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analyses:viechtbauer2007b [2020/06/26 06:54] – Wolfgang Viechtbaueranalyses:viechtbauer2007b [2021/11/08 15:54] – Wolfgang Viechtbauer
Line 11: Line 11:
 dat <- dat[c(7:10,13:25), c(13:16,18:19,11,6,7,9)] dat <- dat[c(7:10,13:25), c(13:16,18:19,11,6,7,9)]
 dat$dosage <- (dat$dosage * 7) / 1000 dat$dosage <- (dat$dosage * 7) / 1000
 +rownames(dat) <- 1:nrow(dat)
 dat dat
 </code> </code>
Line 45: Line 46:
 </code> </code>
 <code output> <code output>
-   ai n1i ci n2i   yi   vi dosage major baseline duration  sei    zi ci.lb ci.ub +   ai n1i ci n2i   yi dosage major baseline duration ci.lb ci.ub  
-1  20  25 11  25 1.82 0.06   2.66     0     19.5        8 0.25  2.42  1.12  2.95 +1  20  25 11  25 1.82   2.66     0     19.5        8  1.12  2.95  
-2  14  20  9  20 1.56 0.08   6.30     0     12.5        4 0.29  1.54  0.89  2.73+2  14  20  9  20 1.56   6.30     0     12.5        4  0.89  2.73
 . .
-13 55 123 57 124 0.97 0.02   6.30     1     21.5        6 0.14 -0.20  0.74  1.28+13 55 123 57 124 0.97   6.30     1     21.5        6  0.74  1.28
 . .
-17 98 186 80 189 1.24 0.01   6.30     1     21.9        6 0.11  2.00  1.00  1.54+17 98 186 80 189 1.24   6.30     1     21.9        6  1.00  1.54
 </code> </code>
 With ''transf=exp'', the values of the outcome measure (i.e., the log relative improvement rates) and corresponding confidence interval bounds are exponentiated and hence transformed back from the log scale. Therefore, variable ''yi'' now indicates the relative improvement rate, and ''ci.lb'' and ''ci.ub'' are the bounds of an approximate 95% confidence interval for the true relative improvement rate in the individual studies (note that this is not a permanent change -- object ''dat'' still contains the log transformed values, which we need for the analyses below). With ''transf=exp'', the values of the outcome measure (i.e., the log relative improvement rates) and corresponding confidence interval bounds are exponentiated and hence transformed back from the log scale. Therefore, variable ''yi'' now indicates the relative improvement rate, and ''ci.lb'' and ''ci.ub'' are the bounds of an approximate 95% confidence interval for the true relative improvement rate in the individual studies (note that this is not a permanent change -- object ''dat'' still contains the log transformed values, which we need for the analyses below).
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 The first model discussed in the article assumes that the //true// relative improvement rates are identical in the various studies and the only reason why the //observed// relative improvement rates differ from each other is due to sampling error/variability. We can fit this model with: The first model discussed in the article assumes that the //true// relative improvement rates are identical in the various studies and the only reason why the //observed// relative improvement rates differ from each other is due to sampling error/variability. We can fit this model with:
 <code rsplus> <code rsplus>
-res <- rma(yi, vi, data=dat, method="FE", digits=2)+res <- rma(yi, vi, data=dat, method="EE", digits=2)
 res res
 </code> </code>
 <code output> <code output>
-Fixed-Effects Model (k = 17)+Equal-Effects Model (k = 17)
  
-Test for Heterogeneity: +I^2 (total heterogeneity / total variability):   68.96% 
 +H^2 (total variability / sampling variability):  3.22 
 + 
 +Test for Heterogeneity:
 Q(df = 16) = 51.55, p-val < .01 Q(df = 16) = 51.55, p-val < .01
  
 Model Results: Model Results:
  
-estimate       se     zval     pval    ci.lb    ci.ub           +estimate    se  zval  pval  ci.lb  ci.ub 
-    0.33     0.05     6.78     <.01     0.23     0.42      *** +    0.33  0.05  6.78  <.01   0.23   0.42  ***
  
 --- ---
-Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 </code> </code>
 Since we are analyzing the log of the relative improvement rates, the model estimate also reflects the log relative rate. For easier interpretation, it is useful to back-transform the results with: Since we are analyzing the log of the relative improvement rates, the model estimate also reflects the log relative rate. For easier interpretation, it is useful to back-transform the results with:
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 H^2 (total variability / sampling variability):  3.22 H^2 (total variability / sampling variability):  3.22
  
-Test for Heterogeneity: +Test for Heterogeneity:
 Q(df = 16) = 51.55, p-val < .01 Q(df = 16) = 51.55, p-val < .01
  
 Model Results: Model Results:
  
-estimate       se     zval     pval    ci.lb    ci.ub           +estimate    se  zval  pval  ci.lb  ci.ub  
-    0.45     0.09     4.87     <.01     0.27     0.63      *** +    0.45  0.09  4.87  <.01   0.27   0.63  *** 
  
 --- ---
Line 151: Line 155:
 R^2 (amount of heterogeneity accounted for):            47.38% R^2 (amount of heterogeneity accounted for):            47.38%
  
-Test for Residual Heterogeneity: +Test for Residual Heterogeneity:
 QE(df = 13) = 27.9903, p-val = 0.0091 QE(df = 13) = 27.9903, p-val = 0.0091
  
-Test of Moderators (coefficient(s) 2,3,4): +Test of Moderators (coefficients 2:4):
 QM(df = 3) = 10.1280, p-val = 0.0175 QM(df = 3) = 10.1280, p-val = 0.0175
  
 Model Results: Model Results:
  
-                                 estimate      se     zval    pval    ci.lb   ci.ub      +                                 estimate      se     zval    pval    ci.lb   ci.ub  
-intrcpt                            0.4763  0.0876   5.4342  <.0001   0.3045  0.6480  *** +intrcpt                            0.4763  0.0876   5.4342  <.0001   0.3045  0.6480  ***  
-I(dosage - 34)                    -0.0058  0.0100  -0.5846  0.5588  -0.0254  0.0138      +I(dosage - 34)                    -0.0058  0.0100  -0.5846  0.5588  -0.0254  0.0138       
-I(baseline - 20)                  -0.0672  0.0352  -1.9086  0.0563  -0.1363  0.0018    . +I(baseline - 20)                  -0.0672  0.0352  -1.9086  0.0563  -0.1363  0.0018    .  
-I(dosage - 34):I(baseline - 20)   -0.0016  0.0034  -0.4555  0.6487  -0.0083  0.0052     +I(dosage - 34):I(baseline - 20)   -0.0016  0.0034  -0.4555  0.6487  -0.0083  0.0052      
  
 --- ---
analyses/viechtbauer2007b.txt · Last modified: 2022/08/03 11:24 by Wolfgang Viechtbauer