Table 1.
Results Produced by the Various Methods for Synthesizing Proportions Among Cochrane Datasets (n = 43,644)
| Method | Failure* | Absolute difference† | Fold change† |
|---|---|---|---|
| Two-step (log) | 260 (0.6%) | 0.9% (0.2%, 2.4%) | 1.10 (1.03, 1.46) |
| Two-step (logit) | 215 (0.5%) | 0.6% (0.2%, 1.8%) | 1.07 (1.02, 1.42) |
| Two-step (arcsine) | 113 (0.3%) | 0.4% (0.0%, 1.3%) | 1.05 (1.01, 1.26) |
| Two-step (DAS-H) | 125 (0.3%) | 0.3% (−0.1%, 1.2%) | 1.06 (1.01, 1.25) |
| Two-step (DAS-G) | 125 (0.3%) | 0.4% (−0.1%, 1.4%) | 1.06 (1.01, 1.26) |
| Two-step (DAS-A) | 125 (0.3%) | 0.5% (0.0%, 1.5%) | 1.06 (1.01, 1.30) |
| Two-step (DAS-IV) | 125 (0.3%) | 0.6% (0.1%, 1.6%) | 1.06 (1.01, 1.36) |
| GLMM (log) | 3822 (8.8%) | 0.0% (−0.4%, 0.0%) | 1.01 (1.00, 1.03) |
| GLMM (probit) | 2766 (6.3%) | 0.0% (0.0%, 0.2%) | 1.00 (1.00, 1.02) |
| GLMM (cauchit) | 5708 (13.1%) | 0.0% (−0.5%, 0.0%) | 1.02 (1.00, 1.10) |
| GLMM (cloglog) | 2818 (6.5%) | 0.0% (−0.2%, 0.0%) | 1.00 (1.00, 1.01) |
| GLMM (logit) | 2131 (4.9%) | Reference | Reference |
*The column of “failure” gives the counts of datasets that led to computational issues when using the various methods. The corresponding proportions are given in parentheses
†The columns of “absolute difference” and “fold change” give the medians of absolute differences and fold changes of the overall proportion estimates produced by the various methods compared with the reference method. The corresponding interquartile ranges are given in parentheses. The fold change is the ratio of a larger estimate of the overall proportion divided by a smaller estimate
Abbreviations: Two-step (log, logit, or arcsine), two-step method with the log, logit, or arcsine-square-root transformation; Two-step (DAS-H, DAS-G, DAS-A, or DAS-IV), two-step method with the Freeman–Tukey double-arcsine (DAS) transformation, using the harmonic (H), geometric (G), or arithmetic (A) mean of study-specific sample sizes, or using the inverse of the variance (IV) of the synthesized result, as the overall sample size; GLMM (log, logit, probit, cauchit, or cloglog), generalized linear mixed model with the log, logit, probit, cauchit, or complementary log-log link