scholarly journals Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

2021 ◽  
Author(s):  
Chong Zhong ◽  
Zhihua Ma ◽  
Junshan Shen ◽  
Catherine Liu
Keyword(s):  
Survival Analysis ◽  
Dirichlet Process ◽  
Survival Function ◽  
Frailty Model ◽  
Survival Models ◽  
Bayesian Paradigm ◽  
Posterior Sampling ◽  
Posterior Inference ◽  
Shared Frailty Model ◽  
Shared Frailty

Bayesian paradigm takes advantage of well-fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this chapter, we aim to display the latest tendency in Bayesian computing, in the sense of automating the posterior sampling, through a Bayesian analysis of survival modeling for multivariate survival outcomes with the complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of the ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis, and Stan relaxes the posterior inference.

scholarly journals A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

2019 ◽  
Vol 29 (8) ◽  
pp. 2295-2306 ◽  
Author(s):  
MC Jones ◽  
Angela Noufaily ◽  
Kevin Burke
Keyword(s):  
Survival Analysis ◽  
Weibull Distribution ◽  
Survival Data ◽  
Frailty Model ◽  
Weibull Model ◽  
Flexible Parametric Model ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
Power Variance ◽  
Parametric Survival

We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we argued in favour of an adapted form of the ‘power generalized Weibull’ distribution as an attractive vehicle for univariate parametric survival analysis. Here, we additionally observe a frailty relationship between a power generalized Weibull distribution with one value of the parameter which controls distributional choice within the family and a power generalized Weibull distribution with a smaller value of that parameter. We exploit this relationship to propose a bivariate shared frailty model with power generalized Weibull marginal distributions linked by the BB9 or ‘power variance function’ copula, then change it to have adapted power generalized Weibull marginals in the obvious way. The particular choice of copula is, therefore, natural in the current context, and the corresponding bivariate adapted power generalized Weibull model a novel combination of pre-existing components. We provide a number of theoretical properties of the models. We also show the potential of the bivariate adapted power generalized Weibull model for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes.

scholarly journals K-means for shared frailty models

2022 ◽  
Vol 22 (1) ◽  
Author(s):  
Usha Govindarajulu ◽  
Sandeep Bedi
Keyword(s):  
Survival Analysis ◽  
Frailty Model ◽  
Real Data ◽  
Current Data ◽  
Frailty Models ◽  
Unmeasured Confounding ◽  
Real Dataset ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
Grouping Algorithm

Abstract Background The purpose of this research was to see how the k-means algorithm can be applied to survival analysis with single events per subject for defining groups, which can then be modeled in a shared frailty model to further allow the capturing the unmeasured confounding not already explained by the covariates in the model. Methods For this purpose we developed our own k-means survival grouping algorithm to handle this approach. We compared a regular shared frailty model with a regular grouping variable and a shared frailty model with a k-means grouping variable in simulations as well as analysis on a real dataset. Results We found that in both simulations as well as real data showed that our k-means clustering is no different than the typical frailty clustering even under different situations of varied case rates and censoring. It appeared our k-means algorithm could be a trustworthy mechanism of creating groups from data when no grouping term exists for including in a frailty term in a survival model or comparing to an existing grouping variable available in the current data to use in a frailty model.

scholarly journals Random effect bivariate survival models and stochastic comparisons

2010 ◽  
Vol 47 (02) ◽  
pp. 426-440 ◽  
Author(s):  
Ramesh C. Gupta ◽  
Rameshwar D. Gupta
Keyword(s):  
Random Effect ◽  
Random Effect Model ◽  
Frailty Model ◽  
Survival Models ◽  
Survival Functions ◽  
Stochastic Comparisons ◽  
Effect Model ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
The Relationship

In this paper we propose a general bivariate random effect model with special emphasis on frailty models and environmental effect models, and present some stochastic comparisons. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well-known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

scholarly journals Random effect bivariate survival models and stochastic comparisons

2010 ◽  
Vol 47 (2) ◽  
pp. 426-440 ◽  
Author(s):  
Ramesh C. Gupta ◽  
Rameshwar D. Gupta
Keyword(s):  
Random Effect ◽  
Random Effect Model ◽  
Frailty Model ◽  
Survival Models ◽  
Survival Functions ◽  
Stochastic Comparisons ◽  
Effect Model ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
The Relationship

In this paper we propose a general bivariate random effect model with special emphasis on frailty models and environmental effect models, and present some stochastic comparisons. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well-known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

scholarly journals Training Load and Baseline Characteristics Associated With New Injury/Pain Within an Endurance Sporting Population: A Prospective Study

2019 ◽  
Vol 14 (5) ◽  
pp. 590-597 ◽  
Author(s):  
Richard Johnston ◽  
Roisin Cahalan ◽  
Laura Bonnett ◽  
Matthew Maguire ◽  
Alan Nevill ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Frailty Model ◽  
Training Load ◽  
Moving Averages ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
History Of ◽  
Baseline Characteristics ◽  
A Prospective Study ◽  
Exponentially Weighted

Purpose: To determine the association between training-load (TL) factors, baseline characteristics, and new injury and/or pain (IP) risk in an endurance sporting population (ESP). Methods: Ninety-five ESP participants from running, triathlon, swimming, cycling, and rowing disciplines initially completed a questionnaire capturing baseline characteristics. TL and IP data were submitted weekly over a 52-wk study period. Cumulative TL factors, acute:chronic workload ratios, and exponentially weighted moving averages were calculated. A shared frailty model was used to explore time to new IP and association to TL factors and baseline characteristics. Results: 92.6% of the ESP completed all 52 wk of TL and IP data. The following factors were associated with the lowest risk of a new IP episode: (a) a low to moderate 7-d lag exponentially weighted moving averages (0.8–1.3: hazard ratio [HR] = 1.21; 95% confidence interval [CI], 1.01–1.44; P = .04); (b) a low to moderate 7-d lag weekly TL (1200–1700 AU: HR = 1.38; 95% CI, 1.15–1.65; P < .001); (c) a moderate to high 14-d lag 4-weekly cumulative TL (5200–8000 AU: HR = 0.33; 95% CI, 0.21–0.50; P < .001); and (d) a low number of previous IP episodes in the preceding 12 mo (1 previous IP episode: HR = 1.11; 95% CI, 1.04–1.17; P = .04). Conclusions: To minimize new IP risk, an ESP should avoid high spikes in acute TL while maintaining moderate to high chronic TLs. A history of previous IP should be considered when prescribing TLs. The demonstration of a lag between a TL factor and its impact on new IP risk may have important implications for future ESP TL analysis.

scholarly journals A time-varying shared frailty model with application to infectious diseases

2014 ◽  
Vol 8 (1) ◽  
pp. 430-447 ◽  
Author(s):  
Doyo G. Enki ◽  
Angela Noufaily ◽  
C. Paddy Farrington
Keyword(s):  
Infectious Diseases ◽  
Frailty Model ◽  
Time Varying ◽  
Shared Frailty Model ◽  
Shared Frailty
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