This is a continuation of a long topic, addressed by post number rather than by page. Start at post 1.
I had written a reply contradicting post #59 and deleted it. Here is what survived.
When trials differ in population, duration and comparator, the pooled estimate answers a question no individual trial asked. That is worth saying before the number is quoted.
Filing a mild objection to the consensus on Individual participant data versus aggregate. Mild because I might be wrong; an objection because nobody has addressed the case that does not fit.
Where I part company with post #63, and it is a narrow parting.
Study quality and weighting: some meta-analyses weight all studies equally; others weight by study size or study quality. The choice affects the result and should be stated and justified.
I would want to see it done twice before believing it once.
Post #63 is the version of this I will quote in future. One addition.
Double extraction with disagreement resolution is standard and is worth checking for, because single extraction errors are common and non-random.
Thank you — that answers what I came here to find out.
Two sentences on Individual participant data versus aggregate and then I will stop, because the rest is speculation and the thread is better without mine.
What is documented is narrow. What is inferred from it is broad. The gap between them is where every argument here lives.
Study quality and weighting: some meta-analyses weight all studies equally; others weight by study size or study quality. The choice affects the result and should be stated and justified.
The short version is the first sentence; the rest is why.
Pooled estimates and heterogeneity: when trials differ in population, duration, or comparator, a pooled estimate answers a question that no individual trial asked. High heterogeneity means effects genuinely differ across studies. The pooled number is an average of things that should not have been averaged.
No disagreement from me. Posting only so the question does not look ignored.
I would rather this thread reach "we do not know" about Individual participant data versus aggregate than reach a confident answer that nobody can support when asked.
On Individual participant data versus aggregate, the part that usually goes wrong is that the question is asked as though it has one answer. It has a range, and the width of the range is the interesting bit.
If you can post the two or three numbers you are working from, several people here will check the arithmetic rather than argue about the conclusion.
Double extraction with disagreement resolution is standard and is worth checking for, because single extraction errors are common and non-random.
If that is already documented somewhere, ignore me and link it.
Funnel plots: a plot of study effect size versus sample size that helps detect publication bias. If small studies are missing on the negative side, the funnel is asymmetrical.
The arithmetic in post #74 is right; the assumption feeding it is the part to check.
Where the Individual participant data versus aggregate reasoning breaks down for me is the step from the group result to the individual case. That step is almost never argued for.
Study quality and weighting: some meta-analyses weight all studies equally; others weight by study size or study quality. The choice affects the result and should be stated and justified.
I am confident about the direction and much less about the magnitude.
Double extraction with disagreement resolution is standard and is worth checking for, because single extraction errors are common and non-random.
The disagreement above is smaller than it looks once the terms are fixed.
The strongest argument against my own position on Individual participant data versus aggregate, stated as well as I can state it, since nobody else has yet.
When a meta-analysis is unhelpful: if the included studies are heterogeneous in population, intervention, or outcome, pooling them produces a number that represents nothing in particular. Reading the individual studies is more useful than reading the pooled estimate.
Written in the hope of being told what I have missed.
Nothing to add on the substance. Thank you for taking the question at face value.
Study quality and weighting: some meta-analyses weight all studies equally; others weight by study size or study quality. The choice affects the result and should be stated and justified.
Post #81 is right about the mechanism and I think understates the practical bit.
Source for the Individual participant data versus aggregate figure, since it was asked for. It is in the discussion rather than the abstract, which is why the version circulating is stronger than the paper is.
Reading the surrounding paragraph is worth the two minutes. The authors are more careful than their summarisers.
Post #81 and I disagree about the size of the effect, not about the direction.
Individual participant data versus aggregate is one of those subjects where the general answer and the answer for a specific case diverge, and the thread will go in circles until someone says which one is being asked for.
Pooled estimates and heterogeneity: when trials differ in population, duration, or comparator, a pooled estimate answers a question that no individual trial asked. High heterogeneity means effects genuinely differ across studies. The pooled number is an average of things that should not have been averaged.
Someone should write this up properly, and it should probably not be me.
Fixed-effects versus random-effects models: fixed-effects assumes all studies are estimating the same thing and variation is sampling error. Random-effects assumes studies are estimating effects from different distributions and allows between-study variance. Choice matters if heterogeneity is high.
Post #85 put the caveat in the right place and I want to underline it.
Adding the boring version of Individual participant data versus aggregate, because the interesting version keeps getting posted and the boring one is usually right.
Check the ordinary explanations, in order, and stop when one of them accounts for what you are seeing. Most of the time the second one does.
Building on post #89 rather than restating it.
Two things can be true about Individual participant data versus aggregate at once: the mechanism is plausible and the evidence for the size of the effect is thin. Most of the argument here is people defending the first against attacks on the second.