Meta-regression is a meta-analysis that uses regression analysis to combine, compare, and synthesize research findings from multiple studies while adjusting for the effects of available covariates on a response variable.
A data set is aggregate when it consists of summary statistics such as the sample mean, effect size, or odds ratio.
Although meta-analysis for observational data is also under extensive research,[1][2] the literature largely centers around combining randomized controlled trials (RCTs).
Meta-analysis (and meta-regression) is often placed at the top of the evidence hierarchy provided that the analysis consists of individual participant data of randomized controlled clinical trials.
[3] Meta-regression plays a critical role in accounting for covariate effects, especially in the presence of categorical variables that can be used for subgroup analysis.
Individual participant data, in particular, allow flexible modeling that reflects different types of response variable(s): continuous, count, proportion, and correlation.
However, aggregate data are generally modeled as a normal linear regression ytk = xtk′β + εtk using the central limit theorem and variable transformation, where the subscript k indicates the kth study or trial, t denotes the tth treatment, ytk indicates the response endpoint for the kth study's tth arm, xtk is the arm-level covariate vector, εtk is the error term that is independently and identically distributed as a normal distribution.
[4] Mixed-effect meta-regression includes a random-effect term in addition to the fixed effects, suggesting that the studies are heterogeneous.
The random coefficient vector γk is then a noisy realization of the real treatment effect denoted by γ.
Recent applications include quantitative reviews of the empirical literature in economics, business, energy and water policy.
[8] Meta-regression analyses have been seen in studies of price and income elasticities of various commodities and taxes,[8] productivity spillovers on multinational companies,[9] and calculations on the value of a statistical life (VSL).
[8] In energy conservation, meta-regression analysis has been used to evaluate behavioral information strategies in the residential electricity sector.