The applicability to systematic reviews of common effect, random effects and fixed effects approaches to meta-analysis

Systematic reviewers planning quantitative meta-analysis usually choose between fixed effect meta-analysis, and random effects meta-analysis. An alternative method is called fixed effects (note the s in the name). This method has the unique property that the target estimand is defined by the variances of the studies found by the systematic review. This article considers each in relation to the quantitative analysis of data to be obtained by systematic review. For clarity, I refer to the traditional fixed effect method as the common effect method and the newer approach as fixed effects (plural). Case studies illustrate the post hoc nature of the fixed effects (plural) method, in which the population under study is determined by the data rather than by the protocol. Mathematical analysis shows that unlike common effect and random effects methods, the fixed effects (plural) method requires an additional, and unrealistic, assumption about the data obtained in systematic reviews. A simulation study demonstrates that confidence intervals from fixed effects (plural) meta-analysis do not account for the post hoc nature of the method. Fixed effects (plural) meta-analysis is neither a slot-in replacement for the common effect method nor for the random effects method of meta-analysis. Of the three methods considered here, the common effect method and the random effects method are potentially valid for the quantitative analysis of systematic reviews.