scholarly journals The Generalized Gamma Shared Frailty Model under Different Baseline Distributions

Author(s):  
Sukhmani Sidhu ◽  
Kanchan Jain ◽  
Suresh K. Sharma Sharma

In the analysis of clustered survival data, shared frailty models are often used when observations in the same group share common unknown risk factors or frailty. There is dependence in the event times belonging to the same group, while event times from different groups are conditionally independent given their covariates. In such models, the known effect on survival time is described using the baseline distribution and regression coefficients while the unknown effect is described through a frailty distribution. In this paper, the Gompertz, log-logistic, and generalized exponential distributions are studied as baseline distributions, under a shared frailty effect described by the generalized gamma distribution. Their hazard functions have been compared and their applicability under different settings and performance with generalized gamma frailty has been explored. These models are fitted to three real life datasets using Bayesian estimation methods and compared using the Bayesian Information Criteria (AIC, BIC, and DIC) and the Bayes Factor.

2019 ◽  
Vol 29 (8) ◽  
pp. 2295-2306 ◽  
Author(s):  
MC Jones ◽  
Angela Noufaily ◽  
Kevin Burke

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.


2017 ◽  
Vol 33 (1) ◽  
pp. 277-297 ◽  
Author(s):  
Sukhmani Sidhu ◽  
Kanchan Jain ◽  
Suresh Kumar Sharma

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Omar Alzeley ◽  
Ehab M. Almetwally ◽  
Ahmed M. Gemeay ◽  
Huda M. Alshanbari ◽  
E. H. Hafez ◽  
...  

In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient’s survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type-I censored data.


2020 ◽  
Vol 30 (Supplement_5) ◽  
Author(s):  
◽  

Abstract A Burden of Disease (BoD) approach can be used to summarise the debilitating effects of morbidity and premature mortality in a population in a consistent and comparable manner. Summary measures of population health such as the Disability-Adjusted Life Year (DALY) have become key metrics for quantifying burden of disease. DALYs quantify the health gap between a life lived in perfect health and current health status, as the number of healthy life years lost due to illness (Years Lived with Disability, YLDs) and premature death (Years of Life Lost, YLLs). DALYs combine the effects of morbidity and mortality in an equitable way, and can therefore be used to identify the leading causes of disease or injury that cause BoD and to quantify the relative importance of specific risk factors. BoD studies are becoming an increasingly popular way to assess national and local population health as a means to influence national and local policy decisions. The increasing prominence of the burden of disease approach, however, comes at a cost. Calculations of DALYs involve multiple components and as such can be difficult for people to interpret. Burden of disease methodology is complex and highly data intensive, which has led to major disparities across researchers and nations in their capacity to perform studies, to interpret the soundness of available estimates, or to evidence and advocate for the use of particular methodological choices. In this skills-building seminar, we will give an overview of the methodology of calculating the DALY. It will outline the single steps to be undertaken, and the necessary assumptions that have to be taken, on the way to the calculation of the DALYs. This workshop will be supported by technical presentations from burden of disease experts about different choices of estimation methods to calculate both the fatal burden (YLL) and the non-fatal burden (YLD). Throughout the presentations, cerebrovascular disease will be used as a case study, giving a complete, real-life example of how DALYs are calculated. Overall, the aim is to demonstrate the importance of the choices researchers make when designing and interpreting BoD studies as a means of supporting evidence-based decision making. The workshop will foresee ample time for interaction with the audience and discussion of the implications of the different methodological choices. Key messages Although burden of disease methodology is complex, with calculations of DALYs involving multiple components, simple roadmaps can be created to enhance methodological knowledge. The choices and assumptions researchers make are important when designing and interpreting burden of disease studies.


Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 700
Author(s):  
Belén Pérez-Sánchez ◽  
Martín González ◽  
Carmen Perea ◽  
Jose J. López-Espín

Simultaneous Equations Models (SEM) is a statistical technique widely used in economic science to model the simultaneity relationship between variables. In the past years, this technique has also been used in other fields such as psychology or medicine. Thus, the development of new estimating methods is an important line of research. In fact, if we want to apply the SEM to medical problems with the main goal being to obtain the best approximation between the parameters of model and their estimations. This paper shows a computational study between different methods for estimating simultaneous equations models as well as a new method which allows the estimation of those parameters based on the optimization of the Bayesian Method of Moments and minimizing the Akaike Information Criteria. In addition, an entropy measure has been calculated as a parameter criteria to compare the estimation methods studied. The comparison between those methods is performed through an experimental study using randomly generated models. The experimental study compares the estimations obtained by the different methods as well as the efficiency when comparing solutions by Akaike Information Criteria and Entropy Measure. The study shows that the proposed estimation method offered better approximations and the entropy measured results more efficiently than the rest.


2021 ◽  
Vol 10 (1) ◽  
Author(s):  
K. M. J. Krishna ◽  
T. Traison ◽  
Sejil Mariya Sebastian ◽  
Preethi Sara George ◽  
Aleyamma Mathew

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.


2019 ◽  
Vol 14 (5) ◽  
pp. 590-597 ◽  
Author(s):  
Richard Johnston ◽  
Roisin Cahalan ◽  
Laura Bonnett ◽  
Matthew Maguire ◽  
Alan Nevill ◽  
...  

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.


Sign in / Sign up

Export Citation Format

Share Document