Frailty Models in Public Health

Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyse the bivariate data on related survival times (e.g., matched pairs experiments, twin or family data), the shared frailty models were suggested. Shared frailty models are used despite their limitations. To overcome their disadvantages correlated frailty models may be used. In this paper, we introduce the gamma correlated frailty models based on reversed hazard rate (RHR) with three different baseline distributions namely, the generalised log-logistic type I, the generalised log-logistic type II and the modified inverse Weibull. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin dataset and a better model is suggested.

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.

ABSTRACTThe unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.

Due to the unavailability of complete data in various circumstances in biological, epidemiological, and medical studies, the analysis of censored data is very common among practitioners. But the analysis of bivariate censored data is not a regular mechanism because it is not necessary to always have independent data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in the data. Ignoring observed and unobserved covariates may have objectionable consequences. But it is not easy to find that whether there is any effect of the unobserved covariate or not. Shared frailty models are the viable choice to counter such scenarios. However, due to certain restrictions such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution generalized Lindley (GL) for reversed hazard rate (RHR) setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under the RHR setup. By assuming exponential Gumbel (EG) and generalized inverted exponential (GIE) baseline distributions, we propose a new class of shared frailty models based on RHR. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been performed for the comparison of models. We analyze Australian twin data and suggest a better model.

Frailty models are used in univariate data to account for individual heterogeneity. In the popular gamma frailty model the marginal hazard has the form of a Burr model. Although the Burr model is very useful and can offer insight on the data, it is far from perfect. The estimation of the covariate effects is linked to the baseline hazard and this makes the model coefficients hard to interpret. At the same time, the frailties are assumed constant over time, while biological reasoning in some cases may indicate that frailties may be time dependent. In this paper we present a relaxation of the Burr model which is based on loosening the link between the estimation of the covariate effects and the baseline hazard. This can be achieved by replacing the cumulative baseline hazard in the Burr model by a set of time functions, and the frailty variance by a vector of coefficients directly estimated from the data using a partial likelihood. We illustrate the similarities of the model with the Burr model and a further extension of the latter, a model with an autoregressive stochastic process for the frailty. We compare the models on simulated data sets with constant and time-dependent frailties and show how the relaxed Burr models performs on two different real data sets. We show that the relaxed Burr model serves as a good approximation to the Burr model when the frailty is constant, and furthermore it gives better results when the frailty is time dependent.

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

In this article, we present a frailty model using the generalized gamma distribution as the frailty distribution. It is a power generalization of the popular gamma frailty model. It also includes other frailty models such as the lognormal and Weibull frailty models as special cases. The flexibility of this frailty distribution makes it possible to detect a complex frailty distribution structure which may otherwise be missed. Due to the intractable integrals in the likelihood function and its derivatives, we propose to approximate the integrals either by Monte Carlo simulation or by a quadrature method and then determine the maximum likelihood estimates of the parameters in the model. We explore the properties of the proposed frailty model and the computation method through a simulation study. The study shows that the proposed model can potentially reduce errors in the estimation, and that it provides a viable alternative for correlated data. The merits of proposed model are demonstrated in analysing the effects of sublingual nitroglycerin and oral isosorbide dinitrate on angina pectoris of coronary heart disease patients based on the data set in Danahy et al. (sustained hemodynamic and antianginal effect of high dose oral isosorbide dinitrate. Circulation 1977; 55:381-387).

BackgroundSaudi Arabia’s health sector is experiencing a significant transformation toward an emphasis on the public health model. This model is a population-based approach to preventing and controlling disease, and its importance becomes evident during infectious outbreaks and pandemics, such as COVID-19. This study aimed to assess the awareness and attitudes of health students in Jazan toward the public health model.MethodsThis study applied a cross-sectional online survey. Data were collected from 3–18 November 2020 using Google Forms. A convenience sampling method was used with a final sample of 425 participants.ResultsMost participants (71%) were aware of the public health model, with an average score of 11.36 out of 16. Multiple regression analysis revealed a significant association between the awareness level of the public health model and participants’ demographics, namely, gender, major of study, year of study, and prior training in public health. Participants who completed public health training (β = 0.220) had higher awareness scores than others. On the other hand, participants from public health (β = −0.342), medicine (β = 0.164), and nursing in Jazan (β = 0.128) had higher awareness of the public health model than the reference group (Nursing at Addayer College). Addayer is an area located in the rural northeast of the Jazan region. In addition, final-year students (β = 0.113) had higher awareness of the public health model than the reference group (year 2 pre-final students). Female participants (β = −0.142) had lower awareness of the public health model than male participants. Most participants (95.3%) believed that the clinical care and public health models are essential for promoting people’s health. However, 4.7% of participants believed that clinical health care is more important than public health.ConclusionHealth students, who are future healthcare professionals, must understand and value the public health model to support the planned health system reforms. It is recommended to evaluate how the education and training of students in public health, medicine, and nursing in Jazan impact the understanding and views of this cohort on the public health model compared to those of students in other health-related majors.

A natural of survival analysis associated the modelling of time-to-failure, consider the time until death or failure. The frailty model could be a random effect unobserved information, wherever the random effect an increasing, impact of baseline hazard function. The frailty model provides a convenient way to introduce random effects, accounts for further variability from unobserved factors, and heterogeneity into models for survival information. This text planned to analyze the frailty gamma distribution has been active to the parameter distribution acting as Weibull, log logistic and log normal distributions with a naturally incidental variable so as to diagnose the prognostic cause that effect the infectious disease patients for survival time. Information analysis is performed victimization STATA software package.
 Keyword: Frailty model; Parametric Distribution; Gamma frailty model -2LL; Tuberculosis Patients

Many analyses in the epidemiological and the prognostic studies and in the studies of event history data require methods that allow for unobserved covariates or “frailties”. We consider the shared frailty model in the framework of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing lifetime data. In this paper, we consider shared gamma frailty model with bivariate exponential of Marshall and Olkin (1967) distribution as baseline hazard for bivariate survival times. We solve the inferential problem in a Bayesian framework with the help of a comprehensive simulation study and real data example. We fit the model to the real-life bivariate survival data set of diabetic retinopathy data. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model and then compare the true values of the parameters with the estimated values for different sample sizes.

In this article, we propose additive shared gamma frailty model and additive shared inverse Gaussian frailty model with Lindley as baseline distribution to analyze the infectious disease data set of McGilchrist and Aisbett. The Bayesian approach of Markov Chain Monte Carlo technique was employed to estimate the parameters involved in the models. A simulation study was also carried out to compare the true values and estimated values of the parameters. Comparison of proposed models and the existing models was also done by using Bayesian information criteria such as BIC, WBIC and Bayes factor. A better model was also recommended for infectious disease data.

Issue It is well accepted that public health decision makers should use the best available research evidence in their decision-making process. However, research evidence alone is insufficient to inform public health decision making. Description of the problem As new challenges to public health emerge, there can be a paucity of high quality research evidence to inform decisions on new topics. Public health decision makers must combine various sources of evidence with their public health expertise to make evidence-informed decisions. The National Collaborating Centre for Methods and Tools (NCCMT) has developed a model which combines research evidence with other critical sources of evidence that can help guide decision makers in evidence-informed decision making. Results The NCCMT's model for evidence-informed public health combines findings from research evidence with local data and context, community and political preferences and actions and evidence on available resources. The model has been widely used across Canada and worldwide, and has been integrated into many public health organizations' decision-making processes. The model is also used for teaching an evidence-informed public health approach in Masters of Public Health programs around the globe. The model provides a structured approach to integrating evidence from several critical sources into public health decision making. Use of the model helps ensure that important research, contextual and preference information is sought and incorporated. Lessons Next steps for the model include development of a tool to facilitate synthesis of evidence across all four domains. Although Indigenous knowledges are relevant for public health decision making and should be considered as part of a complete assessment the current model does not capture Indigenous knowledges. Key messages Decision making in public health requires integrating the best available evidence, including research findings, local data and context, community and political preferences and available resources. The NCCMT’s model for evidence-informed public health provides a structured approach to integrating evidence from several critical sources into public health decision making.

Survival analysis is a group of methods designed to track the association between an exposure variable and the probability of some discrete outcome over time. Some examples of applications of survival analysis include the time to relapse among current smokers who are abstaining, tracking medication nonadherence over time among those living with diabetes, and the prediction of mortality as a function of cognitive ability. We use this latter example to illustrate one approach to survival analysis from the field of cognitive epidemiology. In this chapter we seek to answer the question: is some aspect of executive functioning associated with time until mortality? To achieve this goal, we utilize one of the most important models in biostatistics and public health, the so-called Cox proportional hazards model (Cox 1972). This model will allow us to investigate the survival association of interest while adjusting for important confounding variables. Through this example, we hope that readers will be convinced of the importance of considering the time until an event occurs, as opposed to a binary version of the event, due to the gain in information that the former approach provides.

Hunter-gatherer populations are remarkable for their excellent metabolic and cardiovascular health and thus are often used as models in public health, in an effort to understand the root, evolutionary causes of non-communicable diseases. Here, we review recent work on health, activity, energetics and diet among hunter-gatherers and other small-scale societies (e.g. subsistence farmers, horticulturalists and pastoralists), as well as recent fossil and archaeological discoveries, to provide a more comprehensive perspective on lifestyle and health in these populations. We supplement these analyses with new data from the Hadza, a hunter-gatherer population in northern Tanzania. Longevity among small-scale populations approaches that of industrialized populations, and metabolic and cardiovascular disease are rare. Obesity prevalence is very low (<5%), and mean body fat percentage is modest (women: 24-28%, men: 9-18%). Activity levels are high, exceeding 100mind-1 of moderate and vigorous physical activity, but daily energy expenditures are similar to industrialized populations. Diets in hunter-gatherer and other small-scale societies tend to be less energy dense and richer in fibre and micronutrients than modern diets but are not invariably low carbohydrate as sometimes argued. A more integrative understanding of hunter-gatherer health and lifestyle, including elements beyond diet and activity, will improve public health efforts in industrialized populations.

Frailty models are used in the survival analysis to account for the unobserved heterogeneityin individual risks to disease and death. To analyze the bivariate data on relatedsurvival times (e.g. matched pairs experiments, twin or family data), the shared frailtymodels were suggested. In this manuscript, we propose a new mixture shared inverse Gaussian frailty model based on modified Weibull as baseline distribution. The Bayesian approach of Markov Chain Monte Carlo technique is employed to estimate the parameters involved in the models. In addition, a simulation study is performed to compare the true values of the parameters with the estimated values. A comparison with the existing model was done by using Bayesian comparison techniques. A better model for infectious disease data related to kidney infection is suggested.