Bayesian bivariate survival analysis using the power variance function copula

Generalizing the standard frailty models of survival analysis, we propose to model frailty as a weighted Lévy process. Hence, the frailty of an individual is not a fixed quantity, but develops over time. Formulae for the population hazard and survival functions are derived. The power variance function Lévy process is a prominent example. In many cases, notably for compound Poisson processes, quasi-stationary distributions of survivors may arise. Quasi-stationarity implies limiting population hazard rates that are constant, in spite of the continual increase of the individual hazards. A brief discussion is given of the biological relevance of this finding.

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

Statistical Methods in Medical Research ◽

10.1177/0962280219890893 ◽

2019 ◽

Vol 29 (8) ◽

pp. 2295-2306 ◽

Cited By ~ 1

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.

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The role of endoscopy after upper gastrointestinal bleeding in sub-Saharan Africa: A prospective observational cohort study

Malawi Medical Journal ◽

10.4314/mmj.v32i3.6 ◽

2020 ◽

Vol 32 (3) ◽

pp. 139-145

Author(s):

Jared Gallaher

Keyword(s):

Survival Analysis ◽

Hazard Ratio ◽

Physical Exam ◽

Sub Saharan Africa ◽

Diagnostic Endoscopy ◽

Tertiary Center ◽

Bivariate Survival Analysis ◽

Observational Cohort ◽

Sub Saharan

BackgroundUpper gastrointestinal (UGI) bleed is a common surgical disease in sub-Saharan Africa where there is often a lack of diagnostic and interventional adjuncts such as endoscopy. This study sought to characterize the role of endoscopy in management of acute UGI bleeding.Materials and MethodsThis is a prospective observational analysis of adults presenting with an UGI bleed to a tertiary center in Lilongwe, Malawi, over two years. Patients were classified as having no endoscopy, diagnostic endoscopy, or endoscopy with variceal banding. Bivariate, survival analysis, and logistic regression analyses were used to compare intervention cohorts.Results293 patients were included with 49 patients (16.7%) receiving endoscopy with banding, 65 (22.2%) patients receiving diagnostic endoscopy only, and 179 (61.1%) receiving no endoscopy. Upon survival analysis comparing to the no endoscopy group, cox hazard modelling showed an adjusted hazard ratio over 30 days of 0.12 (95% CI 0.02, 0.88, p=0.038) for the endoscopic banding group and a hazard ratio of 0.39 (95% CI 0.13, 1.16, p=0.090) for the diagnostic endoscopy only group. Physical exam findings consistent with cirrhosis and decreasing age were independent predictors of an endoscopic diagnosis of variceal bleeding.ConclusionEsophagogastric varices are a common cause of UGI bleeding in sub-Saharan Africa and can be predicted with age and physical exam findings. Endoscopy with variceal banding has a survival benefit for patients presenting with acute UGI bleed even with relatively low utilization. Appropriately triaging patients with likely variceal bleeding and improving endoscopy capacity would likely have a significant impact on mortality.

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Frailty models based on Lévy processes

Advances in Applied Probability ◽

10.1239/aap/1051201659 ◽

2003 ◽

Vol 35 (2) ◽

pp. 532-550 ◽

Cited By ~ 21

Author(s):

Håkon K. Gjessing ◽

Odd O. Aalen ◽

Nils Lid Hjort

Keyword(s):

Lévy Process ◽

Levy Process ◽

Frailty Models ◽

Hazard Rates ◽

Survival Functions ◽

Power Variance Function ◽

Fixed Quantity ◽

Power Variance ◽

The Individual ◽

Over Time

Generalizing the standard frailty models of survival analysis, we propose to model frailty as a weighted Lévy process. Hence, the frailty of an individual is not a fixed quantity, but develops over time. Formulae for the population hazard and survival functions are derived. The power variance function Lévy process is a prominent example. In many cases, notably for compound Poisson processes, quasi-stationary distributions of survivors may arise. Quasi-stationarity implies limiting population hazard rates that are constant, in spite of the continual increase of the individual hazards. A brief discussion is given of the biological relevance of this finding.

Download Full-text