Exploring Parameter Relations for Multi-Stage Models in Stage-Wise Constant and Time Dependent Hazard Rates

2016 ◽  
Vol 58 (3) ◽  
pp. 357-376 ◽  
Author(s):  
Hoa Pham ◽  
Alan Branford
Keyword(s):  
Time Dependent ◽  
Hazard Rates ◽  
Stage Models ◽  
Multi Stage ◽  
Parameter Relations

A Bayesian approach for multi-stage models with linear time-dependent hazard rate

2019 ◽  
Vol 25 (4) ◽  
pp. 307-316
Author(s):  
Hoa Pham ◽  
Huong T. T. Pham
Keyword(s):  
Hazard Rate ◽  
Linear Time ◽  
Simulated Data ◽  
Time Dependent ◽  
Stage Model ◽  
Stage Duration ◽  
Stage Models ◽  
Multi Stage ◽  
Mh Algorithm ◽  
Number Of Individuals

Abstract Multi-stage models have been used to describe progression of individuals which develop through a sequence of discrete stages. We focus on the multi-stage model in which the number of individuals in each stage is assessed through destructive samples for a sequence of sampling time. Moreover, the stage duration distributions of the model are effected by a time-dependent hazard rate. The multi-stage models become complex with a stage having time-dependent hazard rate. The main aim of this paper is to derive analytically the approximation of the likelihood of the model. We apply the approximation to the Metropolis–Hastings (MH) algorithm to estimate parameters for the model. The method is demonstrated by applying to simulated data which combine non-hazard rate, stage-wise constant hazard rate and time-dependent hazard rates in stage duration distributions.

A Bayesian approach for parameter estimation in multi-stage models

2018 ◽  
Vol 48 (10) ◽  
pp. 2459-2482 ◽  
Author(s):  
Hoa Pham ◽  
Darfiana Nur ◽  
Huong T. T. Pham ◽  
Alan Branford
Keyword(s):  
Parameter Estimation ◽  
Bayesian Approach ◽  
Stage Models ◽  
Multi Stage

Time-dependent deformations of concrete columns under different construction load histories

2019 ◽  
Vol 22 (8) ◽  
pp. 1845-1854 ◽  
Author(s):  
Dujian Zou ◽  
Chengcheng Du ◽  
Tiejun Liu ◽  
Jun Teng ◽  
Hanbin Cheng
Keyword(s):  
Prediction Models ◽  
Plain Concrete ◽  
Concrete Columns ◽  
In Situ Monitoring ◽  
Time Dependent ◽  
Construction Stage ◽  
Inappropriate Use ◽  
High Rise ◽  
Multi Stage ◽  
Axial Shortening

The adverse effects caused by differential axial shortening in high-rise buildings have received increasing attention with growing building height. However, the axial shortening analysis still lacks accuracy compared to the in-situ monitoring results of practical high-rise buildings during construction stage. It is imperative to identify the error sources, and the applicability of the current shortening prediction models should be test verified. In this study, 14 plain concrete columns were cast, and the multi-stage load method was applied to approximately simulate the loading history of axial concrete members during construction stage. The time-dependent deformations of loaded concrete specimens were measured, and a comparative analysis was conducted between test results and numerical prediction values. It is found that the measured deformations of multi-stage loading cases are all underestimated compared with predicted results, and this underestimation may be mainly caused by the inappropriate use of elastic modulus. It further indicates that the axial shortening analysis of high-rise buildings tends to underestimate the actual shortening value when the traditional calculation method is used. This study provides a reference for explaining the mismatch between the analytical results and the actual shortening values.

scholarly journals A new look at multi-stage models of cancer incidence

2018 ◽  
Author(s):  
Tyler Lian ◽  
Rick Durrett
Keyword(s):  
Branching Process ◽  
Probabilistic Approach ◽  
Process Models ◽  
Hyperbolic Partial Differential Equations ◽  
Main Method ◽  
Stage Models ◽  
Multi Stage ◽  
Cancer Initiation ◽  
Seer Data ◽  
The One

AbstractMulti-stage models have long been used in combination with SEER data to make inferences about the mechanisms underlying cancer initiation. The main method for studying these models mathematically has been the computation of generating functions by solving hyperbolic partial differential equations. Here, we analyze these models using a probabilistic approach similar to the one Durrett and Moseley [7] used to study branching process models of cancer. This more intuitive approach leads to simpler formulas and new insights into the behavior of these models. Unfortunately, the examples we consider suggest that fitting multi-stage models has very little power to make inferences about the number of stages unless parameters are constrained to take on realistic values.

scholarly journals Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

2018 ◽  
Author(s):  
Anthony J. Webster
Keyword(s):  
Complex Systems ◽  
Mathematical Framework ◽  
Failure Rates ◽  
Cancer Model ◽  
Engineering Project ◽  
Sums Of Random Variables ◽  
Stage Models ◽  
Engineering Project Management ◽  
Multi Stage ◽  
Rate Limiting

AbstractComplex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

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