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In metaanalysis results are often reported in forest plots, where multiple studies are included.

Different, continuous outcome scales are used to measure the effect of a treatment on the course of a specific disease. Because of heterogeneity in clinical studies, random effects models are used for the calculation of the forest plots. Results are reported as standardised mean difference (SMD), corresponding to the Cohens d. Estimations as to how big the cohens d has to be for beeing named as "big" or "small" effects.

Regarding the results of such a forest-plot I have the following questions:

  1. Is it possible to draw another, maybe more practical, or concise result from a reported "cohens d", other than that the overall effect is "small" or "big" for example?

    • a) Is it possible to relate the reported effects to specific changes in the initially used outcome scales? Since the forest plot results are in a different form than the originally used outcome scales.
    • b) Is it possible to "recalculate" with the pooled effect (cohen d/SMD) the possible/theoretical changes for every included outcome measurement scale used in the single included studies? For example: The pooled effect of a metaanalysis is d=0,4 and the standard deviation of one of the included studies "A" is 5. Does this mean that the possible/theoretical effect on the used outcome scale would be a "2"? (The idea would be to just bring the results into a more comprehensible format for non statisticians)
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  • $\begingroup$ I do not think that there is a connection between heterogeneity and random-effects modelling. Moreover, question 2 b is vague and specific example for calculating effect-size does not appear to be statistically valid. $\endgroup$
    – user10619
    Commented Aug 3, 2017 at 14:54

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Two comments.

Although people commonly say that they have decided to choose a random effects model on the basis of observed heterogeneity this is strictly speaking not correct. The two models, fixed and random, are based on different assumptions. Loosely speaking fixed effects say - there is an underlying true effect and it is my job to estimate it. Random effects says there is no true effect but rather a distribution of true effects and my job is to estimate its parameters which if I assume normality as people usually do would be the mean and variance.

Yes, you can back calculate as you suggest. Of course the result will depend on what variance you imputed but I guess you already know that.

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