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

Abstract

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.

Keywords: Computational mathematics; Dependence meta-analytic; Hierarchical Bayesian delta-splitting; Mathematics.

Figure 1

Trace plots of ${\beta }_0,\mathrm{...},{\beta }_7$ for the HBDS model.

Figure 2

Density plots of ${\beta }_0,\mathrm{...},{\beta }_7$ for the HBDS model.

Figure 3

Density plot of $\tau$ for the HBDS model.

Figure 4

Trace plot of $\tau$ for the HBDS model.

Figure 5

(a) Density plot of ${\beta }_0$ and (b) trace plot of ${\beta }_0$ (case study).