Estimate meta-analytic standardized mean difference across multiple two group studies (all paired, all independent, or a mix).

meta_d2 is suitable for synthesizing across multiple two-group studies (paired or independent) with a continuous outcome measure but where not all studies are measured on the same scale, and instead the magnitude of difference for each study is expressed as d_s or d_avg.

Usage

meta_d2(
  data,
  ds,
  comparison_ns,
  reference_ns,
  r = NULL,
  labels = NULL,
  moderator = NULL,
  contrast = NULL,
  effect_label = "My effect",
  assume_equal_variance = FALSE,
  random_effects = TRUE,
  conf_level = 0.95
)

Arguments

data: A data frame or tibble
ds: Set of bias-adjusted cohen's d_s or d_avg values, 1 for each study
comparison_ns: Set of comparison_group sample sizes, positive integers, 1 for each study
reference_ns: Set of reference_groups sample sizes, positive integers, 1 for each study
r: optional correlation between measures for w-s studies, NA otherwise
labels: Optional set of labels, 1 for each study
moderator: Optional factor as a categorical moderator; should have k > 2 per group
contrast: Optional vector specifying a contrast between moderator levels
effect_label: Optional character providing a human-friendly label for the effect
assume_equal_variance: Defaults to FALSE
random_effects: Boolean; TRUE for a random effects model; otherwise fixed effects
conf_level: The confidence level for the confidence interval. Given in decimal form. Defaults to 0.95.

Value

An esci-estimate object; a list of data frames and properties. Returned tables include:

es_meta - A data frame of meta-analytic effect sizes. If a moderator was defined, there is an additional row for each level of the moderator.
- effect_label - Study label
- effect_size - Effect size
- LL - Lower bound of conf_level% confidence interval
- UL - Upper bound of conf_level% confidence interval
- SE - Expected standard error
- k - Number of studies
- diamond_ratio - ratio of random to fixed effects meta-analytic effect sizes
- diamond_ratio_LL - lower bound of conf_level% confidence interval for diamond ratio
- diamond_ratio_UL - upper bound of conf_level% confidence interval for diamond ratio
- I2 - I2 measure of heterogeneity
- I2_LL - Lower bound of conf_level% confidence interval for I2
- I2_UL - upper bound of conf_level% confidence interval for I2
- PI_LL - lower bound of conf_level% of prediction interval
- PI_UL - upper bound of conf_level% of prediction interval
- p - p value for the meta-analytic effect size, based on null of exactly 0
- *width - width of the effect-size confidence interval
- FE_effect_size - effect size of the fixed-effects model (regardless of if fixed effects was selected
- RE_effect_size - effect size of the random-effects model (regardless of if random effects was selected
- FE_CI_width - width of the fixed-effects confidence interval, used to calculate diamond ratio
- RE_CI_width - width of the fixed-effects confidence interval, used to calculate diamond ratio
es_heterogeneity - A data frame of of heterogeneity values and conf_level% CIs for the meta-analytic effect size. If a moderator was defined also reports heterogeneity estimates for each level of the moderator.
- effect_label - study label
- moderator_variable_name - if moderator passed, gives name of the moderator
- moderator_level - 'Overall' and each level of moderator, if passed
- measure - Name of the measure of heterogeneity
- estimate - Value of the heterogeneity estimate
- LL - lower bound of conf_level% confidence interval
- UL - upper bound of conf_level% confidence interval
raw_data - A data from with one row for each study that was passed
- label - study label
- effect_size - effect size
- weight - study weight in the meta analysis
- sample_variance - expected level of sampling variation
- SE - expected standard error
- LL - lower bound of conf_level% confidence interval
- UL - upper bound of conf_level% confidence interval
- mean - used to calculate study p value; this is the d value entered for the study
- sd - use to calculate study p value; set to 1 for each study
- n - study sample size
- p - p value for the study, based on null of exactly 0

Details

Once you generate an estimate with this function, you can visualize it with plot_meta().

Each study's effect size should be expressed as: Cohen's d_s: (comparison_mean - reference_mean) / sd_pooled or Cohen_'s d_avg: (comparison_mean - reference_mean) / sd_avg

To enter d_s, set assume_equal_variance to TRUE To enter d_avg, set assume_equal_variance to FALSE

And the d values should all be corrected for bias. The function CI_smd_ind_contrast() can assist with converting raw data from each study to d_s or d_avg with bias correction. It also has more details on calculation of these forms of d and their CIs.

The meta-analytic effect size, confidence interval and heterogeneity estimates all come from metafor::rma().

The diamond ratio and its confidence interval come from CI_diamond_ratio().

Examples

# Data set -- see Introduction to the New Statistics, 1st edition
data("data_damischrcj")

# Meta-analysis, random effects, assuming equal variance, no moderator
estimate <- esci::meta_d2(
  data = esci::data_damischrcj,
  ds = "Cohen's d unbiased",
  comparison_ns = "n Control",
  reference_ns = "n Lucky",
  labels = Study,
  assume_equal_variance = TRUE,
  random_effects = TRUE
)

# Forest plot
myplot_forest <- esci::plot_meta(estimate)


# Add a categorical moderator
estimate_moderator <- esci::meta_d2(
  data = esci::data_damischrcj,
  ds = "Cohen's d unbiased",
  comparison_ns = "n Control",
  reference_ns = "n Lucky",
  labels = "Study",
  moderator = "Research Group",
  assume_equal_variance = TRUE,
  random_effects = TRUE
)

# Forest plot
myplot_forest_moderator <- esci::plot_meta(estimate_moderator)
#> Scale for x is already present.
#> Adding another scale for x, which will replace the existing scale.
#> Scale for y is already present.
#> Adding another scale for y, which will replace the existing scale.