CI_diamond_ratio {esci}

Estimate the diamond ratio for a meta-analytic effect, a measure of heterogeneity

Description

CI_diamond_ratio returns the diamond ratio and CI for a meta-analytic effect, the ratio of the random-effects CI width to the fixed-effects CI width. The diamond ratio is a measure of effect-size heterogeneity.

Usage

CI_diamond_ratio(RE, FE, vi, conf_level = 0.95)

Arguments

RE

metafor object with random effects result

FE

metafor object with fixed effects result

vi

vector of effect size variances

conf_level

The confidence level for the confidence interval. Given in decimal form. Defaults to 0.95.

Details

Calculation of the CI is based on code provided by Maxwell Cairns (see Cairns et al., 2022). Specifically, this function implements what Cairns et al (2022) called the Sub-Q approach, which provides the best CI coverage in simulations. For comparison, this function also returns the CI produced by the bWT-DL approach (which generally has worse performance).

Value

Returns a list with 3 properties:

• diamond_ratio

• LL - lower limit of the conf_level% CI, Sub-Q approach

• UL - upper limit of the conf_level% CI, Sub-Q approach

• LL_bWT_DL - lower limit of the conf_level% CI, bWT-DL approach

• UL_bWT_DL - upper limit of the conf_level% CI, bWT-DL approach

Source

Cairns, Maxwell, Geoff Cumming, Robert Calin‐Jageman, and Luke A. Prendergast. “The Diamond Ratio: A Visual Indicator of the Extent of Heterogeneity in Meta‐analysis.” British Journal of Mathematical and Statistical Psychology 75, no. 2 (May 2022): 201–19. https://doi.org/10.1111/bmsp.12258.

Examples

mydata <- esci::data_mccabemichael_brain

# Use esci to obtain effect sizes and sample variances, storing only raw_data
mydata <- esci::meta_mdiff_two(
  data = mydata,
  comparison_means = "M Brain",
  comparison_ns = "n Brain",
  comparison_sds = "s Brain",
  reference_means = "M No Brain",
  reference_ns = "n No Brain",
  reference_sds = "s No Brain",
  random_effects = FALSE
)$raw_data

# Conduct fixed effects meta-analysis
FE <- metafor::rma(
  data = mydata,
  yi = effect_size,
  vi = sample_variance,
  method="FE"
)
# Conduct random effect meta-analysis
RE <- metafor::rma(
  data = mydata,
  yi = effect_size,
  vi = sample_variance,
  method="DL"
)

# Get the diamond ratio
res <- esci::CI_diamond_ratio(
  RE = RE,
  FE = FE,
  vi = mydata$sample_variance
)