Meta-analysis of proportions versus simple pooling of data

[R_cubed]

You might want to take a look at the link I posted in this thread, which compares and contrasts “pooling” ie. treating all of the reports as a single large trial, and “combining” – ie. averaging in proportion to sample size.

Meta-analysis with incomplete data

Good question. If I understand what you want to do, you want to sum the values in each column (ie. pooling), and treating the data as if it was one large, study. Is that correct? That is a seductive method, but probably wrong according to this article. Simple Pooling versus Combining in Meta-Analysis Dena M. Bravata, Ingram Olkin (2001) Evaluation in the Health Professions (link) I am assuming that all of the studies are reasonably homogeneous, and that combining by meta-analysis is approp…

Pooling studies by treating the data of the individual articles as if it came from one large trial, is not valid in the general case due to Simpson’s paradox. The paper in the link is open access and goes into the mathematical details.

You might want to check out my thread on meta-analysis, because there are a lot of techniques recommended in the secondary sources that do not stand up to mathematical scrutiny.

I really should organize these better, but there are a lot of useful papers here.

Nonparametric Effect Size estimation, Likelihood Methods, and Meta Analysis

Posted as a new topic at Prof. Harrell’s request. Study heterogeneity is a big issue in research synthesis, and is related to various issues in robust statistics. I have an intuition that those involved in research synthesis might be better served by using nonparametric estimates of effect (Hodges-Lehmann estimates/generalized odds ratios, etc), instead of necessarily relying upon standardized mean differences reported by primary researchers. But I am also persuaded by the work of Richard Roy…