Exploring Methods of Estimating Heterogeneity Parameters in Statistical Meta-Analysis

It has been widely recognized that statistical meta-analysis is not only important for estimating average effect size from several studies; but also equally important for investigating and estimating potential sources of heterogeneity of those studies. While the former is known as analytic meta-analysis, we focus more on the latter, which is called exploratory meta-analysis. In meta-analyses, combining results from different studies is likely to imply the existence of heterogeneity due to systematic sources of variation and, possibly, random components which should be considered in a model for exploratory meta-analysis. We refer to the parameter (a scalar or a matrix) describing the variation of the random components as the "heterogeneity" parameter. When a meta-analysis is done, investigators should consider models which provide for heterogeneity regardless of the size of the heterogeneity parameter as measured by either a scalar quantifying variation (i.e., a variance) or the determinant of a positive definite matrix. This research develops an alternative estimation method, a "Hybrid" method for estimating heterogeneity parameters in random-effects meta-analysis. It is a "Hybrid" method because it combines the methods of both moments and iterations in the estimation procedures. Unlike the Sidik and Jonkman method the Hybrid method does not depend on the initial or crude value of the heterogeneity parameter, and it can also be extended to meta-regression and multivariate models. It is a method that provides a positive heterogeneity parameter estimate no matter how homogenous the studies are. In this dissertation, real and simulated data were used to compute the heterogeneity parameters and to compare the performances of the Hybrid method with other estimation methods including the DerSimonian and Laird (DL) method(1986), the maximum likelihood (ML) method (Sidik and Jonkman, 2007), and the restricted maximum likelihood (REML) method (Sidik and Jonkman, 2007). Coverage probabilities of the overall population effect size and bias of the heterogeneity parameter were the basis for comparison in the simulation for one-way and meta-regression models. This research extends to multivariate meta-analysis in random-effects models to compare the Hybrid method with other methods of multivariate meta-analysis. In addition to the Hybrid method, the extended version of Sidik and Jonkman method(2005) is also applied in estimating a matrix of heterogeneity parameters and evaluated against other methods, namely, the extended DerSimonian and Laird methods of Jackson, et al. (2009) and Chen, et al. (2012). In multivariate setup, the extended DL, the restricted maximum likelihood and the maximum likelihood methods are extensively discussed and compared with the underlying Hybrid and the Sidik and Jonkman methods in estimated heterogeneity matrices in terms of distance from the true matrix. Although there are several approaches and methods used in estimating the heterogeneity parameters in random-effects meta-analyses, the proposed Hybrid method is an attractive alternative due to several reasons: it always yields a unique positive value in the univariate case, and a positive definite matrixestimate in multivariate case with better performance in terms of bias from the true parameter and coverage rates closer to the nominal value.