# [R-meta] Rationale for performing a moderator test without heterogeneity

Michael Dewey ||@t@ @end|ng |rom dewey@myzen@co@uk
Sat Mar 5 17:10:31 CET 2022

```Comments in-line

On 05/03/2022 15:34, racasuso wrote:
> Dear all,
>
> I am performing a meta-analysis on the effects of muscle disuse on
> muscle loss. We choose age, duration of the intervention and initial
> muscle strength as a priory moderators. The meta-analysis for muscle
> loss is as follows:
> Random-Effects Model (k = 30; tau^2 estimator: DL)
>    logLik  deviance       AIC       BIC      AICc
> -17.9973   27.8366   39.9946   42.7970   40.4391
>    tau^2 (estimated amount of total heterogeneity): 0 (SE = 0.0511)
> tau (square root of estimated tau^2 value):      0
> I^2 (total heterogeneity / total variability):   0.00%
> H^2 (total variability / sampling variability):  1.00
> Test for Heterogeneity:
> Q(df = 29) = 27.8366, p-val = 0.5267
> Model Results:
> estimate      se     zval    pval    ci.lb    ci.ub
> -0.3986  0.0803  -4.9619  <.0001  -0.5561  -0.2412  ***
>
> My first question is if there is any rationale to further perform the
> moderator test. In fact, when I perform it for initial force the test of
> moderators is significant. How can I interpret this?

If you had decided a priori to test those moderators then you would
usually do that irrespective of observed heterogeneity and report the
results. It can happen that the amount of heterogeneity is not
sufficient for the Q value to exceed some level of statistical
significance but there is still enough for the moderators to explain
some of it.

>
> Second, I am a little bit confused on how to interpret the test for
> moderators when I perform it for each variable in separate and when all
> moderators are analysed together. For instance, when I perform the
> moderators test for muscle strength it is significant; however, when
> both duration and strength are introduced in the model while the
> moderator test is significant, only duration reached a significant effect.

Suppose you include two moderators, A and B. The overall test is a test
of whether they together account for sufficient variation. The
individual test for A is a test of whether, if you already have B in the
model, adding A adds anything. Similarly for the test of B. It can
happen that, if A and B are closely related that neither A nor B is
individually significant but their combination is. Suppose in your case
you had two measures of muscle strength, left hand and right hand.
Knowing left right adds little since (I assume) they are correlated and
vice versa. Together on the other hand they might be massively important.

Michael

>
> Thank you very much,
> Kind regards
>
>
>

--
Michael
http://www.dewey.myzen.co.uk/home.html

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