---
title: "Meta-analysis"
chunk: 4/7
source: "https://en.wikipedia.org/wiki/Meta-analysis"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:26:08.077779+00:00"
instance: "kb-cron"
---

===== Bayesian framework =====
Specifying a Bayesian network meta-analysis model involves writing a directed acyclic graph (DAG) model for general-purpose Markov chain Monte Carlo (MCMC) software such as WinBUGS. In addition, prior distributions have to be specified for a number of the parameters, and the data have to be supplied in a specific format. Together, the DAG, priors, and data form a Bayesian hierarchical model. To complicate matters further, because of the nature of MCMC estimation, overdispersed starting values have to be chosen for a number of independent chains so that convergence can be assessed. Recently, multiple R software packages were developed to simplify the model fitting (e.g., metaBMA and RoBMA) and even implemented in statistical software with graphical user interface (GUI): JASP. Although the complexity of the Bayesian approach limits usage of this methodology, recent tutorial papers are trying to increase accessibility of the methods. Methodology for automation of this method has been suggested but requires that arm-level outcome data are available, and this is usually unavailable. Great claims are sometimes made for the inherent ability of the Bayesian framework to handle network meta-analysis and its greater flexibility. However, this choice of implementation of framework for inference, Bayesian or frequentist, may be less important than other choices regarding the modeling of effects (see discussion on models above).

===== Frequentist multivariate framework =====
On the other hand, the frequentist multivariate methods involve approximations and assumptions that are not stated explicitly or verified when the methods are applied (see discussion on meta-analysis models above). For example, the mvmeta package for Stata enables network meta-analysis in a frequentist framework. However, if there is no common comparator in the network, then this has to be handled by augmenting the dataset with fictional arms with high variance, which is not very objective and requires a decision as to what constitutes a sufficiently high variance. The other issue is use of the random effects model in both this frequentist framework and the Bayesian framework. Senn advises analysts to be cautious about interpreting the 'random effects' analysis since only one random effect is allowed for but one could envisage many. Senn goes on to say that it is rather naıve, even in the case where only two treatments are being compared to assume that random-effects analysis accounts for all uncertainty about the way effects can vary from trial to trial. Newer models of meta-analysis such as those discussed above would certainly help alleviate this situation and have been implemented in the next framework.

===== Generalized pairwise modelling framework =====
An approach that has been tried since the late 1990s is the implementation of the multiple three-treatment closed-loop analysis. This has not been popular because the process rapidly becomes overwhelming as network complexity increases. Development in this area was then abandoned in favor of the Bayesian and multivariate frequentist methods which emerged as alternatives. Very recently, automation of the three-treatment closed loop method has been developed for complex networks by some researchers as a way to make this methodology available to the mainstream research community. This proposal does restrict each trial to two interventions, but also introduces a workaround for multiple arm trials: a different fixed control node can be selected in different runs. It also utilizes robust meta-analysis methods so that many of the problems highlighted above are avoided. Further research around this framework is required to determine if this is indeed superior to the Bayesian or multivariate frequentist frameworks. Researchers willing to try this out have access to this framework through a free software.

==== Diagnostic test accuracy meta-analysis ====
Diagnostic test accuracy (DTA) meta-analyses differ methodologically from those assessing intervention effects, as they aim to jointly synthesize pairs of sensitivity and specificity values. These parameters are typically analyzed using hierarchical models that account for the correlation between them and between-study heterogeneity. Two commonly used models are the bivariate random-effects model and the hierarchical summary receiver operating characteristic (HSROC) model. These approaches are recommended by the Cochrane Handbook for Systematic Reviews of Diagnostic Test Accuracy and are widely used in reviews of screening tests, imaging tools, and laboratory diagnostics.
Beyond the standard hierarchical models, other approaches have been developed to address various complexities in diagnostic accuracy synthesis. These include methods that incorporate differences in threshold effects, account for covariates through meta-regression, or improve applicability by considering test setting and clinical variation. Some frameworks aim to adapt the synthesis to reflect intended use conditions more directly. These extensions are part of an evolving body of methodology that reflects growing experience in the field and increasing demands from clinical and policy decision-makers.

==== Aggregating IPD and AD ====
Meta-analysis can also be applied to combine IPD and AD. This is convenient when the researchers who conduct the analysis have their own raw data while collecting aggregate or summary data from the literature. The generalized integration model (GIM) is a generalization of the meta-analysis. It allows that the model fitted on the individual participant data (IPD) is different from the ones used to compute the aggregate data (AD). GIM can be viewed as a model calibration method for integrating information with more flexibility.