[R-meta] residual heterogeneity in meta-regression

[Daniel Mønsted Shabanzadeh]

Dear Wolfgang

Picking up the thread once more...Regarding the many studies included in
the meta-regression model (up to 450 studies) I do expect very large Q
statistics and cannot aim to explain all heterogeneity through
meta-regression. Is there a better way to express heterogeneity in this
case? I have read that the tau is a better way, however I am not sure of
the interpretation and what I may conclude regarding the model and
heterogeneity using tau.

Regards,
Daniel


On Mon, Nov 18, 2019 at 4:27 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Daniel,
>
> Roughly, the QE-test statistic should tend to decrease when R^2 is large.
> Whether this is strictly true depends on how tau^2 is being estimated.
> However, the QE-test could very well be significant even if R^2 is large.
> It simply means that there is still a significant amount of residual
> heterogeneity left.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: Daniel Mønsted Shabanzadeh [mailto:dmshaban using gmail.com]
> Sent: Thursday, 14 November, 2019 11:09
> To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
> Subject: residual heterogeneity in meta-regression
>
> Dear Wolfgang
>
> I am performing a meta-regression on multiple one-arm non-randomised
> studies in order to explore the impact of moderators on complications
> following a surgical intervention. Adding moderators (age catrgory of the
> patient, surgical technique etc.) increases the R2:
>
> Mixed-Effects Model (k = 183; tau^2 estimator: REML)
>
> tau^2 (estimated amount of residual heterogeneity):     0.0074 (SE =
> 0.0010)
> tau (square root of estimated tau^2 value):             0.0860
> I^2 (residual heterogeneity / unaccounted variability): 99.20%
> H^2 (unaccounted variability / sampling variability):   125.63
> R^2 (amount of heterogeneity accounted for):            36.78%
>
> Test for Residual Heterogeneity:
> QE(df = 156) = 4730.2255, p-val < .0001
>
> Test of Moderators (coefficient(s) 2:27):
> QM(df = 26) = 115.5671, p-val < .0001
>
> However, I am unaware of how to interpretate the rising R2 when QE
> tests keep on beeing significant. So far I understand that the rising R2
> indicates that the heterogeneity is beeing partly explained by moderators,
> however does QE change in case most heterogeneity is explained by
> moderators?
>
> Regards,
> Daniel
>
> Daniel Mønsted Shabanzadeh
> MD, PhD
> Department of Gastroenterology, Surgical Unit
> Hvidovre Hospital
> Mobile +45 2546 5251
>

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