Thanks for this reply. But the key irrefutable mathematical facts against the inverse variance weighted random effects methods for a set of randomized clinical trials are (1) they make contradictory assumptions and (2) they apply linear weighted distribution theory in an illegitimate manner (weights are not constants to a high degree of accuracy). Any statistician, who in a situation that might involve public health policy, uses these methods in such a situation or as a reviewer who allows the use of these methods is potentially risking scientifically unsupportable inferences.
Fixed-effects are legitimate for the narrow hypothesis that the true effect sizes are zero for all studies. The resulting confidence intervals, which today are the crux of our inferences, cannot be trusted under the more general and realistic random effects scenario.
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Jonathan Shuster
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