (HR=1. 01, P<0. 001),LDL (HR=0. 99, P<0. 001),Hyperlipidemia (HR=0. 72, P<0. 014). The nonparametric frailty is desirable, due to potential misspecification of the parametric form and as a method for detecting clusters of groups with similar frailties.

In the survival analysis, when there is a cure fraction and the occurrence times of events are correlated, the cure frailty model is utilized. The main objective is to propose a method of analysis for two types of correlated frailty in the non-mixture cured model in order to separate the individual and shared heterogeneity between subjects. The cure models with correlated frailty and promotion time are considered. In both models, the likelihood function are based on piecewise exponential distribution for hazard function. To estimate the parameters, hierarchical Bayesian modeling is employed. Due to non-closed forms of the posteriors, they are estimated by MCMC algorithms. The Cox correlated frailty model is used as a benchmark and models are compared by DIC Criterion. The results show the superiority of cure models with correlated frailty.

Automatic topic detection seems unavoidable in social media analysis due to big text data which their users generate. Clustering-based methods are one of the most important and up-to-date categories in topic detection. The goal of this research is to have a wide study on this category. Therefore, this paper aims to study the main components of clustering-based-topic-detection, which are embedding methods, distance metrics, and clustering algorithms. Transfer learning and consequently pretrained language models and word embeddings have been considered in recent years. Regarding the importance of embedding methods, the efficiency of five new embedding methods, from earlier to recent ones, are compared in this paper. To conduct our study, two commonly used distance metrics, in addition to five important clustering algorithms in the field of topic detection, are implemented by the authors. As COVID-19 has turned into a hot trending topic on social networks in recent years, a dataset including one-month tweets collected with COVID-19-related hashtags is used for this study. More than 7500 experiments are performed to determine tunable parameters. Then all combinations of embedding methods, distance metrics and clustering algorithms (50 combinations) are evaluated using Silhouette metric. Results show that T5 strongly outperforms other embedding methods, cosine distance is weakly better than other distance metrics, and DBSCAN is superior to other clustering algorithms.

Background: In recent years, fertility in Iran has reached below the replacement level; decreasing marriage and increasing divorce rates are the most important reasons of this phenomenon. In this situation, remarriage can have an important effect on total fertility rate in addition to reducing various social and psychological harms of divorced women. Considering the importance of this issue, the aim of this study was to investigate the factors affecting the remarriage time of divorced women using survival frailty models. Methods: In this study, the information from the marriage questionnaire of 448 divorced women who were on the verge of remarriage was used. The samples were randomly selected from among women who had referred to laboratories in provincial centers for premarital tests and whose data had been collected by the Civil Registration Organization of Iran, during 2017 and 2018. In this article, the effect of selected variables on the remarriage time of these women was investigated using survival frailty models. Findings: According to the results, most of the women were in the age group of 20-40 years, unemployed, with consanguineous marriages, and the monthly income of the father's family of less than 2 million Tomans. Based on Akaike's criteria, the log-logistic model with gamma shared frailty was chosen as the final model. Based on this model, age, having a child from the first marriage, and the monthly income of the father's family had significant effects on the time of these women's remarriage. Conclusion: Ignoring frailty in the analysis of data where there is similarity among people belonging to a certain group leads to misleading conclusion. According to the results, younger women, childless from their previous marriage, and with lower monthly income of their father's family remarried faster than other women.

Background and objectives: Birth spacing is an important variable for identification of fertility acceleration, total fertility rate, and maternal and fetal health. Therefore, special attention has been paid to this issue by researchers in the fields of medical sciences, health, and population. In addition, proper analysis of this concept is of foremost importance. Application of classical analytical techniques with no attention to their assumptions (e. g., independence of events) is associated with inefficient results. As such, this study aimed to present frailty models as effective models for this analysis. Methods: Frailty models consider the dependence between unobserved intervals and dispersions by exerting a random impact on the model. Different types of these models include shared, conditional, correlated and time-dependent frailty, each of which along with their applications were presented in the current research using two examples. Results: In practice, the shared frailty model is highly applied due to its simplicity. Nevertheless, since most of the unknown factors affecting the birth spacing are not common between different births, the shared frailty models must be used with caution. Conclusion: Use of classical statistical methods, such as the Cox proportional hazards model, the important assumption of which is the dependence of events occurred, is not appropriate for the accurate analysis of birth spacing. On the other hand, frailty models consider the correlation between the intervals and are an effective method for analysis of birth spacing, use of which is recommended to researchers in fields of medicine and population.

Background: Breast cancer is one of the non-communicable diseases and the main origin of the loss of life in the world. In Ethiopia, breast cancer is the second common cancer health problem for women. The main objective of this study was to identify the potential risk factors affecting the survival time of breast cancer patients in Southwest Ethiopia. Study design: A retrospective study design. Methods: The data were taken from the patients’ medical records that registered from January 1, 2015, to January 31, 2020. A retrospective study design was used in this study. Different shared frailty survival models were employed to analyze the dataset. Results: Out of 642 recorded breast cancer patients, 447(69. 6%) cases died during the study period, and 195 (30. 4%) patients lost follow-up for unknown reasons. The median time to death for breast cancer patients was 10 months, and hospitals were used as a cluster effect. The result revealed that women with no smoking habit had about 3. 35 times higher survival time than patients who had a smoking habit, and as breast cancer patients age increased, the survival time decreased by 0. 99. Moreover, breast cancer patients in rural areas had about 0. 14 times lower survival time, compared to breast cancer patients who were urban residents. Conclusions: Age, place of residence, treatment taken, stage, histologic grade, tumor size, oral contraceptives, and smoking habits led to a shorter survival time. To reduce the burden of breast cancer, awareness should be given to the community.

We present a Bayesian analysis for recurrent events data using a nonhomogeneous mixed Poisson point process with a dynamic subject-specific frailty function and a dynamic baseline intensity function.The dynamic subject-specific frailty employs a dynamic piecewise constant function with a known pre-specified grid and the baseline intensity uses an unknown grid for the piecewise constant function. Implementation of Bayesian inference using a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is developed to handle the change of the dimension in the parameter space for models with a random number of change points. A data set provided by Grubbs et al. (1991) with recurrent times to mammary tumors for 59 rats is used to illustrate the application of the new models. We compare several models including constant or piecewise constant subject-specific frailty and a fixed number or a random number for the change points in the baseline using the pseudo-marginal likelihood criterion. We show that models with a random number of change points in the baseline improve upon that of a fixed number.