The random-effects proportional hazards model with grouped survival data: a comparison between the grouped continuous and continuation ratio versions

2005 ◽  
Vol 168 (1) ◽  
pp. 83-94 ◽  
Author(s):  
Leonardo Grilli
Keyword(s):  
Random Effects ◽  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Hazards Model ◽  
Continuation Ratio

scholarly journals A Multilevel Hazards Model for Child Mortality In Nigeria

2019 ◽  
Vol 1 (1) ◽  
pp. 9-23
Author(s):  
Chukwu A.U ◽  
Oyamakin S.O ◽  
James-Daniel V.E
Keyword(s):  
Statistical Methods ◽  
Child Mortality ◽  
Random Effects ◽  
Survival Data ◽  
Multilevel Models ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Community Factors ◽  
Hazards Model ◽  
The Impact

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.

scholarly journals A tutorial on frailty models

2020 ◽  
Vol 29 (11) ◽  
pp. 3424-3454 ◽  
Author(s):  
Theodor A Balan ◽  
Hein Putter
Keyword(s):  
Random Effects ◽  
Recurrent Events ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Unobserved Heterogeneity ◽  
Frailty Models ◽  
Survival Outcomes ◽  
Time To Event ◽  
Homogeneous Population ◽  
Hazards Model

The hazard function plays a central role in survival analysis. In a homogeneous population, the distribution of the time to event, described by the hazard, is the same for each individual. Heterogeneity in the distributions can be accounted for by including covariates in a model for the hazard, for instance a proportional hazards model. In this model, individuals with the same value of the covariates will have the same distribution. It is natural to think that not all covariates that are thought to influence the distribution of the survival outcome are included in the model. This implies that there is unobserved heterogeneity; individuals with the same value of the covariates may have different distributions. One way of accounting for this unobserved heterogeneity is to include random effects in the model. In the context of hazard models for time to event outcomes, such random effects are called frailties, and the resulting models are called frailty models. In this tutorial, we study frailty models for survival outcomes. We illustrate how frailties induce selection of healthier individuals among survivors, and show how shared frailties can be used to model positively dependent survival outcomes in clustered data. The Laplace transform of the frailty distribution plays a central role in relating the hazards, conditional on the frailty, to hazards and survival functions observed in a population. Available software, mainly in R, will be discussed, and the use of frailty models is illustrated in two different applications, one on center effects and the other on recurrent events.

Modelling heterogeneity in survival data

1991 ◽  
Vol 28 (03) ◽  
pp. 695-701 ◽  
Author(s):  
Philip Hougaard
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Mixture Distribution ◽  
Survival Models ◽  
Risk Of Death ◽  
Hazards Model ◽  
Occupational Mortality ◽  
Heterogeneity Distribution ◽  
Biased Estimates

Ordinary survival models implicitly assume that all individuals in a group have the same risk of death. It may, however, be relevant to consider the group as heterogeneous, i.e. a mixture of individuals with different risks. For example, after an operation each individual may have constant hazard of death. If risk factors are not included, the group shows decreasing hazard. This offers two fundamentally different interpretations of the same data. For instance, Weibull distributions with shape parameter less than 1 can be generated as mixtures of constant individual hazards. In a proportional hazards model, neglect of a subset of the important covariates leads to biased estimates of the other regression coefficients. Different choices of distributions for the unobserved covariates are discussed, including binary, gamma, inverse Gaussian and positive stable distributions, which show both qualitative and quantitative differences. For instance, the heterogeneity distribution can be either identifiable or unidentifiable. Both mathematical and interpretational consequences of the choice of distribution are considered. Heterogeneity can be evaluated by the variance of the logarithm of the mixture distribution. Examples include occupational mortality, myocardial infarction and diabetes.

A Proportional Hazards Neural Network for Performing Reliability Estimates and Risk Prognostics for Mobile Systems Subject to Stochastic Covariates

2005 ◽  
Author(s):  
George M. Lloyd ◽  
Timothy Hasselman ◽  
Thomas Paez
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Mobile Systems ◽  
Linear Network ◽  
Model Free ◽  
Hazards Model ◽  
Reliability Estimates ◽  
Non Linear ◽  
Stochastic Covariates

We present a proportional hazards model (PHM) that establishes a framework suitable for performing reliability estimates and risk prognostics on complex multi-component systems which are transferred at arbitrary times among a discrete set of non-stationary stochastic environments. Such a scenario is not at all uncommon for portable and mobile systems. It is assumed that survival data, possibly interval censored, is available at several “typical” environments. This collection of empirical survival data forms the foundation upon which the basic effects of selected covariates are incorporated via the proportional hazards model. Proportional hazards models are well known in medical statistics, and can provide a variety of data-driven risk models which effectively capture the effects of the covariates. The paper describes three modifications we have found most suitable for this class of systems: development of suitable survival estimators that function well under realistic censoring scenarios, our modifications to the PHM which accommodate time-varying stochastic covariates, and implementation of said model in a non-linear network context which is itself model-free. Our baseline hazard is a parameterized reliability model developed from the empirical reliability estimates. Development of the risk score for arbitrary covariates arising from movement among different random environments is through interaction of the non-linear network and training data obtained from a Markov chain simulation based on stochastic environmental responses generated from Karhunen-Loe`ve models.

Multiplicative Piecewise Gamma in Survival Data Analysis

2014 ◽  
Vol 70 (1) ◽  
Author(s):  
Noraslinda Mohamed Ismail ◽  
Zarina Mohd Khalid ◽  
Norhaiza Ahmad
Keyword(s):  
Survival Data ◽  
Hazard Function ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Bayesian Estimator ◽  
Proportional Hazard ◽  
Proportional Hazard Model ◽  
Hazards Model ◽  
Proposed Model ◽  
Leukemia Data

The proportional hazard model is the most general of the regression models since it is not based on any assumptions concerning the nature or shape of the underlying survival distribution. The model assumes that the underlying hazard rate is a function of the covariates (independent variables) and there are no assumptions about the nature or shape of the hazard function. Proportional hazards model in survival analysis is used to estimate the effects of different covariates which was influenced by the survival data. This paper proposes the new multiplicative piecewise gamma in the hazard function using OpenBugs Statistical Packages. The proposed model is a flexible survival model for any types of non-informative censored data in estimating the parameters using Bayesian approach and also an alternative model to the existing model. We used the Markov Chain Monte Carlo method in computing the Bayesian estimator on leukemia data. The results obtained show that the proposed model can be an alternative to the existing multiplicative model since it can estimate the parameters using any types of survival data compared to the existing model that can only be used for leukemia data.  

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