This function meta-analyzes the study-specific effect sizes by applying the (weighted) median of medians method (McGrath et al., 2019) in one-sample contexts and the (weighted) median of the difference of median method (McGrath et al., 2020) in two-sample contexts.
pool.med(yi, wi, norm.approx = TRUE, coverage.prob = 0.95)
A list with components
Pooled estimate
Lower bound of confidence interval
Upper bound of confidence interval
Theoretical coverage of the confidence interval around the pooled estimate. When norm.approx
is set to TRUE
, the theoretical coverage is the same as the value specified by coverage.prob
. When norm.approx
is set to FALSE
, the theoretical coverage is set to the smallest possible value greater than the value specified by coverage.prob
.
vector of the study-specific effect sizes (e.g., the medians or the difference of medians)
optional vector of positive, study-specific weights (e.g., sample sizes)
optional logical scalar indicating whether normality approximation of the binomial should be used to construct an approximate confidence interval (the default is TRUE
).
optional numeric scalar indicating the desired coverage probability (the default is 0.95
).
For one-group studies, authors may report the sample median or mean. If these measures are supplied for yi
and weights are not provided for wi
, the function implements the median of medians (MM) method (McGrath et al., 2019).
For two-group studies, authors may report the difference of medians or the difference of means across both groups. If these measures are supplied for yi
and weights are not provided for wi
, the function implements the median of the difference of medians (MDM) method (McGrath et al., 2020).
Analogous weighted versions of the MM and MDM methods can be applied when study-specific sample sizes are provided for wi
.
The confidence interval around the pooled estimate is constructed by inverting the sign test.
McGrath S., Zhao X., Qin Z.Z., Steele R., and Benedetti A. (2019). One-sample aggregate data meta-analysis of medians. Statistics in Medicine, 38, 969-984.
McGrath S., Sohn H., Steele R., and Benedetti A. (2020). Meta-analysis of the difference of medians. Biometrical Journal, 62, 69-98.
## Storing data (study-specific difference of medians)
yi <- c(5.23, 3.10, 0.50, 0.78, 3.48, 0.59, 2.20, 5.06, 4.00)
## Meta-analysis of the difference of medians
pool.med(yi)
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