cd {metamedian}

Meta-Analysis via the confidence distribution approach

Description

The function applies the confidence distribution (CD) approach of Ozturk and Balakrishnan (2020) to meta-analyze one-group studies where each study reports one of the following summary measures:

• C1 (and C2): lower and upper bounds of a confidence interval around the median, and coverage probability

• C3: median, variance estimate of the median, and sample size

• C4: mean, standard deviation, and sample size.

• C5: median, first and third quartiles, and sample size

The function estimates the pooled median.

Usage

cd(
  q1,
  med,
  q3,
  n,
  mean,
  sd,
  med.var,
  med.ci.lb,
  med.ci.ub,
  alpha.1,
  alpha.2,
  pooled.median.ci.level = 0.95,
  method = "RE",
  pool_studies = FALSE
)

Arguments

q1

vector of study-specific sample first quartile values. See 'Details'.

med

vector of study-specific sample median values. See 'Details'.

q3

vector of study-specific sample third quartile values. See 'Details'.

n

vector of study-specific sample sizes. See 'Details'.

mean

vector of study-specific sample mean values. See 'Details'.

sd

vector of study-specific sample standard deviation values. See 'Details'.

med.var

vector of study-specific estimates of the variance of the median. See 'Details'.

med.ci.lb

vector of study-specific lower confidence interval bounds around the medians

med.ci.ub

vector of study-specific upper confidence interval bounds around the medians

alpha.1

vector of the study-specific \alpha_1 values from Ozturk and Balakrishnan (2020)

alpha.2

vector of the study-specific \alpha_2 values from Ozturk and Balakrishnan (2020)

pooled.median.ci.level

optional numeric scalar indicating the desired coverage probability for the pooled median estimate. The default is 0.95.

method

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

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.

Value

A list with components

pooled.est

Pooled estimate of the median

pooled.est.var

Estimated variance of the pooled median estimator

pooled.est.ci.lb

Lower bound of confidence interval for the pooled median

pooled.est.ci.ub

Upper bound of confidence interval for the pooled median

tausq.est

Estimate of between-study variance (applicable only when method is set to RE)

yi

Study-specific point estimates

vi

Study-specific sampling variances

References

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

## Example 1:
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 CD method
cd(q1 = q1.vals, med = med.vals, q3 = q3.vals, n = n.vals)