[R-meta] residual heterogeneity in meta-regression

[Viechtbauer, Wolfgang (SP)]

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