metamedian {metamedian}

Meta-Analysis of the (difference of) medians

Description

This function is a wrapper function for the qe, cd, and pool.med functions. The function implements the methods of McGrath et al. (2019), McGrath et al. (2020), and Ozturk and Balakrishnan (2020) to estimate the pooled (difference of) medians in a meta-analysis. Specifically, the function implements the (weighted) median of medians method, the Ozturk and Balakrishnan (2020) method, and the quantile matching estimation method to meta-analyze one-group studies; the function implements the (weighted) median of the difference of medians method and quantile matching estimation method to meta-analyze two-group studies.

Usage

metamedian(
  data,
  median_method = "qe",
  single.family = FALSE,
  loc.shift = FALSE,
  norm.approx = TRUE,
  coverage.prob = 0.95,
  cd_method = "RE",
  pool_studies = TRUE,
  ...
)

Arguments

data

data frame containing the study-specific summary data. For one-group studies, this data frame can contain the following columns:

min.g1	minimum value.
q1.g1	first quartile.
med.g1	median.
q3.g1	third quartile.
max.g1	maximum value.
n.g1	sample size.
mean.g1	sample mean.
sd.g1	sample standard deviation.
med.var.g1	sampling variance of the median (only applicable when median_method="cd").
med.ci.lb.g1	lower confidence interval bound around the median (only applicable when median_method="cd").
med.ci.ub.g1	upper confidence interval bound around the median (only applicable when median_method="cd").
alpha.1.g1	\alpha_1 values from Ozturk and Balakrishnan (2020) (only applicable when median_method="cd").
alpha.2.g1	\alpha_2 values from Ozturk and Balakrishnan (2020) (only applicable when median_method="cd").

For two group studies, this data frame can also contain the following columns for the summary data of the second group: min.g2, q1.g2, med.g2, q3.g2, max.g2, n.g2, mean.g2, and sd.g2.

median_method

character string specifying the approach used to estimate the study-specific means and their standard errors. The options are

"mm"	Median of Medians (McGrath et al. 2019) for one-group studies and Median of the Difference of Medians (McGrath et al. 2020) for two group studies.
"wm"	Weighted Median of Medians (McGrath et al. 2019) for one-group studies and Weighted Median of the Difference of Medians (McGrath et al. 2020) for two group studies.
"qe"	Quantile Matching Estimation (McGrath et al. 2020). This approach is applicable for one-group studies or two-group studies. This is the default option.
"cd"	Confidence Distribution (Ozturk and Balakrishnan 2020). This approach is applicable for one-group studies.

single.family

(only applicable when median_method is set to "qe") logical scalar indicating that for two-group studies, the parametric family of distributions is assumed to be the same across both groups. The default is FALSE. See 'Details' of qe.study.level.

loc.shift

(only applicable when median_method is set to "qe") logical scalar indicating that for two-group studies, distributions are assumed to only differ by a location shift. The default is FALSE. See 'Details' of qe.study.level.

norm.approx

(only applicable when median_method is set to "mm" or "wm") logical scalar indicating whether normality approximation of the binomial should be used to construct an approximate confidence interval. The default is TRUE.

coverage.prob

(only applicable when median_method is set to "mm", "wm", or "cd") numeric scalar indicating the desired coverage probability for the pooled (difference of medians) estimate. The default is 0.95.

cd_method

(only applicable when median_method is set to "cd") character string specifying whether a fixed effect or random effects model is used. The options are FE (fixed effect) are RE (random effects). The default is RE.

pool_studies

logical scalar specifying whether to meta-analyze the studies. If this argument is set to FALSE, function will not meta-analyze the studies and will return a list with components yi containing the study-specific outcome measure estimates and sei containing the study-specific within-study standard error estimates. The default is TRUE.

...

(only applicable when median_method is set to "qe") optional arguments that are passed into the rma.uni function for pooling. See documentation of rma.uni.

Value

an object of class "rma.uni" (when median_method is set to "qe") or a list (when median_method is set to "mm", "wm", or "cd"). For additional details, see rma.uni (when median_method is set to "qe"), pool.med (when median_method is set to "mm" or "wm"), and cd (when median_method is set to "cd").

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.

McGrath S., Zhao X., Ozturk O., Katzenschlager S., Steele R., and Benedetti A. (in press). metamedian: An R package for meta-analyzing studies reporting medians. Research Synthesis Methods.

Ozturk O. and Balakrishnan N. (2020). Meta‐analysis of quantile intervals from different studies with an application to a pulmonary tuberculosis data. Statistics in Medicine, 39, 4519-4537.

Examples

## Quantile Matching Estimation method
metamedian(data = dat.age, median_method = "qe")

## Median of the Difference of Medians method
metamedian(data = dat.age, median_method = "mm")

## Weighted Median of the Difference of Medians method
metamedian(data = dat.age, median_method = "wm")