Bayesian analysis of meta-analytic models incorporating dependency: new approaches for the hierarchical Bayesian delta-splitting model

Dependence between studies in meta-analysis is an assumption which is imposed on the structure of hierarchical Bayesian meta-analytic models. Dependence in meta-analysis can occur as a result of study reports using the same data or from the same authors. In this paper, the hierarchical Bayesian delta-splitting (HBDS) model (Steven and Taylor, 2009), which allows for dependence between studies and sub-studies by introducing dependency at the sampling and hierarchical levels, is developed using Bayesian approaches. Parameter estimation obtained from the joint posterior distributions of all parameters for the HBDS model was conducted using the Metropolis within Gibbs algorithm. The estimation of parameters for simulation studies using R code confirmed the consistency of the model parameters. These parameters were then tested successfully on studies to assess the effects of native-language vocabulary aids on second language reading as a case study.

[1]  John R. Stevens Meta-analytic approaches for microarray data , 2005 .

[2]  Yun Chen,et al.  An assessment of a TNF polymorphic marker for the risk of HCV infection: meta-analysis and a new clinical study design. , 2009, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

[3]  Evangelos Kontopantelis,et al.  Performance of statistical methods for meta-analysis when true study effects are non-normally distributed: A simulation study , 2012, Statistical methods in medical research.

[4]  Jennifer G. Robinson,et al.  Meta-analysis of the relationship between non-high-density lipoprotein cholesterol reduction and coronary heart disease risk. , 2009, Journal of the American College of Cardiology.

[5]  Keith R Abrams,et al.  Meta‐analysis of heterogeneously reported trials assessing change from baseline , 2005, Statistics in medicine.

[6]  K. Beard,et al.  A Meta‐Analytic Review of Corridor Effectiveness , 2010, Conservation biology : the journal of the Society for Conservation Biology.

[7]  Claudio J. Verzilli,et al.  A Comparison of Bayesian and Frequentist Approaches to Incorporating External Information for the Prediction of Prostate Cancer Risk , 2012, Genetic epidemiology.

[8]  John R. Stevens,et al.  Metahdep: Meta-analysis of Hierarchically Dependent Gene Expression Studies , 2009, Bioinform..

[9]  P. Gurian,et al.  Variance in Bacillus anthracis virulence assessed through Bayesian hierarchical dose–response modelling , 2012, Journal of applied microbiology.

[10]  William DuMouchel,et al.  Computer-modeling and Graphical Strategies for Meta-analysis , 2000 .

[11]  Erin E. Joyce Which Words Should Be Glossed in L2 Reading Materials? A Study of First, Second, and Third Semester French Students' Recall. , 1997 .

[12]  John R. Stevens,et al.  Hierarchical Dependence in Meta-Analysis , 2009 .

[13]  Peter D. Hoff,et al.  A First Course in Bayesian Statistical Methods , 2009 .

[14]  Jeffrey E. Harris,et al.  Bayes Methods for Combining the Results of Cancer Studies in Humans and other Species , 1983 .

[15]  Russell B. Millar,et al.  Non‐linear state space modelling of fisheries biomass dynamics by using Metropolis‐Hastings within‐Gibbs sampling , 2000 .

[16]  Evaluation of underlying risk as a source of heterogeneity in meta-analyses: a simulation study of Bayesian and frequentist implementations of three models. , 2007, Preventive veterinary medicine.

[17]  Geoffrey J. McLachlan,et al.  The 2nd special issue on advances in mixture models , 2014, Computational Statistics & Data Analysis.

[18]  David J. Lunn,et al.  Fully Bayesian hierarchical modelling in two stages, with application to meta-analysis , 2013, Journal of the Royal Statistical Society. Series C, Applied statistics.