Fixed effect and random effects methods

In fixed effect meta-analysis it is assumed that the true effect of treatment is the same value in each study, or fixed, the differences between study results being due solely to the play of chance. The assumption of a fixed effect can be tested using a test of homogeneity (see below).

In a random effects meta-analysis the treatment effects for the individual studies are assumed to vary around some overall average treatment effect. Usually the effect sizes 8. are assumed have a Normal distribution with mean 8 and variance r2. In essence the test of homogeneity described below tests whether r2 is zero. The smaller the value of r2 the more similar are the fixed and random effects analyses.

Peto describes his method for obtaining a summary odds ratio as assumption free,7 arguing that it does not assume that all the studies are estimating the same treatment effect, but it is generally considered to be most similar to a fixed effect method.

There is no consensus about whether to use fixed or random effects models.12 All of the methods given below are fixed effect approaches except the DerSimonian and Laird method.

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