Sorry to have to dispute those commonly taught beliefs about fixed vs random effects, but I regard them as quite misleading because they only pertain to analyses without meta-covariate adjustment. Such analyses can be as misleading as single-study analyses that examine only average effects. Some of the meta-analysis literature has been seriously distorted by merging heterogeneous estimates using random effects instead of predictors, thus ignoring study-level covariates and clear signals of the causes of heterogeneity.

I think of random effects as at best a last resort when failing to explain heterogeneity across studies using measured study covariates. One first needs to seek predictors of differences using fixed-effect meta-regression, preferably in using a shared “natural parameter” that is rescaled to the same units across studies, e.g., change in log hazard ratio by average age of the treated groups in decades (if adults) or years (if children). Random effects enter as a residual only if needed after explanatory covariates are examined. It should be noted however that meta-regression is a form of ecologic (aggregate) regression when a covariate is a summary across individuals (such as average age) rather than a study property such as design type (e.g., randomized vs. observational cohort indicator). Furthermore, quality scores can be highly misleading as predictors due to their merging of disparate quality components.

As R-cubed noted, we discussed these issues long ago in

Greenland, S. (1994). A critical look at some popular meta-analytic methods. American Journal of Epidemiology, 140, 290-296,

Greenland, S. (1994). Quality scores are useless and potentially misleading. American Journal of Epidemiology, 140, 300-301,

Greenland, S. (1994). Can meta-analysis be salvaged?. American Journal of Epidemiology, 140, 783-787,

Poole, C., Greenland, S. (1999). Random-effects meta-analyses are not always conservative. American Journal of Epidemiology, 150, 469-475,

Greenland, S., O’Rourke, K. (2001). On the bias produced by quality scores in meta-analysis, and a hierarchical view of proposed solutions. Biostatistics, 2, 463-471,

and the meta-analysis chapter of Modern Epidemiology 3rd ed. 2008 (Ch. 33, also with the late Keith O’Rourke).

We gave a method of fixed-effects meta-regression for dose-response analyses in

Greenland, S., Longnecker, M. P. (1992). Methods for trend estimation from summarized dose-response data, with applications to meta-analysis. American Journal of Epidemiology, 135, 1301-1309,

which according to Google has been used quite a bit, thanks to its Stata implementation in

Orsini, N., Bellocco, R., Greenland, S. (2006). Generalized least squares for trend estimation of summarized dose-response data. The Stata Journal, 6, 40-57.