analyses:yusuf1985
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analyses:yusuf1985 [2019/03/02 16:57] – external edit 127.0.0.1 | analyses:yusuf1985 [2021/11/08 15:20] – 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 '' | + | 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 '' |
The data can be loaded with: | The data can be loaded with: | ||
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dat$grp_ratios <- round(dat$n1i / dat$n2i, 2) | dat$grp_ratios <- round(dat$n1i / dat$n2i, 2) | ||
</ | </ | ||
- | (I copy the dataset into ' | + | (I copy the dataset into ''dat'', which is a bit shorter and therefore easier to type further below). The last command adds the ratio of the group sizes as a variable to the data frame. This will be useful for checking on strong imbalances in group sizes. Note that the dataset actually includes the data from multiple tables. Table 6 (p. 343) from the article includes the results from short-term trials of oral beta blockers: |
<code rsplus> | <code rsplus> | ||
dat[dat$table==" | dat[dat$table==" | ||
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</ | </ | ||
<code output> | <code output> | ||
- | Fixed-Effects Model (k = 21) | + | Equal-Effects Model (k = 21) |
- | Test for Heterogeneity: | + | I^2 (total heterogeneity / total variability): |
+ | H^2 (total variability / sampling variability): | ||
+ | |||
+ | 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 | + | estimate |
- | | + | |
Model Results (OR scale): | Model Results (OR scale): | ||
- | estimate | + | estimate |
- | 0.9332 | + | 0.9332 |
</ | </ | ||
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: | ||
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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) | + | Peto's method actually is equivalent to using a standard (inverse-variance) |
<code rsplus> | <code rsplus> | ||
dat <- escalc(measure=" | dat <- escalc(measure=" | ||
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Note that with '' | Note that with '' | ||
- | 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=" | + | res <- rma(yi, vi, data=dat, method=" |
res | res | ||
</ | </ | ||
<code output> | <code output> | ||
- | Fixed-Effects Model (k = 18) | + | Equal-Effects Model (k = 18) |
+ | |||
+ | I^2 (total heterogeneity / total variability): | ||
+ | H^2 (total variability / sampling variability): | ||
- | 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 | + | estimate |
- | | + | |
--- | --- | ||
- | Signif. codes: | + | Signif. codes: |
</ | </ | ||
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