metamedian (version 1.1.0)

qe: Meta-Analysis via quantile estimation method

Description

The function applies the quantile estimation (QE) method (McGrath et al., 2020) to meta-analyze one-group or two-group studies where each study reports one of the following summary measures:

• S1: median, minimum and maximum values, and sample size

• S2: median, first and third quartiles, and sample size

• S3: median, minimum and maximum values, first and third quartiles, and sample size

• S4: mean, standard deivation, and sample size.

For one-group studies, the function estimates the pooled median. For two-group studies, the function estimates the pooled raw difference of medians across groups. The convention used for calculating differences in two-group studies is: value in group 1 minus value in group 2.

Usage

qe(
  min.g1,
  q1.g1,
  med.g1,
  q3.g1,
  max.g1,
  n.g1,
  mean.g1,
  sd.g1,
  min.g2,
  q1.g2,
  med.g2,
  q3.g2,
  max.g2,
  n.g2,
  mean.g2,
  sd.g2,
  single.family = FALSE,
  loc.shift = FALSE,
  pool_studies = TRUE,
  ...
)

Value

An object of class "rma.uni". See documentation of rma.uni.

Arguments

min.g1

vector of study-specific sample minimum values (first group for two-group studies). See 'Details'.

q1.g1

vector of study-specific sample first quartile values (first group for two-group studies). See 'Details'.

med.g1

vector of study-specific sample median values (first group for two-group studies). See 'Details'.

q3.g1

vector of study-specific sample third quartile values (first group for two-group studies). See 'Details'.

max.g1

vector of study-specific sample maximum values (first group for two-group studies). See 'Details'.

n.g1

vector of study-specific sample sizes (first group for two-group studies). See 'Details'.

mean.g1

vector of study-specific sample mean values (first group for two-group studies). See 'Details'.

sd.g1

vector of study-specific sample standard deviation values (first group for two-group studies). See 'Details'.

min.g2

vector of study-specific sample minimum values of the second group for two-group studies. See 'Details'.

q1.g2

vector of study-specific sample first quartile values of the second group for two-group studies. See 'Details'.

med.g2

vector of study-specific sample median values of the second group for two-group studies. See 'Details'.

q3.g2

vector of study-specific sample third quartile values of the second group for two-group studies. See 'Details'.

max.g2

vector of study-specific sample maximum values of the second group for two-group studies. See 'Details'.

n.g2

vector of study-specific sample sizes of the second group for two-group studies. See 'Details'.

mean.g2

vector of study-specific sample mean values of the second group for two-group studies. See 'Details'.

sd.g2

vector of study-specific sample standard deviation values of the second group for two-group studies. See 'Details'.

single.family

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

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.

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 effect size estimates and sei containing the study-specific within-study standard error estimates. The default is TRUE.

...

optional arguments for pooling. See documentation of rma.uni.

Details

Letting \(k\) denote the number of studies, provide study-specific summary data as vectors of length \(k\). If a study does not report a given summary measure (e.g., the minimum value), give a value of NA for the position in the relevant vector. If no studies report a given summary measure, a vector of only NA values need not be provided. See 'Examples' for appropriate use.

The sampling variance of the effect size for each study is estimated via the QE method. The default starting values and box constraints of the parameters in the minimization algorithm (qe.fit) are used. After estimating the sampling variances for all studies, studies are meta-analyzed using the rma.uni function.

References

McGrath S., Sohn H., Steele R., and Benedetti A. (2020). Meta-analysis of the difference of medians. Biometrical Journal, 62, 69-98.

Examples

## Example 1: Meta-analysis of one-group studies

## Storing data
## Note: All 6 studies report S2
med.vals <- c(6.1, 5.2, 3.1, 2.8, 4.5)
q1.vals <- c(2.0, 1.6, 2.6, 0.9, 3.2)
q3.vals <- c(10.2, 13.0, 8.3, 8.2, 9.9)
n.vals <- c(100, 92, 221, 81, 42)

## Meta-analyze studies via QE method
qe(q1.g1 = q1.vals, med.g1 = med.vals, q3.g1 = q3.vals, n.g1 = n.vals)


## Example 2: Meta-analysis of one-group studies

## Storing data
## Note: Studies 1, 2, 3, and 4 report S1, S2, S3, and S4, respectively
min.vals <- c(0.7, NA, 1.1, NA)
q1.vals <- c(NA, 5.2, 5.3, NA)
med.vals <- c(8.7, 10.7, 11.0, NA)
q3.vals <- c(NA, 15.2, 15.3, NA)
max.vals <- c(22.2, NA, 24.7, NA)
n.vals <- c(52, 34, 57, 90)
sd.vals <- c(NA, NA, NA, 4.2)
mean.vals <- c(NA, NA, NA, 12.2)

## Meta-analyze studies via QE method
qe(min.g1 = min.vals, q1.g1 = q1.vals, med.g1 = med.vals, q3.g1 = q3.vals,
   max.g1 = max.vals, n.g1 = n.vals, mean.g1 = mean.vals, sd.g1 = sd.vals)


## Example 3: Meta-analysis of two-group studies

## Storing data
## Note: All 4 studies report S3
min.g1 <- c(2.3, 3.2, 1.9, 1.7)
q1.g1 <- c(6.0, 7.1, 3.5, 3.8)
med.g1 <- c(8.7, 9.5, 5.9, 6.0)
q3.g1 <- c(11.3, 13.1, 10.8, 11.0)
max.g1 <- c(20.6, 25.3, 17.0, 18.6)
n.g1 <- c(53, 49, 66, 75)
min.g2 <- c(0.4, 0.9, 0.5, 0.3)
q1.g2 <- c(2.5, 3.1, 2.7, 2.3)
med.g2 <- c(5.1, 6.2, 4.9, 4.7)
q3.g2 <- c(9.6, 10.1, 8.8, 9.2)
max.g2 <- c(20.2, 21.4, 18.8, 19.2)
n.g2 <- c(50, 45, 60, 73)

## Meta-analyze studies via QE method
qe(min.g1 = min.g1, q1.g1 = q1.g1, med.g1 = med.g1, q3.g1 = q3.g1,
   max.g1 = max.g1, n.g1 = n.g1, min.g2 = min.g2, q1.g2 = q1.g2,
   med.g2 = med.g2, q3.g2 = q3.g2, max.g2 = max.g2, n.g2 = n.g2)