analyses:vanhouwelingen1993
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analyses:vanhouwelingen1993 [2021/10/22 14:45] – Wolfgang Viechtbauer | analyses:vanhouwelingen1993 [2022/04/22 10:53] – [Random-Effects Conditional Logistic Model] Wolfgang Viechtbauer | ||
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==== The Methods and Data ==== | ==== The Methods and Data ==== | ||
- | The paper by van Houwelingen et al. (1993) is an early (and unfortunately often overlooked) paper on meta-analytic methods for 2×2 table data that describes a variety of rather sophisticated models and methods, including the fixed/random-effects conditional logistic | + | The paper by van Houwelingen et al. (1993) is an early (and unfortunately often overlooked) paper on meta-analytic methods for 2×2 table data that describes a variety of rather sophisticated models and methods, including the equal- and random-effects conditional logistic |
<code rsplus> | <code rsplus> | ||
library(metafor) | library(metafor) | ||
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No information about this outcome was available for 2 trials, so the results below are based on the remaining 25 trials. Also, note that van Houwelingen et al. (1993) analyze the log odds ratios of persistent or recurrent bleedings in the control group versus the treatment group, so that positive values indicate a lower risk in the treatment group and hence a positive treatment effect. | No information about this outcome was available for 2 trials, so the results below are based on the remaining 25 trials. Also, note that van Houwelingen et al. (1993) analyze the log odds ratios of persistent or recurrent bleedings in the control group versus the treatment group, so that positive values indicate a lower risk in the treatment group and hence a positive treatment effect. | ||
- | ==== Fixed-Effects Conditional Logistic Model ==== | + | ==== Equal-Effects Conditional Logistic Model ==== |
- | Among the models considered by the authors is the fixed-effects conditional logistic model (described as a " | + | Among the models considered by the authors is the equal-effects conditional logistic model (described as a " |
<code rsplus> | <code rsplus> | ||
llplot(measure=" | llplot(measure=" | ||
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One study (number 10) has a single zero cell (none of the patients in the treatment group experienced persistent or recurrent bleedings), which implies that the MLE of the odds ratio is infinite. The dashed line in the figure corresponds to this study. Also, one study (number 14) has two zero cells (none of the patients in the entire study experienced persistent or recurrent bleedings), which implies a flat likelihood for the odds ratio. The dotted line in the figure corresponds to this study.((Note that the '' | One study (number 10) has a single zero cell (none of the patients in the treatment group experienced persistent or recurrent bleedings), which implies that the MLE of the odds ratio is infinite. The dashed line in the figure corresponds to this study. Also, one study (number 14) has two zero cells (none of the patients in the entire study experienced persistent or recurrent bleedings), which implies a flat likelihood for the odds ratio. The dotted line in the figure corresponds to this study.((Note that the '' | ||
- | The results from a corresponding | + | The results from a corresponding |
<code rsplus> | <code rsplus> | ||
res <- rma.glmm(measure=" | res <- rma.glmm(measure=" | ||
- | data=dat, model=" | + | data=dat, model=" |
summary(res, | summary(res, | ||
</ | </ | ||
<code output> | <code output> | ||
- | Fixed-Effects Model (k = 24) | + | Equal-Effects Model (k = 24) |
Model Type: Conditional Model with Exact Likelihood | Model Type: Conditional Model with Exact Likelihood | ||
- | logLik | + | logLik |
- | -53.68 | + | -53.68 |
- | Tests for Heterogeneity: | + | Tests for Heterogeneity: |
- | Wld(df = 23) = 32.54, p-val = 0.09 | + | Wld(df = 23) = 32.52, p-val = 0.09 |
LRT(df = 23) = 40.34, p-val = 0.01 | LRT(df = 23) = 40.34, p-val = 0.01 | ||
Model Results: | Model Results: | ||
- | estimate | + | estimate |
- | 0.12 | + | 0.12 0.10 1.22 0.22 -0.07 |
--- | --- | ||
- | Signif. codes: | + | Signif. codes: |
</ | </ | ||
These results match what is reported on page 2275. In particular, the log odds ratio is estimated to be $\hat{\theta} = 0.12$ (with 95% confidence interval: $-0.07$ to $0.32$). The log likelihood for this model is $ll = -53.68$. | These results match what is reported on page 2275. In particular, the log odds ratio is estimated to be $\hat{\theta} = 0.12$ (with 95% confidence interval: $-0.07$ to $0.32$). The log likelihood for this model is $ll = -53.68$. | ||
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</ | </ | ||
<code output> | <code output> | ||
- | Fixed-Effects Model (k = 25) | + | Equal-Effects Model (k = 25) |
- | Test for Heterogeneity: | + | I^2 (total heterogeneity / total variability): |
+ | H^2 (total variability / sampling variability): | ||
+ | |||
+ | Test for Heterogeneity: | ||
Q(df = 23) = 34.82, p-val = 0.05 | Q(df = 23) = 34.82, p-val = 0.05 | ||
Model Results (log scale): | Model Results (log scale): | ||
- | estimate | + | estimate |
- | 0.12 | + | 0.12 0.10 1.22 0.22 -0.07 |
Model Results (OR scale): | Model Results (OR scale): | ||
- | estimate | + | estimate |
- | 1.13 | + | 1.13 |
Cochran-Mantel-Haenszel Test: CMH = 1.37, df = 1, p-val = 0.24 | Cochran-Mantel-Haenszel Test: CMH = 1.37, df = 1, p-val = 0.24 | ||
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Model Type: Conditional Model with Exact Likelihood | Model Type: Conditional Model with Exact Likelihood | ||
- | logLik | + | logLik |
- | -52.99 | + | -52.99 |
tau^2 (estimated amount of total heterogeneity): | tau^2 (estimated amount of total heterogeneity): | ||
tau (square root of estimated tau^2 value): | tau (square root of estimated tau^2 value): | ||
- | I^2 (total heterogeneity / total variability): | + | I^2 (total heterogeneity / total variability): |
H^2 (total variability / sampling variability): | H^2 (total variability / sampling variability): | ||
- | Tests for Heterogeneity: | + | Tests for Heterogeneity: |
- | Wld(df = 23) = 32.54, p-val = 0.09 | + | Wld(df = 23) = 32.52, p-val = 0.09 |
LRT(df = 23) = 40.34, p-val = 0.01 | LRT(df = 23) = 40.34, p-val = 0.01 | ||
Model Results: | Model Results: | ||
- | estimate | + | estimate |
- | 0.17 | + | 0.17 0.14 1.28 0.20 -0.09 |
--- | --- | ||
- | Signif. codes: | + | Signif. codes: |
</ | </ | ||
- | These results match what is reported on page 2277. In particular, the estimated average log odds ratio is $\hat{\mu} = 0.17$ (with 95% confidence interval: $-0.09$ to $0.44$).((Note that this interval is slightly different than the confidence profile interval reported by the authors on page 2278. The interval obtained here is a Wald-type interval.)) | + | These results match what is reported on page 2277. In particular, the estimated average log odds ratio is $\hat{\mu} = 0.17$ (with 95% confidence interval: $-0.09$ to $0.44$),((Note that this interval is slightly different than the confidence profile interval reported by the authors on page 2278. The interval obtained here is a Wald-type interval.)) |
==== Mixture Model ==== | ==== Mixture Model ==== |
analyses/vanhouwelingen1993.txt · Last modified: 2022/08/03 11:22 by Wolfgang Viechtbauer