Clustered Survival Data Research Articles

A Multilevel Hazards Model for Child Mortality In Nigeria

Many researchers have devoted considerable attention to the impact of individual-level factors on child mortality, but little is known about how family and community characteristics affect health of children. Trend in child mortality as well as its determinants, has long been the subject of academic and policy debates. In spite of this, the problem of child mortality remains as daunting as ever. In fact, advancement in medical sciences and the upsurge in information and telecommunication technology equipment have not significantly reduced child mortality in the country, unlike in the West. The Multilevel proportional hazards model for data that are hierarchically clustered at three levels was applied to the study of covariates of child mortality in Nigeria. This study merges two parallel developments of statistical tools for data analysis: statistical methods known as hazard models that are used for analyzing event-duration data and statistical methods for analyzing hierarchically clustered data known as multilevel models. These developments have rarely been integrated in research practice and the formalization and estimation of models for hierarchically clustered survival data remain largely uncharted. The model was estimated using the Newton-Raphsons numerical search approach. The model accounts for hierarchical clustering with three random effects or frailty effects. We assume that the random effects are independent and follow the Exponential and Weibull distribution. The results indicate that bio-demographic factors are more important in infancy while socioeconomic factors and household and environmental conditions have a greater effect in childhood. Furthermore, there is significant variation in child mortality risks even after controlling for measured determinants of mortality. Also, factors that fall under family and community level are more significant indicating that child survival is most controlled or determined by family and community factors and variables at the child level is not weighty. This suggests that there may exits unobserved or unobservable factors related to mortality.

Modelling Clustered Survival Data with Competing Risk

Modelling Clustered Survival Data with Competing Risk

Modelling Clustered Survival Data with Competing Risk

La methode des risques proportionnels de Cox est la methode semi-parametrique la plus populaire qui est utilisee pour etablir les risques dus aux facteurs en jeu dans une population homogene dans l'analyse de survie avec un temps continu. Cependant, cette methode repose sur l'hypothese que les temps de survie ne peuvent se repeter. La methode logit basee sur un temps discret a ete largement appliquee pour gerer les egalites de temps de survie s'il y a une seule cause generatrice des evenements. Dans certaines situations, un individu peut etre a risque selon plusieurs facteurs et souvent seule la survenance du premier echec est pris en compte. Dans ce papier, le modele logit binaire pour des risques competitifs, reposant sur des melanges des fonction de risques pour des donnees en grappes est etudie selon un temps discret.

Multilevel model with random effects for clustered survival data with multiple failure outcomes.

We present a multilevel frailty model for handling serial dependence and simultaneous heterogeneity in survival data with a multilevel structure attributed to clustering of subjects and the presence of multiple failure outcomes. One commonly observes such data, for example, in multi-institutional, randomized placebo-controlled trials in which patients suffer repeated episodes (eg, recurrent migraines) of the disease outcome being measured. The model extends the proportional hazards model by incorporating a random covariate and unobservable random institution effect to respectively account for treatment-by-institution interaction and institutional variation in the baseline risk. Moreover, a random effect term with correlation structure driven by a first-order autoregressive process is attached to the model to facilitate estimation of between patient heterogeneity and serial dependence. By means of the generalized linear mixed model methodology, the random effects distribution is assumed normal and the residual maximum likelihood and the maximum likelihood methods are extended for estimation of model parameters. Simulation studies are carried out to evaluate the performance of the residual maximum likelihood and the maximum likelihood estimators and to assess the impact of misspecifying random effects distribution on the proposed inference. We demonstrate the practical feasibility of the modeling methodology by analyzing real data from a double-blind randomized multi-institutional clinical trial, designed to examine the effect of rhDNase on the occurrence of respiratory exacerbations among patients with cystic fibrosis.

결측치가 있는 군집화된 생존 자료에서 의사결정 나무 분석을 이용한 예측모형 개발

본 연구는 군집분석을 통해 크론병 환자들을 비슷한 특징을 갖는 군집으로 묶은 후 각 군집 내에서 재발시간에 대한 생존곡선의 비교 분석과 질병 재발에 영향을 주는 인자들을 의사결정 나무 분석을 통해 실시하였다. 본 분석에 들어가기 전 공변량들에 존재하는 결측치들은 단일 대체법을 이용하여 대체하였다. 분석 결과 비슷한 특징을 갖고 있는 군집 2개가 선택이 되었고 각 군집에서 생존시간에 대한 분포 차이는 유의하게 나타났다 (p0.001). 의사 결정 나무 분석 결과 재발에 영향을 끼치는 변수들은 군집마다 상이하게 나타났다. 첫 번째 군집에서는 수술명, 수술 이유와 진단 후 수술기간이 최적 분리 변수들로 선택이 되었고 두 번째 군집에서는 진단 후 수술기간만이 선택이 되었다. 본 연구의 결과는 각 군집마다 서로 다른 예측 모형을 세우는 것이 필요하다는 것을 나타내고 있다. 환자의 성별, 질병 상태, 가족력 등과 같은 요소들을 고려한 환자 맞춤식 분석을 통한 예측 모형의 구축은 새로운 환자들의 질병 재발에 대한 위험을 낮추고 의료진들의 정확하고 효율적인 진단과 치료에 긍정적인 역할을 할 수 있을 것으로 기대한다.

Geecure: An R-package for marginal proportional hazards mixture cure models

Background and objective: Most of available software packages for mixture cure models to analyze survival data with a cured fraction assume independent survival times, and they are not suitable for correlated survival times, such as clustered survival data. The objective of this paper is to present a software package to fit a marginal mixture cure model to clustered survival data with a cured fraction.Methods: We developed an R package geecure that fits the marginal proportional hazards mixture cure (PHMC) models to clustered right-censored survival data with a cured fraction. The dependence among the cure statuses and among the survival times of uncured patients within a cluster are modeled by working correlation matrices through the generalized estimating equations, and the Expectation-Solution algorithm is used to estimate the parameters. The variances of the estimated regression parameters are estimated by either a sandwich method or a bootstrap method.Results: The package geecure can fit the marginal PHMC model where the cumulative baseline hazard function is either a two-parameter Weibull distribution or specified nonparametrically. Fitting the parametric PHMC model with the Weibull baseline hazard function on average takes less time than fitting the semiparametric PHMC model does. Two variance estimation methods are comparable in the simulation study. The sandwich method takes much less time than the bootstrap method in variance estimation.Conclusions: The package geecure provides an easy access to the marginal PHMC models for clustered survival data with a cured fraction in routine survival analysis. It is easy to use and will make the wide applications of the marginal PHMC models possible.

Comparison of missing data methods in clustered survival data using Bayesian adaptive B-Spline estimation

Comparison of missing data methods in clustered survival data using Bayesian adaptive B-Spline estimation

Semiparametric generalized exponential frailty model for clustered survival data

In this paper, we propose a novel and mathematically tractable frailty model for clustered survival data by assuming a generalized exponential (GE) distribution for the latent frailty effect. Both parametric and semiparametric versions of the GE frailty model are studied with main focus for the semiparametric case, where an EM-algorithm is proposed. Our EM-based estimation for the GE frailty model is simpler, faster and immune to a flat likelihood issue affecting, for example, the semiparametric gamma model, as illustrated in this paper through simulated and real data. We also show that the GE model is at least competitive with respect to the gamma frailty model under misspecification. A broad analysis is developed, with simulation results explored via Monte Carlo replications, to evaluate and compare models. A real application using a clustered kidney catheter data is considered to demonstrate the potential for practice of the GE frailty model.

Semiparametric regression analysis of clustered survival data with semi-competing risks

Analysis of semi-competing risks data is becoming increasingly important in medical research in which a subject may experience both nonterminal and terminal events, and the time to the intermediate nonterminal event (e.g. onset of a disease) is subject to dependent censoring by the terminal event (e.g. death) but not vice versa. Typically, both two types of events are dependent. In many applications, subjects may also be nested within clusters, such as patients in a multi-center study, leading to possible association among event times due to unobserved shared factors across subjects. To incorporate dependency within clusters and association between two types of event times, we propose a new flexible semiparametric modeling framework where a copula model is employed for the joint distribution of the nonterminal and terminal events, and their marginal distributions are modeled by Cox proportional hazards models with random effects. A nonparametric maximum likelihood estimation procedure is developed and implemented through a Monte Carlo EM algorithm. The proposed estimator is also shown to enjoy desirable asymptotic properties. Results from extensive simulation studies indicate that the proposed method performs very well in finite samples and is especially robust against misspecification of the random effects distribution. We further illustrate the practical utility of the method by analyzing data from a multi-institutional study of breast cancer.

Assessing Survival Time of Women with Cervical Cancer Using Various Parametric Frailty Models: A Case Study at Tikur Anbessa Specialized Hospital, Addis Ababa, Ethiopia

Cervical cancer is one of the leading causes of death in the world and represents a tremendous burden on patients, families and societies. It is estimated that over one million women worldwide currently have cervical cancer; most of them have not been diagnosed or have no access to treatment that could cure them or prolong their lives. The goal of this study is to investigate potential risk factors affecting survival time of women with cervical cancer at Tikur Anbessa specialized hospital. Data were taken from patients’ medical record card that enrolled during September 2011–September 2015. Kaplan–Meier estimation method, Cox proportional hazard model and parametric shared frailty model were used to analysis survival time of cervical cancer patients. Study subjects (cervical cancer patients) in this study came from clustered community and hence clustered survival data correlated at the regional level. Parametric frailty models will be explored assuming that women with in the same cluster (region for this study) shares similar risk factors. We used Exponential, Weibull, Log logistics and Log normal distributions and based on AIC criteria, all models were compared for their performance. The lognormal inverse Gaussian model has the minimum AIC value among the models compared. The results implied that not giving birth up to the study ends and married after twenty years were significantly prolong the survival time of patients while age class 51–60, 61–70, > 70, smoking cigarettes, patients with stage III and IV disease, family history of cervical cancer, history of abortion and living with HIV AIDS were significantly shorten survival time of patients. The findings of this study suggested that age, smoking cigarettes, stage, family history, abortion history, living with HIV AIDS, age at first marriage and age at first birth were major factors to survival time of patients. Heterogeneity between the regions in the survival time of cervical cancer patients, indicating that one needs to account for this clustering variable using frailty models. The fit statistics showed that lognormal inverse-Gaussian frailty model described the survival time of cervical cancer patients dataset better than other distributions used in this study.

Screening group variables in the proportional hazards model

We propose a method to screen group variables under the high dimensional group variable setting for the proportional hazards model. We study the sure screening property of the proposed method for independent and clustered survival data. The simulation study shows that the proposed method performs better for group variable screening than some existing procedures.

Regression standardization and attributable fraction estimation with between-within frailty models for clustered survival data.

The between-within frailty model has been proposed as a viable analysis tool for clustered survival time outcomes. Previous research has shown that this model gives consistent estimates of the exposure-outcome hazard ratio in the presence of unmeasured cluster-constant confounding, which the ordinary frailty model does not, and that estimates obtained from the between-within frailty model are often more efficient than estimates obtained from the stratified Cox proportional hazards model. In this paper, we derive novel estimation techniques for regression standardization with between-within frailty models. We also show how between-within frailty models can be used to estimate the attributable fraction function, which is a generalization of the attributable fraction for survival time outcomes. We illustrate the proposed methods by analyzing a large cohort on preterm birth and attention deficit hyperactivity disorder. To facilitate use of the proposed methods, we provide R code for all analyses.

Competing risk model with bivariate random effects for clustered survival data

Competing risks are often observed in clinical trial studies. As exemplified in two data sets, the bone marrow transplantation study for leukaemia patients and the primary biliary cirrhosis study, patients could experience two competing events which may be correlated due to shared unobservable factors within the same cluster. With the presence of random hospital/cluster effects, a cause-specific hazard model with bivariate random effects is proposed to analyse clustered survival data with two competing events. This model extends earlier work by allowing random effects in two hazard function parts to follow a bivariate normal distribution, which gives a generalized model with a correlation parameter governing the relationship between two events due to the hospital/cluster effects. By adopting the GLMM formulation, random effects are incorporated in the model via the linear predictor terms. Estimation of parameters is achieved via an iterative algorithm. A simulation study is conducted to assess the performance of the estimators, under the proposed numerical estimation scheme. Application to the two sets of data illustrates the usefulness of the proposed model.

Log-normal frailty models fitted as Poisson generalized linear mixed models

Background and objectivesThe equivalence of a survival model with a piecewise constant baseline hazard function and a Poisson regression model has been known since decades. As shown in recent studies, this equivalence carries over to clustered survival data: A frailty model with a log-normal frailty term can be interpreted and estimated as a generalized linear mixed model with a binary response, a Poisson likelihood, and a specific offset. Proceeding this way, statistical theory and software for generalized linear mixed models are readily available for fitting frailty models. This gain in flexibility comes at the small price of (1) having to fix the number of pieces for the baseline hazard in advance and (2) having to “explode” the data set by the number of pieces. MethodsIn this paper we extend the simulations of former studies by using a more realistic baseline hazard (Gompertz) and by comparing the model under consideration with competing models. Furthermore, the SAS macro %PCFrailty is introduced to apply the Poisson generalized linear mixed approach to frailty models. ResultsThe simulations show good results for the shared frailty model. Our new %PCFrailty macro provides proper estimates, especially in case of 4 events per piece. ConclusionsThe suggested Poisson generalized linear mixed approach for log-normal frailty models based on the %PCFrailty macro provides several advantages in the analysis of clustered survival data with respect to more flexible modelling of fixed and random effects, exact (in the sense of non-approximate) maximum likelihood estimation, and standard errors and different types of confidence intervals for all variance parameters.

PSEUDO-VALUE APPROACH FOR CONDITIONAL QUANTILE RESIDUAL LIFETIME ANALYSIS FOR CLUSTERED SURVIVAL AND COMPETING RISKS DATA WITH APPLICATIONS TO BONE MARROW TRANSPLANT DATA.

Quantile residual lifetime analysis is conducted to compare remaining lifetimes among groups for survival data. Evaluating residual lifetimes among groups after adjustment for covariates is often of interest. The current literature is limited to comparing two groups for independent data. We propose a pseudo-value approach to compare quantile residual lifetimes given covariates between multiple groups for independent and clustered survival data. The proposed method considers clustered event times and clustered censoring times in addition to independent event times and censoring times. We show that the method can also be used to compare multiple groups on the cause specific residual life distribution in the competing risk setting, for which there are no current methods which account for clustering. The empirical Type I errors and statistical power of the proposed study are examined in a simulation study, which shows that the proposed method controls Type I errors very well and has higher power than an existing method. The proposed method is illustrated by a bone marrow transplant data set.

Sparsely clustered survival data: application to the evaluation of the safety and effectiveness of medical devices

ABSTRACTThe effectiveness and safety of implantable medical devices is a critical public health concern. We consider analysis of data in which it is of interest to compare devices but some individuals may be implanted with two or more devices. Our motivating example is based on orthopedic devices, where the same individual can be implanted with as many as two devices for the same joint but on different sides of the body, referred to as bilateral cases. Different methods of analysis are considered in a simulation study and real data example, including both marginal and conditional survival models, fitting single and separate models for bilateral and non-bilateral cases, and combining estimates from these two models. The results of simulations suggest that in the context of orthopedic devices, where implants failures are rare, models fit on both bilateral and non-bilateral cases simultaneously could be quite misleading, and that combined estimates from fitting two separate models performed better under homogeneity. A real data example illustrates the issues surrounding analysis of orthopedic device data with bilateral cases. Our findings suggest that research studies of orthopedic devices should at minimum consider fitting separate models to bilateral and non-bilateral cases.

SEMIPARAMETRIC EFFICIENT ESTIMATION FOR SHARED-FRAILTY MODELS WITH DOUBLY-CENSORED CLUSTERED DATA.

In this paper, we investigate frailty models for clustered survival data that are subject to both left- and right-censoring, termed "doubly-censored data". This model extends current survival literature by broadening the application of frailty models from right-censoring to a more complicated situation with additional left censoring. Our approach is motivated by a recent Hepatitis B study where the sample consists of families. We adopt a likelihood approach that aims at the nonparametric maximum likelihood estimators (NPMLE). A new algorithm is proposed, which not only works well for clustered data but also improve over existing algorithm for independent and doubly-censored data, a special case when the frailty variable is a constant equal to one. This special case is well known to be a computational challenge due to the left censoring feature of the data. The new algorithm not only resolves this challenge but also accommodate the additional frailty variable effectively. Asymptotic properties of the NPMLE are established along with semi-parametric efficiency of the NPMLE for the finite-dimensional parameters. The consistency of Bootstrap estimators for the standard errors of the NPMLE is also discussed. We conducted some simulations to illustrate the numerical performance and robustness of the proposed algorithm, which is also applied to the Hepatitis B data.

Extending the Archimedean Copula Methodology to Model Multivariate Survival Data Grouped in Clusters of Variable Size

Summary For the analysis of clustered survival data, two different types of model that take the association into account are commonly used: frailty models and copula models. Frailty models assume that, conditionally on a frailty term for each cluster, the hazard functions of individuals within that cluster are independent. These unknown frailty terms with their imposed distribution are used to express the association between the different individuals in a cluster. Copula models in contrast assume that the joint survival function of the individuals within a cluster is given by a copula function, evaluated in the marginal survival function of each individual. It is the copula function which describes the association between the lifetimes within a cluster. A major disadvantage of the present copula models over the frailty models is that the size of the different clusters must be small and equal to set up manageable estimation procedures for the different model parameters. We describe a copula model for clustered survival data where the clusters are allowed to be moderate to large and varying in size by considering the class of Archimedean copulas with completely monotone generator. We develop both one- and two-stage estimators for the copula parameters. Furthermore we show the consistency and asymptotic normality of these estimators. Finally, we perform a simulation study to investigate the finite sample properties of the estimators. We illustrate the method on a data set containing the time to first insemination in cows, with cows clustered in herds.

Confidence intervals for the difference between two median survival times for clustered survival data

ABSTRACTClustered survival data arise often in clinical trial design, where the correlated subunits from the same cluster are randomized to different treatment groups. Under such design, we consider the problem of constructing confidence interval for the difference of two median survival time given the covariates. We use Cox gamma frailty model to account for the within-cluster correlation. Based on the conditional confidence intervals, we can identify the possible range of covariates over which the two groups would provide different median survival times. The associated coverage probability and the expected length of the proposed interval are investigated via a simulation study. The implementation of the confidence intervals is illustrated using a real data set.

Spatial Data Analysis.

With increasing accessibility to geographic information systems (GIS) software, statisticians and data analysts routinely encounter scientific data sets with geocoded locations. This has generated considerable interest in statistical modeling for location-referenced spatial data. In public health, spatial data routinely arise as aggregates over regions, such as counts or rates over counties, census tracts, or some other administrative delineation. Such data are often referred to as areal data. This review article provides a brief overview of statistical models that account for spatial dependence in areal data. It does so in the context of two applications: disease mapping and spatial survival analysis. Disease maps are used to highlight geographic areas with high and low prevalence, incidence, or mortality rates of a specific disease and the variability of such rates over a spatial domain. They can also be used to detect hot spots or spatial clusters that may arise owing to common environmental, demographic, or cultural effects shared by neighboring regions. Spatial survival analysis refers to the modeling and analysis for geographically referenced time-to-event data, where a subject is followed up to an event (e.g., death or onset of a disease) or is censored, whichever comes first. Spatial survival analysis is used to analyze clustered survival data when the clustering arises from geographical regions or strata. Illustrations are provided in these application domains.