[R-meta] Different tau2s

Nathan Pace n.l.pace at utah.edu
Wed Aug 23 07:19:03 CEST 2017


I have questions about estimating separate tau2s.

My previous email was sent prematurely and incorrectly edited.

Please ignore.

Nathan

On 2208//2017, 11:02 PM, "R-sig-meta-analysis on behalf of Nathan Pace" <r-sig-meta-analysis-bounces at r-project.org on behalf of n.l.pace at utah.edu> wrote:

    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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