metamedian: Meta-Analysis of Medians

The metamedian package implements methods to meta-analyze studies that report estimates of the median of the outcome of interest.

Methods Included

Median-Based Methods

This package implements several methods to directly meta-analyze studies reporting sample medians. When the primary studies are one-group studies, the methods of McGrath et al. (2019) and Ozturk and Balakrishnan (2020) can be applied to estimate the pooled median. In the two-group context, the methods of McGrath et al. (2020a) can be applied to estimate the pooled difference of medians between groups.

The package also implements methods to meta-analyze median survival times. The package can apply the methods described by McGrath et al. (2025) to meta-analyze the median survival time, difference of median survival times between groups, and the ratio of median survival times between groups.

Mean-Based Methods

These methods estimate the study-specific means and their standard errors from studies reporting sample medians in order to estimate the pooled (difference of) means. Specifically, one can apply the following methods:

• Hozo et al. (2005)
• Wan et al. (2014)
• Bland (2015)
• Luo et al. (2018)
• Shi et al. (2020a)
• Shi et al. (2020b)
• McGrath et al. (2020b)
• Cai et al. (2021)
• Yang et al. (2022)
• McGrath et al. (2023)
• Shi et al. (2023)

Installation

You can install the released version of metamedian from CRAN with:

install.packages("metamedian")

After installing the devtools package (i.e., calling install.packages(devtools)), the development version of metamedian can be installed from GitHub with:

devtools::install_github("stmcg/metamedian")

Usage

See McGrath et al. (2024) for a detailed guide on using the metamedian package. Below, we include the code used in the main examples in the paper. The examples are based on the dataset dat.age included in the package.

Loading the package:

library(metamedian)

Setting a random number seed for reproducibility:

set.seed(1234)

Descriptive Analyses

describe_studies(data = dat.age, group_labels = c ("Nonsurvivors", "Survivors"))
#> DESCRIPTION OF PRIMARY STUDIES
#>                                                       Nonsurvivors Survivors
#> N. studies:                                                     51        51
#> N. studies reporting the median:                                29        29
#>   N. studies reporting S1 (min, med, max, n):                    0         0
#>   N. studies reporting S2 (q1, med, q3, n):                     29        29
#>   N. studies reporting S3 (min, q1, med, q3, max, n):            0         0
#> N. studies reporting the mean:                                  22        22
#>   N. studies reporting the mean, sd, and n:                     22        22
#> Bowley skewness                                                             
#>   Minimum:                                                 -0.4000   -0.6000
#>   First quartile:                                          -0.0818   -0.1304
#>   Median:                                                   0.0000   -0.0526
#>   Mean:                                                    -0.0087   -0.0250
#>   Third quartile:                                           0.0909    0.1458
#>   Maximum:                                                  0.3846    0.4167

Mean-Based Methods

The analyses below may take 5-10 minutes to run on a standard laptop. For faster runtime, consider using fewer bootstrap replicates for the QE, BC, and MLN methods.

res_wan <- metamean(dat.age, mean_method = "hozo/wan/bland")
res_luo <- metamean(dat.age, mean_method = "luo")
res_shi <- metamean(dat.age, mean_method = "shi_lognormal")
res_qe_mean <- metamean(dat.age, mean_method = "qe")
res_bc <- metamean(dat.age, mean_method = "bc")
res_mln <- metamean(dat.age, mean_method = "mln")
res_yang <- metamean(dat.age, mean_method = "yang")

The output of res_mln is illustrated below:

res_mln
#> 
#> Random-Effects Model (k = 51; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 28.0379 (SE = 7.0239)
#> tau (square root of estimated tau^2 value):      5.2951
#> I^2 (total heterogeneity / total variability):   86.72%
#> H^2 (total variability / sampling variability):  7.53
#> 
#> Test for Heterogeneity:
#> Q(df = 50) = 357.0967, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se     zval    pval    ci.lb    ci.ub      
#>  12.8650  0.8342  15.4222  <.0001  11.2300  14.4999  *** 
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Median-Based Methods

res_mm <- metamedian(dat.age, median_method = "mm")
res_wm <- metamedian(dat.age, median_method = "wm")
res_qe_median <- metamedian(dat.age, median_method = "qe")

The output of res_qe_median is illustrated below:

res_qe_median
#> 
#> Random-Effects Model (k = 51; tau^2 estimator: REML)
#> 
#> tau^2 (estimated amount of total heterogeneity): 33.5585 (SE = 8.3883)
#> tau (square root of estimated tau^2 value):      5.7930
#> I^2 (total heterogeneity / total variability):   86.95%
#> H^2 (total variability / sampling variability):  7.66
#> 
#> Test for Heterogeneity:
#> Q(df = 50) = 373.6841, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate      se     zval    pval    ci.lb    ci.ub      
#>  13.2238  0.9121  14.4980  <.0001  11.4361  15.0115  *** 
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Reference

To cite this package, use:

McGrath S, Zhao X, Ozturk O, Katzenschlager S, Steele R, Benedetti A. metamedian: An R package for meta-analyzing studies reporting medians. Research Synthesis Methods. 2024; 15(2):332-346. doi:10.1002/jrsm.1686

For a BibTeX citation, use:

@article{mcgrath2024metamedian,
  title={metamedian: An R package for meta-analyzing studies reporting medians},
  author={McGrath, Sean and Zhao, XiaoFei and Ozturk, Omer and Katzenschlager, Stephan and Steele, Russell and Benedetti, Andrea},
  journal={Research Synthesis Methods},
  volume={15},
  number={2},
  pages={332--346},
  year={2024},
  publisher={Wiley Online Library}
}