- Title
- Meta-analysis adjusting for heterogeneity, dependence and non-normality: a Bayesian parametric approach
- Creator
- Junaidi, S. Si
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2015
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Independence and dependence between studies in meta-analysis are assumptions which are imposed on the structure of hierarchical Bayesian meta-analytic models. Whilst independence assumes that two or more studies have no correlation in meta-analysis, dependence can occur as a result of study reports using the same data or authors (Stevens & Taylor, 2009). In this thesis, the relaxation of the assumption of independence, and/or of a normal distribution for the true study effects is investigated. A variety of statistical meta-analytic models were developed and extended in this thesis. These include the DuMouchel (DuMouchel, 1990) model and hierarchical Bayesian meta-regression (HBMR) (Jones et al., 2009) model, which assume independence within and between studies or between subgroups. Also investigated were the hierarchical Bayesian linear model (HBLM) (Stevens, 2005) and hierarchical Bayesian delta-splitting (HBDS) (Stevens & Taylor, 2009) model, which allow for dependence between studies and sub-studies, introducing dependency at the sampling and hierarchical levels. Overall the General Bayesian Linear Model (GBLM) theorems, the Gibbs sampler, the Metropolis-Hasting and the Metropolis within Gibbs algorithms were shown to be produce good estimates for specific models. The analytical forms of the joint posterior distributions of all parameters for the DuMouchel and the HBMR models were derived using the general Bayesian linear model (GBLM) theorems; with models presented in the form of matrices to which the theorems could be directly applied. The GBLM theorems were shown to be useful alternative meta-analytic approaches. The Gibbs sampler algorithm was demonstrated to be an appropriate approach for approximating the parameters of the DuMouchel model, for which sensitivity analyses were conducted by imposing different prior distributions at the study level. In contrast in the HBMR model, different prior specifications at the subgroup level were imposed. An extended GBLM theorem was used to approximate the joint posterior distribution of parameters in the HBMR, given the analytical derivation of the posterior distribution for the HBMR model can be computationally intractable due to the integration of multiple functions. The DuMouchel model and the HBMR model developed were demonstrated on a data set related to the incidence of Ewing’s sarcoma (Honoki et al., 2007) and on a study relating to exposure to certain chemicals and reproductive health (Jones et al., 2009), respectively. Consistency of results suggested that the GBLM Theorem and the Gibbs sampler algorithm were good alternative approaches to parameter estimation for the DuMouchel and HBMR models. Parameter estimates were generally not sensitive to the imposition of different prior distributions on the mean and variance for the DuMouchel model, and were close to the true values when different values were specified for the hyper-parameters for the HBMR model, indicating robust models. The HBLM and HBDS models were introduced to allow for dependency at the sampling and hierarchical levels. The Gibbs sampler and Metropolis within Gibbs algorithms were used to estimate the joint posterior distributions of all parameters for the HBLM and HBDS models, respectively. The Gibbs sampler algorithm was shown to successfully approximate the joint posterior distribution of parameters in the HBLM. The analytical form of the HBLM for the l-dependence group was derived by calculating the conditional posterior distribution of each parameter, as the distributions were in standard form. The joint posterior distribution of all parameters for the HBDS model, however, was derived using the Metropolis within Gibbs algorithm, chosen as the conditional posterior distributions of some parameters were in non-standard form. The formula for the joint posterior distribution was tested successfully on studies to assess the effects of native-language vocabulary aids on second language reading. Non-normal analogues of the independent and dependent DuMouchel and HBLM were developed in the thesis. The multivariate normal distribution at the true study effects for the DuMouchel model and the HBLM being replaced by the non-central multivariate t distribution. The joint posterior distribution of all parameters for the non-normal DuMouchel model and the non-normal HBLM were approximated using the Metropolis-Hasting algorithm due to its ability to deal with the non-standard form of conditional posterior distribution of parameters. Estimation of parameters of the non-normal models was successfully conducted using R. The Metropolis-Hasting algorithm was demonstrated to be a useful approach by which to estimate the joint posterior distribution for the hierarchical Bayesian model when a non-standard form of the joint posterior is encountered. It is shown that conducting a meta-analysis which allows for dependency and/or a non-normal distribution at the true study effects for hierarchical Bayesian models can lead to good overall conclusions.
- Subject
- meta-analysis; heterogeneity; dependence; non-normality; Bayesian
- Identifier
- http://hdl.handle.net/1959.13/1296543
- Identifier
- uon:19277
- Rights
- Copyright 2015 S. Si Junaidi
- Language
- eng
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