[R-meta] Different tau2s
Nathan Pace
n.l.pace at utah.edu
Wed Aug 23 07:02:20 CEST 2017
Dear Wolfgang,
I have used the methods in
http://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates (Meta-Regression with All Studies but Different Amounts of (Residual) Heterogeneity).
I have some questions about the interpretation.
The measure is SMD with k = 29.
surgery dose study me sde ne mc sdc nc year yi vi
1 open >= 2 Bryson 2010 3.900 3.0000 44 4.60 2.6000 46 2010 -0.2476 0.0448
2 open < 2 Cassuto 1985 17.500 9.4800 10 35.50 17.3900 10 1985 -1.2308 0.2379
3 open >= 2 Grady 2012 4.000 2.3000 31 4.90 1.9000 31 2012 -0.4213 0.0659
4 open < 2 Herroeder 2007 4.800 1.8700 31 5.60 1.7600 29 2007 -0.4344 0.0683
5 open >= 2 Maquoi 2016 20.000 14.8100 33 20.00 14.8100 34 2016 0.0000 0.0597
6 open >= 2 Staikou 2014 1.000 1.0000 20 3.00 2.1000 20 2014 -1.1918 0.1178
7 open < 2 Weinberg 2016 1.748 1.9290 27 4.00 2.6800 22 2016 -0.9655 0.0920
8 open < 2 Yardeni 2009 4.000 0.6000 30 4.53 1.2000 30 2009 -0.5514 0.0692
9 lap >= 2 Ahn 2015 32.500 9.8500 25 46.80 10.9000 25 2015 -1.3549 0.0984
10 lap < 2 Dewinter 2016 3.600 2.2000 39 3.40 1.8000 40 2016 0.0987 0.0507
11 lap >= 2 Kaba 2007 20.000 22.3607 20 30.00 22.3607 20 2007 -0.4383 0.1024
12 lap >= 2 Kim TH 2011 28.500 8.4900 22 38.00 13.7400 21 2011 -0.8210 0.1009
13 lap >= 2 Kim TH 2013 43.000 16.4900 17 63.00 16.4900 17 2013 -1.1842 0.1383
14 lap >= 2 Lauwick 2008 3.000 1.4800 25 3.00 1.4800 24 2008 0.0000 0.0817
15 lap >= 2 Ortiz 2016 2.670 2.5000 21 3.55 2.4600 22 2016 -0.3484 0.0945
16 lap >= 2 Saadawy 2010 1.800 0.8000 40 4.70 1.1000 40 2010 -2.9862 0.1057
17 lap >= 2 Wuethrich 2012 2.000 2.9600 32 2.00 1.4800 32 2012 0.0000 0.0625
18 lap >= 2 Yon 2014 45.370 12.3700 17 59.26 17.4600 19 2014 -0.8890 0.1224
19 other >= 2 Choi KW 2016a 3.000 0.7400 41 3.00 0.7400 43 2016 0.0000 0.0476
20 other >= 2 Farag 2013 4.200 5.2800 57 5.35 4.9500 58 2013 -0.2233 0.0350
21 other < 2 Grigoras 2012 16.790 18.9900 17 21.90 22.6300 19 2012 -0.2380 0.1122
22 other < 2 Insler 1995 3.500 1.5000 44 3.10 0.7800 45 1995 0.3328 0.0456
23 other >= 2 Kang 2011 27.000 11.3100 32 33.50 11.3100 32 2011 -0.5677 0.0650
24 other >= 2 Kim KT 2014b 25.000 6.2500 25 30.60 6.3738 26 2014 -0.8733 0.0859
25 other >= 2 McKay 2009 3.100 2.0400 29 4.50 2.9000 27 2009 -0.5541 0.0743
26 other < 2 Omar 2013 3.000 2.2200 24 4.00 2.2200 24 2013 -0.4431 0.0854
27 other >= 2 Slovack (unpublished) 2.900 2.6000 19 2.70 2.4000 17 2014 0.0780 0.1115
28 other >= 2 Striebel 1992 49.000 20.0000 20 40.00 14.0700 20 1992 0.5101 0.1033
29 other >= 2 Terkawi 2014 2.940 2.7400 37 3.88 2.9200 34 2014 -0.3288 0.0572
I ran two rma.mv models
painearly1surgery.rma <- rma.mv(yi = yi, V = vi, mods = ~ surgery,
data = painearly.df, digits = 3)
painearly2surgery.rma <- rma.mv(yi = yi, V = vi, mods = ~ surgery,
random = ~ surgery | study, struct = 'DIAG',
data = painearly.df, digits = 3)
and compared with anova.
anova(update(painearly1surgery.rma, method = 'ML'), update(painearly2surgery.rma, method = 'ML'))
painearly1surgery.rma
Multivariate Meta-Analysis Model (k = 29; method: REML)
Variance Components: none
Test for Residual Heterogeneity:
QE(df = 26) = 121.000, p-val < .001
Test of Moderators (coefficient(s) 2:3):
QM(df = 2) = 14.209, p-val < .001
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.487 0.097 -5.033 <.001 -0.676 -0.297 ***
surgerylap -0.149 0.135 -1.104 0.269 -0.413 0.115
surgeryother 0.292 0.124 2.363 0.018 0.050 0.534 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Painearly2su
Multivariate Meta-Analysis Model (k = 29; method: REML)
Variance Components:
outer factor: study (nlvls = 29)
inner factor: surgery (nlvls = 3)
estim sqrt k.lvl fixed level
tau^2.1 0.082 0.287 8 no open
tau^2.2 0.759 0.871 10 no lap
tau^2.3 0.086 0.294 11 no other
Test for Residual Heterogeneity:
QE(df = 26) = 121.000, p-val < .001
Test of Moderators (coefficient(s) 2:3):
QM(df = 2) = 5.285, p-val = 0.071
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.547 0.143 -3.817 <.001 -0.828 -0.266 ***
surgerylap -0.231 0.325 -0.711 0.477 -0.869 0.406
surgeryother 0.339 0.186 1.817 0.069 -0.027 0.704 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
df AIC BIC AICc logLik LRT pval QE
Full 6 55.911 64.115 59.729 -21.955 121.000
Reduced 3 107.259 111.361 108.219 -50.630 57.348 <.001 121.000
Modify Chunk OptionsRun Current ChunkModify Chunk OptionsRun All Chunks AboveRun Current Chunk
Show in New WindowClear OutputExpand/Collapse Output
Loading tidyverse: ggplot2
Loading tidyverse: tibble
Loading tidyverse: tidyr
Loading tidyverse: readr
Loading tidyverse: purrr
Loading tidyverse: dplyr
Conflicts with tidy packages -----------------------------------------------------------------------
filter(): dplyr, stats
lag(): dplyr, stats
Loading required package: Matrix
Attaching package: ‘Matrix’
The following object is masked from ‘package:tidyr’:
expand
Loading 'metafor' package (version 2.0-0). For an overview
and introduction to the package please type: help(metafor).
Show in New WindowClear OutputExpand/Collapse Output
Random-Effects Model (k = 29; tau^2 estimator: REML)
tau^2 (estimated amount of total heterogeneity): 0.3391 (SE = 0.1128)
tau (square root of estimated tau^2 value): 0.5823
I^2 (total heterogeneity / total variability): 81.89%
H^2 (total variability / sampling variability): 5.52
Test for Heterogeneity:
Q(df = 28) = 135.2084, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.5011 0.1208 -4.1470 <.0001 -0.7380 -0.2643 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Mixed-Effects Model (k = 29; tau^2 estimator: REML)
tau^2 (estimated amount of residual heterogeneity): 0.349 (SE = 0.118)
tau (square root of estimated tau^2 value): 0.591
I^2 (residual heterogeneity / unaccounted variability): 82.23%
H^2 (unaccounted variability / sampling variability): 5.63
R^2 (amount of heterogeneity accounted for): 0.00%
Test for Residual Heterogeneity:
QE(df = 27) = 132.341, p-val < .001
Test of Moderators (coefficient(s) 2):
QM(df = 1) = 0.323, p-val = 0.570
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt -0.388 0.234 -1.659 0.097 -0.847 0.070 .
dose>= 2 -0.156 0.274 -0.568 0.570 -0.694 0.382
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
df AIC BIC AICc logLik LRT pval QE tau^2 R^2
Full 3 63.0005 67.1024 63.9605 -28.5002 132.3410 0.3171
Reduced 2 61.3516 64.0862 61.8132 -28.6758 0.3511 0.5535 135.2084 0.3234 1.96%
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