pool.med {metamedian}

Meta-Analysis via median of (the difference of) medians method

Description

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.

Usage

pool.med(yi, wi, norm.approx = TRUE, coverage.prob = 0.95)

Arguments

yi

vector of the study-specific effect sizes (e.g., the medians or the difference of medians)

wi

optional vector of positive, study-specific weights (e.g., sample sizes)

norm.approx

optional logical scalar indicating whether normality approximation of the binomial should be used to construct an approximate confidence interval (the default is TRUE).

coverage.prob

optional numeric scalar indicating the desired coverage probability (the default is 0.95).

Details

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.

Value

A list with components

pooled.est

Pooled estimate

ci.lb

Lower bound of confidence interval

ci.ub

Upper bound of confidence interval

cov.level

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.

References

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.

Examples

## 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)