Centre-level variation in the survival of patients receiving haemodialysis in India: findings from a nationwide private haemodialysis network.

Background: There are no large studies examining survival in patients receiving haemodialysis in India or considering centre-level effects on survival. We measured survival variation between dialysis centres across India and evaluated the extent to which differences are explained by measured centre characteristics. Methods: This is a multilevel analysis of patient survival in centres of the NephroPlus dialysis network consisting of 193 centres across India. Patients receiving haemodialysis at a centre for ≥90 days between April 2014 and June 2019 were included, with analyses restricted to centres with ≥10 such patients. The primary outcome was all-cause mortality, measured from 90 days after joining a centre. Proportional hazards models with shared frailty were used to model centre- and patient-level effects on survival. Findings: Amongst 23,601 patients (median age 53 years; 29% female), the unadjusted centre-specific 180-day Kaplan-Meier survival estimates ranged between 55% (95% confidence interval [CI] 38-80%) and 100%, with a median of 88% (interquartile interval 83%-92%). After accounting for multilevel factors, estimated 180-day survival ranged between 83% (73-89%) and 97% (95-98%), with 90% 180-day survival in the average centre. The mortality rate in patients attending rural centres was 32% (Hazard Ratio 1.32; 95% CI 1.06-1.65) higher than those at urban centres in adjusted analyses. Multiple patient characteristics were associated with mortality. Interpretation: This is the first national benchmark for survival amongst dialysis patients in India. Centre- and patient-level characteristics are associated with survival but there remains unexplained variation between centres. As India continues to widen dialysis access, ongoing quality improvement programs will be an important part of ensuring that patients experience the best possible outcomes at the point of care. Funding: This project received no external funding.

Modelling alternately recurring events using subject specific hazard estimation approach.

The motivation for this paper is to account for subject specific variations in a Cox proportional hazard model for alternating recurrent events. This is done through two sets of frailty components, whose marginal distributions are bound together by a copula function. The likelihood function involves unobservable variables, which requires the use of the EM algorithm. This leads to intractable integrals, which after some approximations, are solved using computationally intensive techniques. The results are applied to a real-life data. A simulation study is also carried out to check for consistency.

Extended excess hazard models for spatially dependent survival data.

Relative survival represents the preferred framework for the analysis of population cancer survival data. The aim is to model the survival probability associated with cancer in the absence of information about the cause of death. Recent data linkage developments have allowed for incorporating the place of residence into the population cancer databases; however, modeling this spatial information has received little attention in the relative survival setting. We propose a flexible parametric class of spatial excess hazard models (along with inference tools), named "Relative Survival Spatial General Hazard," that allows for the inclusion of fixed and spatial effects in both time-level and hazard-level components. We illustrate the performance of the proposed model using an extensive simulation study, and provide guidelines about the interplay of sample size, censoring, and model misspecification. We present a case study using real data from colon cancer patients in England. This case study illustrates how a spatial model can be used to identify geographical areas with low cancer survival, as well as how to summarize such a model through marginal survival quantities and spatial effects.

Correlates of age at first birth among women in Ethiopia: use of multilevel survival analysis models.

Introduction: the timing of birth of the first child has a direct relationship with fertility in general and health and future career including further education of a mother in particular. The objective of this study was to identify factors significantly associated with the time to the first birth among women in Ethiopia. Methods: a cross-sectional study was conducted using data from the 2016 Ethiopian Demographic and Health Survey (EDHS). The study subjects were married women and men aged 15 to 49 in randomly selected households across Ethiopia and two stage stratified random sampling technique was used to select study subjects. Log logistic-Gamma shared frailty model was used to identify factors associated with the length of time spent until the first birth. Results: the median age at first birth for women living in Ethiopia was 20 years, whereas the minimum and maximum ages at first birth were 11 and 49 years respectively. Age at first sex, age at first cohabitation, sex of household head, place of residence, religion, education level, contraceptive use and exposure to media were significant correlates of age at first birth of women in Ethiopia. Higher level of education was associated with increased age at first birth. Women who use contraceptive, women living in urban areas, women having exposure to media and female headed households had longer time to first birth compared to their counterparts. Conclusion: the different regions of Ethiopia have significant differences in the age of women during their first birth. Most of the factors associated with the time to first child in this study were related to education of women. Investing in education and educating women plays critical roles in regulating fertility of a nation and health of women.

Female "Paradox" in Atrial Fibrillation-Role of Left Truncation Due to Competing Risks.

Female sex in patients with atrial fibrillation (AF) is a controversial and paradoxical risk factor for stroke-controversial because it increases the risk of stroke only among older women of some ethnicities and paradoxical because it appears to contradict male predominance in cardiovascular diseases. However, the underlying mechanism remains unclear. We conducted simulations to examine the hypothesis that this sex difference is generated non-causally through left truncation due to competing risks (CR) such as coronary artery diseases, which occur more frequently among men than among women and share common unobserved causes with stroke. We modeled the hazards of stroke and CR with correlated heterogeneous risk. We assumed that some people died of CR before AF diagnosis and calculated the hazard ratio of female sex in the left-truncated AF population. In this situation, female sex became a risk factor for stroke in the absence of causal roles. The hazard ratio was attenuated in young populations without left truncation and in populations with low CR and high stroke incidence, which is consistent with real-world observations. This study demonstrated that spurious risk factors can be identified through left truncation due to correlated CR. Female sex in patients with AF may be a paradoxical risk factor for stroke.

A flexible class of generalized joint frailty models for the analysis of survival endpoints.

This article focuses on shared frailty models for correlated failure times, as well as joint frailty models for the simultaneous analysis of recurrent events (eg, appearance of new cancerous lesions or hospital readmissions) and a major terminal event (typically, death). As extensions of the Cox model, these joint models usually assume a frailty proportional hazards model for each of the recurrent and terminal event processes. In order to extend these models beyond the proportional hazards assumption, our proposal is to replace these proportional hazards models with generalized survival models, for which the survival function is modeled as a linear predictor through a link function. Depending on the link function considered, these can be reduced to proportional hazards, proportional odds, additive hazards, or probit models. We first consider a fully parametric framework for the time and covariate effects. For proportional and additive hazards models, our approach also allows the use of smooth functions for baseline hazard functions and time-varying coefficients. The dependence between recurrent and terminal event processes is modeled by conditioning on a shared frailty acting differently on the two processes. Parameter estimates are provided using the maximum (penalized) likelihood method, implemented in the R package frailtypack (function GenfrailtyPenal). We perform simulation studies to assess the method, which is also illustrated on real datasets.

Bayesian design of clinical trials using joint models for recurrent and terminating events.

Joint models for recurrent event and terminating event data are increasingly used for the analysis of clinical trials. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the effect of an investigational product (IP) on both recurrent event and terminating event processes considered as multiple primary endpoints, using a multifrailty joint model. Dependence between the recurrent and terminating event processes is accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. We propose an approach for sample size determination to ensure the trial design has a high power and a well-controlled type I error rate, with both operating characteristics defined from a Bayesian perspective. We also consider a generalization of the proposed parametric model that uses a nonparametric mixture of Dirichlet processes to model the frailty distributions and compare its performance to the proposed approach. We demonstrate the methodology by designing a colorectal cancer clinical trial with a goal of demonstrating that the IP causes a favorable effect on at least one of the two outcomes but no harm on either.

A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies.

The hazard ratio (HR) is often reported as the main causal effect when studying survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in selection bias in the HR, because similarly to the truncation by death problem, the HR conditions on post-treatment survival. A recently proposed alternative, inspired by the Survivor Average Causal Effect, is the causal HR, defined as the ratio between hazards across treatment groups among the study participants that would have survived regardless of their treatment assignment. We discuss the challenge in identifying the causal HR and present a sensitivity analysis identification approach in randomized controlled trials utilizing a working frailty model. We further extend our framework to adjust for potential confounders using inverse probability of treatment weighting. We present a Cox-based and a flexible non-parametric kernel-based estimation under right censoring. We study the finite-sample properties of the proposed estimation methods through simulations. We illustrate the utility of our framework using two real-data examples.

Using marginal structural joint models to estimate the effect of a time-varying treatment on recurrent events and survival: An application on arrhythmogenic cardiomyopathy.

In many clinical applications to evaluate the effect of a treatment, randomized control trials are difficult to carry out. On the other hand, clinical observational registries are often available and they contain longitudinal data regarding clinical parameters, drug therapies, and outcomes. In the past, much research has addressed causal methods to estimate treatment effects from observational studies. In the context of time-varying treatments, marginal structural models are often used. However, most analyses have focused on binary outcomes or time-to-the-first event analyses. The novelty of our approach is to combine the marginal structural methodology with the case where correlated recurrent events and survival are the outcomes of interest. Our work focuses on solving the nontrivial problem of defining the measures of effect, specifying the model for the time-dependent weights and the model to estimate the outcome, implementing them, and finally estimating the final treatment effects in this life-history setting. Our approach provides a strategy that allows obtaining treatment effect estimates both on the recurrent events and the survival with a clear causal and clinical interpretation. At the same time, the strategy we propose is based on flexible modeling choices such as the use of joint models to capture the correlation within events from the same subject and the specification of time-dependent treatment effects. The clinical problem which motivated our work is the evaluation of the treatment effect of beta-blockers in arrhythmogenic right ventricular cardiomyopathy (ARVC/D), and the dataset comes from the Trieste Heart Muscle Disease Registry.

The Effect of B-Cell Lymphoma 2 and BCL2-Associated X Polymorphisms on the Survival of Acute Lymphoblastic Leukemia Patients: Application of Frailty Survival Models.

Background: B-cell lymphoma 2 (BCL-2) and BCL-2 associated X (BAX) polymorphisms are important in the apoptosis process, response to treatment and survival in Acute Lymphoblastic Leukemia (ALL) patients. We aimed to investigate the effect of these genes with other predictors corresponding to the survival of ALL patients with an appropriate frailty survival model. Methods: Our study was performed in 2020 on sixty-two cases of childhood aged 3-16 (year) with ALL disease who were selected by convenience sampling from the two hospitals of Tabriz, Iran. RFLPPCR method was used for genotyping the promoter region of the BAX and BCL-2 genes. We used different frailty survival models, to control heterogeneity between individuals due to unmeasured factors affecting their survival. All analyses were implemented using Stata 16. Results: Based on the result of log-logistic model along with frailty gamma, the proportional odds (standard error) of survival for a CC allele of BCL-2 patient compared to a AA allele patient were 6.0 (1.47); P<0.001 and for a AC of BCL-2 allele patient were 0.57 (1.23); P=0.009. Patients with AG allele of BAX had 2.05 (1.26) times greater odds of surviving than a AA allele patient (P=0.003). The odds of survival of patients with abnormal white blood cell (WBC) were 92% less than normal WBC (P<0.001). Conclusion: With controlling unmeasured factors affecting, the BCL-2 and BAX genes promoter polymorphism are effective in the survival rates for ALL.

Heavy-tailed phase-type distributions: a unified approach.

A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable and conceptually attractive to model physical phenomena due to their interpretation in terms of a hidden Markov structure. Three recent extensions of regular phase-type distributions give rise to models which allow for heavy tails: discrete- or continuous-scaling; fractional-time semi-Markov extensions; and inhomogeneous time-change of the underlying Markov process. In this paper, we present a unifying theory for heavy-tailed phase-type distributions for which all three approaches are particular cases. Our main objective is to provide useful models for heavy-tailed phase-type distributions, but any other tail behavior is also captured by our specification. We provide relevant new examples and also show how existing approaches are naturally embedded. Subsequently, two multivariate extensions are presented, inspired by the univariate construction which can be considered as a matrix version of a frailty model. We provide fully explicit EM-algorithms for all models and illustrate them using synthetic and real-life data.

Long-term exposure to PM2.5 and cardiovascular disease incidence and mortality in an Eastern Mediterranean country: findings based on a 15-year cohort study.

BACKGROUND: Evidence concerning the impact of long-term exposure to fine Particulate Matter ≤2.5 µm (PM2.5) on Cardio-Vascular Diseases (CVDs) for those people subject to ambient air pollution in developing countries remains relatively scant. This study assessed the relationship of 15-year PM2.5 exposure with cardiovascular incidence and mortality rate in Isfahan province, Iran. METHODS: The cohort comprised 3081 participants over 35 years old who were free of CVDs. They were selected through multi-stage cluster sampling in Isfahan, Iran. PM2.5 exposure was determined separately for each individual via satellite-based spatiotemporal estimates according to their residential addresses. In this context, CVD is defined as either fatal and non-fatal Acute Myocardial Infarctions (AMI) or stroke and sudden cardiac death. The incidence risk for CVD and the ensuing mortality was calculated based on the average PM2.5 exposure within a study period of 15 years using the Cox proportional hazards frailty model upon adjusting individual risk factors. The mean annual rate of PM2.5 and the follow-up data of each residential area were combined. RESULTS: Mean three-year PM2·5 exposure for the cohort was measured at 45.28 µg/m3, ranging from 20.01 to 69.80 µg/m3. The median time period for conducting necessary follow-ups was 12.3 years for the whole population. Notably, 105 cardiovascular and 241 all-cause deaths occurred among 393,786 person-months (27 and 61 per 100,000 person-months, respectively). In well-adjusted models, 10 µg/m3 increase in PM2.5 corresponded to a 3% increase in the incidence rate of CVDs [0.95 CI = 1.016, 1.036] (in case of p = 0.000001 per 10 µg/m3 increase in PM2.5, the Hazard Ratio (HR) for AMI and Ischemic Heart Disease (IHD) was 1.031 [0.95 CI = 1.005, 1.057] and 1.028 [0.95 CI = 1.017, 1.039]), respectively. No consistent association was observed between PM2.5 concentration and fatal CVD (fatal AMI, fatal stroke, SCD (Sudden Cardiac Death)) and all-cause mortality. CONCLUSIONS: Results from analyses suggest that the effect of PM2.5 on cardiovascular disease occurrence was stronger in the case of older people, smokers, and those with high blood pressure and diabetes. The final results revealed that long-term exposure to ambient PM2.5 with high concentrations positively correlated with IHD incidence and its major subtypes, except for mortality. The outcome accentuates the need for better air quality in many countries.

Penalized variable selection for cause-specific hazard frailty models with clustered competing-risks data.

Competing risks data usually arise when an occurrence of an event precludes other types of events from being observed. Such data are often encountered in a clustered clinical study such as a multi-center clinical trial. For the clustered competing-risks data which are correlated within a cluster, competing-risks models allowing for frailty terms have been recently studied. To the best of our knowledge, however, there is no literature on variable selection methods for cause-specific hazard frailty models. In this article, we propose a variable selection procedure for fixed effects in cause-specific competing risks frailty models using a penalized h-likelihood (HL). Here, we study three penalty functions, LASSO, SCAD, and HL. Simulation studies demonstrate that the proposed procedure using the HL penalty works well, providing a higher probability of choosing the true model than LASSO and SCAD methods without losing prediction accuracy. The proposed method is illustrated by using two kinds of clustered competing-risks cancer data sets.

Impact of recurrent sexually transmitted infections on HIV seroconversion: Results from multi-state frailty models.

After several decades of research, South Africa is still considered to be the epicentre of HIV epidemic. The country also has the highest burden of sexually transmitted infections (STIs) which have been frequently linked to increasing rates of HIV transmission due to biological and behavioural associations between these two pathogeneses. We investigated the cumulative impact of recurrent STIs on subsequent HIV seroconversion among a cohort of South African women. We used the 'frailty' models which can account for the heterogeneity due to the recurrent STIs in a longitudinal setting. The lowest HIV incidence rate was 5.0/100 person-year among women who had no baseline STI and remained negative during the follow-up. This estimate was three times higher among those who had recurrent STIs in the follow-up period regardless of their STI status at baseline (15.8 and 14.0/100 person-year for women with and without STI diagnosis at baseline, respectively). Besides younger age and certain partnership characteristics, our data provided compelling evidence for the impact of recurrent STI. diagnoses on increasing rates of HIV. At the population-level, 65% of HIV infections collectively associated with recurrent STIs. These results have significant clinical and epidemiological implications and may play critical role in the trajectory of the infections in the region.

Survival models induced by zero-modified power series discrete frailty: Application with a melanoma data set.

Survival models with a frailty term are presented as an extension of Cox's proportional hazard model, in which a random effect is introduced in the hazard function in a multiplicative form with the aim of modeling the unobserved heterogeneity in the population. Candidates for the frailty distribution are assumed to be continuous and non-negative. However, this assumption may not be true in some situations. In this paper, we consider a discretely distributed frailty model that allows units with zero frailty, that is, it can be interpreted as having long-term survivors. We propose a new discrete frailty-induced survival model with a zero-modified power series family, which can be zero-inflated or zero-deflated depending on the parameter value. Parameter estimation was obtained using the maximum likelihood method, and the performance of the proposed models was performed by Monte Carlo simulation studies. Finally, the applicability of the proposed models was illustrated with a real melanoma cancer data set.

Residential green space structures are associated with a lower risk of bipolar disorder: A nationwide population-based study in Taiwan.

Although many researchers have identified the potential psychological benefits offered by greenness, the association between green space structures and mental disorders is not well understood. The purpose of this study was to identify associations between green space structures and the incidence of bipolar disorder. To this end, we investigated 1,907,776 individuals collected from Taiwan's National Health Insurance Research Database. After a follow-up investigation from 2005 to 2016, among those with no history of bipolar disorder, 20,548 individuals were further found to be diagnosed with bipolar disorder. A geographic information system and landscape index were used to quantify three indices of green space structures: mean patch area (area and edge), mean fractal dimension index (shape), and mean proximity index (proximity). Additionally, greenness indices, the normalized difference vegetation index, and the enhanced vegetation index were used to confirm the association between greenness and incidence of bipolar disorder. These five indices were used to represent the individual's exposure according to the township of the hospital that they most frequently visited with symptoms of the common cold. Spearman's correlation analysis was performed to select variables by considering their collinearity. Subsequently, the frailty model for each index was used to examine the specific associations between those respective indices and the incidence of bipolar disorder by adjusting for related risk factors, such as socioeconomic status, metabolic syndrome, and air pollution. A negative association was identified between the mean patch area and the mean proximity index, and the incidence of bipolar disorder. In contrast, a positive association was found between the mean fractal dimension index and the incidence of bipolar disorder. We observed similar results in sensitivity testing and subgroup analysis. Exposure to green spaces with a larger area, greater proximity, lower complexity, and greener area may reduce the risk of bipolar disorder.

Modeling multi-level survival data in multi-center epidemiological cohort studies: Applications from the ELAPSE project.

BACKGROUND: We evaluated methods for the analysis of multi-level survival data using a pooled dataset of 14 cohorts participating in the ELAPSE project investigating associations between residential exposure to low levels of air pollution (PM2.5 and NO2) and health (natural-cause mortality and cerebrovascular, coronary and lung cancer incidence). METHODS: We applied five approaches in a multivariable Cox model to account for the first level of clustering corresponding to cohort specification: (1) not accounting for the cohort or using (2) indicator variables, (3) strata, (4) a frailty term in frailty Cox models, (5) a random intercept under a mixed Cox, for cohort identification. We accounted for the second level of clustering due to common characteristics in the residential area by (1) a random intercept per small area or (2) applying variance correction. We assessed the stratified, frailty and mixed Cox approach through simulations under different scenarios for heterogeneity in the underlying hazards and the air pollution effects. RESULTS: Effect estimates were stable under approaches used to adjust for cohort but substantially differed when no adjustment was applied. Further adjustment for the small area grouping increased the effect estimates' standard errors. Simulations confirmed identical results between the stratified and frailty models. In ELAPSE we selected a stratified multivariable Cox model to account for between-cohort heterogeneity without adjustment for small area level, due to the small number of subjects and events in the latter. CONCLUSIONS: Our study supports the need to account for between-cohort heterogeneity in multi-center collaborations using pooled individual level data.

Estimation of the cumulative baseline hazard function for dependently right-censored failure time data.

In this paper, we study the properties of a special class of frailty models when the frailty is common to several failure times. The models are closely linked to Archimedean copula models. We establish a useful formula for cumulative baseline hazard functions and develop a new estimator for cumulative baseline hazard functions in bivariate frailty regression models. Based on our proposed estimator, we present a graphical model checking procedure. We fit a leukemia data set using our model and end our paper with some discussions.

Risk Factors Affecting Survival Time of Breast Cancer Patients: The case of Southwest Ethiopia.

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.

Bayesian frailty modeling of correlated survival data with application to under-five mortality.

BACKGROUND: There is high rate of under-five mortality in West Africa with little effort made to study determinants that significantly increase or decrease its risk across the West African sub-region. This is important since it will help in the design of effective intervention programs for each country or the entire region. The overall objective of this research evaluates the determinants of under-five mortality prior to the end of the 2015 Millennium Development Goals, to guide West African countries implement strategies that will aid them achieve the Sustainable Development Goal 3 by 2030. METHOD: This study used the Demographic and Health Survey (DHS) data from twelve (12) out of the eighteen West African countries; Ghana, Benin, Cote d' Ivoire, Guinea, Liberia, Mali, Niger, Nigeria, Sierra Leone, Burkina Faso, Gambia and Togo. Data were extracted from the children and women of reproductive age files as provided in the DHS report. The response or outcome variable of interest is under-five mortality rate. A Bayesian exponential, Weibull and Gompertz regression models via a gamma shared frailty model were used for the analysis. The deviance information criteria and Bayes factors were used to discriminate between models. These analyses were carried out using Stata version 15 software. RESULTS: The study recorded 101 (95% CI: 98.6-103.5) deaths per 1000 live births occurring among the twelve countries. Burkina Faso (124.4), Cote D'lvoire (110.1), Guinea (116.4), Nigeria (120.6) and Niger (118.3) recorded the highest child under-5 mortality rate. Gambia (48.1), Ghana (60.1) and Benin (70.4) recorded the least unde-5 mortality rate per 1000 livebirths. Multiple birth children were about two times more likely to die compared to singleton birth, in all except Gambia, Nigeria and Sierra Leone. We observed significantly higher hazard rates for male compared to female children in the combined data analysis (HR: 1.14, 95% CI: [1.10-1.18]). The country specific analysis in Benin, Cote D'lvoire, Guinea, Liberia, Mali and Nigeria showed higher under-5 mortality hazard rates among male children compared to female children whilst Niger was the only country to report significantly lower hazard rate of males compared to females. CONCLUSION: There is still quite a substantial amount of work to be done in order to meet the Sustainable Development Goal 3 in 2030 in West Africa. There exist variant differences among some of the countries with respect to mortality rates and determinants which require different interventions and policy decisions.