Parameter estimation for stage-duration models

Author: Thi Pham

Pham, Thi, 2017 Parameter estimation for stage-duration models, Flinders University, School of Computer Science, Engineering and Mathematics

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Multi-stage time evolving models, so called stage-duration models, have been studied in various biological contexts. We consider stage-duration models that describe single cohort stage-frequency data with destructive samples. These models can give an understanding of the maturation of biological systems, industrial processes or the progression of disease. The main goal of this thesis is to estimate the stage-dependent maturation parameters and hazard rate parameters of the models. The contributions of the thesis are as follows: First, we obtain novel methods for estimating maturation parameters in models with stage-wise constant hazard rates and with linear time-dependent hazard rates. We use Laplace transform methods with the assumption of constant scale parameters or constant shape parameters. The key result is the exploration of the relationships between the stage-dependent maturation parameters in each stage. Second, we obtain methods for estimating maturation parameters and hazard rate parameters without imposing unrealistic conditions as in previous studies. In particular, by using a Bayesian approach, we derive estimators of the maturation parameters and the hazard rate parameters in each stage simultaneously, without initial knowledge about maturation parameters. The Metropolis-Hastings (MH) algorithm based on deterministic transformations is applied in order to accelerate the convergence of the Markov process. We embed the relationships of the stage-dependent maturation parameters within the deterministic MH algorithms. The number of sampling times for the deterministic MH methods is reduced compared to the Laplace transform methods. Third, the application of the methodology in the models is evaluated using both simulated data and case studies including cattle parasitic data and breast development data of New Zealander schoolgirls. From the simulated data, results show that the proposed methods are able to estimate parameters in situations where non-trivial hazard rates apply. The methods also work well when the assumptions of maturation parameters are relaxed. From the case studies, the results show that parameter estimation is better using these methods in comparison to Laplace transform methods in previous studies.

Keywords: Multi-stage models, Stage duration, Stage frequency data, Bayesian analysis, Destructive samples.
Subject: Statistical Science thesis, Computer Science thesis, Mathematics thesis

Thesis type: Doctor of Philosophy
Completed: 2017
School: School of Computer Science, Engineering and Mathematics
Supervisor: Professor Jerzy Filar