Frailty Models

2016 ◽  
pp. 461-477
Keyword(s):  
Frailty Models

Gamma frailty model for survival risk estimation: an application to cancer data

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
K. M. J. Krishna ◽  
T. Traison ◽  
Sejil Mariya Sebastian ◽  
Preethi Sara George ◽  
Aleyamma Mathew
Keyword(s):  
Proportional Hazards ◽  
Risk Estimation ◽  
Univariate Analysis ◽  
Frailty Model ◽  
Cox Proportional Hazards ◽  
Information Criteria ◽  
Frailty Models ◽  
Event Analysis ◽  
Global Test ◽  
Cancer Data

Abstract Objectives: In time to event analysis, the risk for an event is usually estimated using Cox proportional hazards (CPH) model. But CPH model has the limitation of biased estimate due to unobserved hidden heterogeneity among the covariates, which can be tackled using frailty models. The best models were usually being identified using Akaike information criteria (AIC). Apart from AIC, the present study aimed to assess predictability of risk models using survival concordance measure. Methods: CPH model and frailty models were used to estimate the risk for breast cancer patient survival, and the frailty variable was assumed to follow gamma distribution. Schoenfeld global test was used to check the proportionality assumption. Survival concordance, AIC and simulation studies were used to identify the significance of frailty. Results: From the univariate analysis it was observed that for the covariate age, the frailty has a significant role (θ = 2.758, p-value: 0.0004) and the corresponding hazard rate was 1.93 compared to that of 1.38 for CPH model (age > 50 vs. ≤ 40). Also the covariates radiotherapy and chemotherapy were found to be significant (θ = 5.944, p-value: <0.001 and θ = 16, p-value: <0.001 respectively). Even though there were only minor differences in hazard rates, the concordance was higher for frailty than CPH model for all the covariates. Further the simulation study showed that the bias and root mean square error (RMSE) obtained for both the methods was almost the same and the concordance measures were higher for frailty model by 12–15%. Conclusions: We conclude that the frailty model is better compared to CPH model as it can account for unobserved random heterogeneity, and if the frailty coefficient doesn’t have an effect it gives exactly the same risk as that of CPH model and this has been established using survival concordance.

Correlated gamma frailty models for bivariate survival time data

2018 ◽  
Vol 28 (10-11) ◽  
pp. 3437-3450
Author(s):  
Adelino Martins ◽  
Marc Aerts ◽  
Niel Hens ◽  
Andreas Wienke ◽  
Steven Abrams
Keyword(s):  
Survival Time ◽  
Frailty Models ◽  
Current Status Data ◽  
Current Status ◽  
Mortality Data ◽  
Time Data ◽  
Additive Decomposition ◽  
Bivariate Survival ◽  
Gamma Frailty ◽  
Survival Time Data

Frailty models have been developed to quantify both heterogeneity as well as association in multivariate time-to-event data. In recent years, numerous shared and correlated frailty models have been proposed in the survival literature allowing for different association structures and frailty distributions. A bivariate correlated gamma frailty model with an additive decomposition of the frailty variables into a sum of independent gamma components was introduced before. Although this model has a very convenient closed-form representation for the bivariate survival function, the correlation among event- or subject-specific frailties is bounded above which becomes a severe limitation when the values of the two frailty variances differ substantially. In this article, we review existing correlated gamma frailty models and propose novel ones based on bivariate gamma frailty distributions. Such models are found to be useful for the analysis of bivariate survival time data regardless of the censoring type involved. The frailty methodology was applied to right-censored and left-truncated Danish twins mortality data and serological survey current status data on varicella zoster virus and parvovirus B19 infections in Belgium. From our analyses, it has been shown that fitting more flexible correlated gamma frailty models in terms of the imposed association and correlation structure outperforms existing frailty models including the one with an additive decomposition.

Frailty models: Applications to biomedical and genetic studies

2011 ◽  
Vol 30 (22) ◽  
pp. 2754-2764 ◽  
Author(s):  
Usha S. Govindarajulu ◽  
Haiqun Lin ◽  
Kathryn L. Lunetta ◽  
R.B. D'Agostino
Keyword(s):  
Frailty Models ◽  
Genetic Studies
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