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analyses:yusuf1985 [2021/10/22 14:45] – Wolfgang Viechtbaueranalyses:yusuf1985 [2022/08/03 11:25] (current) – Wolfgang Viechtbauer
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 ==== The Methods and Data ==== ==== The Methods and Data ====
  
-The meta-analysis by Yusuf et al. (1985) on the effectiveness of beta blockers for reducing mortality and reinfarction is usually cited as the reference for what is sometimes called Peto's (one-step or modified Mantel-Haenszel) method for meta-analyzing 2×2 table data. The method provides a weighted estimate of the (log) odds ratio under a fixed-effects model and is particularly advantageous when the event of interest is rare. However, it should only be used when the group sizes within the individual studies are not too dissimilar and effect sizes are generally small (Greenland & Salvan, 1990; Sweeting et al., 2004; Bradburn et al., 2007). This method is implemented in the ''rma.peto()'' function and can be illustrated with this dataset.+The meta-analysis by Yusuf et al. (1985) on the effectiveness of beta blockers for reducing mortality and reinfarction is usually cited as the reference for what is sometimes called Peto's (one-step or modified Mantel-Haenszel) method for meta-analyzing 2×2 table data. The method provides a weighted estimate of the (log) odds ratio under an equal-effects model and is particularly advantageous when the event of interest is rare. However, it should only be used when the group sizes within the individual studies are not too dissimilar and effect sizes are generally small (Greenland & Salvan, 1990; Sweeting et al., 2004; Bradburn et al., 2007). This method is implemented in the ''rma.peto()'' function and can be illustrated with this dataset.
  
 The data can be loaded with: The data can be loaded with:
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 <code rsplus> <code rsplus>
 par(mfrow=c(1,2)) par(mfrow=c(1,2))
-llplot(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, +llplot(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
        subset=(table=="6"), drop00=FALSE, lwd=1, xlim=c(-5,5))        subset=(table=="6"), drop00=FALSE, lwd=1, xlim=c(-5,5))
-llplot(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat, +llplot(measure="OR", ai=ai, n1i=n1i, ci=ci, n2i=n2i, data=dat,
        subset=(table=="6"), drop00=FALSE, lwd=1, xlim=c(-5,5), scale=FALSE)        subset=(table=="6"), drop00=FALSE, lwd=1, xlim=c(-5,5), scale=FALSE)
 </code> </code>
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 </code> </code>
 <code output> <code output>
-Fixed-Effects Model (k = 21)+Equal-Effects Model (k = 21)
  
-Test for Heterogeneity: +I^2 (total heterogeneity / total variability):  0.00% 
 +H^2 (total variability / sampling variability): 0.64 
 + 
 +Test for Heterogeneity:
 Q(df = 17) = 10.8275, p-val = 0.8654 Q(df = 17) = 10.8275, p-val = 0.8654
  
 Model Results (log scale): Model Results (log scale):
  
-estimate       se     zval     pval    ci.lb    ci.ub  +estimate      se     zval    pval    ci.lb   ci.ub 
- -0.0692   0.1194  -0.5794   0.5623  -0.3031   0.1648 + -0.0692  0.1194  -0.5794  0.5623  -0.3031  0.1648
  
 Model Results (OR scale): Model Results (OR scale):
  
-estimate    ci.lb    ci.ub  +estimate   ci.lb   ci.ub 
-  0.9332   0.7385   1.1792+  0.9332  0.7385  1.1792
 </code> </code>
-Or, to round the estimated odds ratio to 2 digits, we can use: +Or, to round the estimated odds ratio to 2 digits, we can use:
 <code rsplus> <code rsplus>
 predict(res, transf=exp, digits=2) predict(res, transf=exp, digits=2)
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 ==== Analysis via the Inverse-Variance Method ==== ==== Analysis via the Inverse-Variance Method ====
  
-Peto's method actually is equivalent to using a standard (inverse-variance) fixed-effects model approach, but estimating the (log) odds ratio and corresponding sampling variance within each study based on the efficient score and Fisher's information evaluated at $\theta_i = 0$ (where $\theta_i$ is the true log odds ratio). We can do this explicitly with:+Peto's method actually is equivalent to using a standard (inverse-variance) equal-effects model approach, but estimating the (log) odds ratio and corresponding sampling variance within each study based on the efficient score and Fisher's information evaluated at $\theta_i = 0$ (where $\theta_i$ is the true log odds ratio). We can do this explicitly with:
 <code rsplus> <code rsplus>
 dat <- escalc(measure="PETO", ai=ai, n1i=n1i, ci=ci, n2i=n2i, dat <- escalc(measure="PETO", ai=ai, n1i=n1i, ci=ci, n2i=n2i,
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 Note that with ''add=0'', no adjustments to the observed counts are made, so that studies with zero events are essentially dropped from further analyses. Note that with ''add=0'', no adjustments to the observed counts are made, so that studies with zero events are essentially dropped from further analyses.
  
-Now, a fixed-effects model using the standard (inverse-variance) approach can be fitted with:+Now, an equal-effects model using the standard (inverse-variance) approach can be fitted with:
 <code rsplus> <code rsplus>
-res <- rma(yi, vi, data=dat, method="FE")+res <- rma(yi, vi, data=dat, method="EE")
 res res
 </code> </code>
 <code output> <code output>
-Fixed-Effects Model (k = 18)+Equal-Effects Model (k = 18) 
 + 
 +I^2 (total heterogeneity / total variability):   0.00% 
 +H^2 (total variability / sampling variability):  0.64
  
-Test for Heterogeneity: +Test for Heterogeneity:
 Q(df = 17) = 10.8275, p-val = 0.8654 Q(df = 17) = 10.8275, p-val = 0.8654
  
 Model Results: Model Results:
  
-estimate       se     zval     pval    ci.lb    ci.ub           +estimate      se     zval    pval    ci.lb   ci.ub 
- -0.0692   0.1194  -0.5794   0.5623  -0.3031   0.1648          + -0.0692  0.1194  -0.5794  0.5623  -0.3031  0.1648
  
 --- ---
-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>
 The estimated log odds ratio can be back-transformed through exponentiation: The estimated log odds ratio can be back-transformed through exponentiation:
analyses/yusuf1985.txt · Last modified: 2022/08/03 11:25 by Wolfgang Viechtbauer