Estimate meta-analytic difference in means across multiple two-group studies.

meta_mdiff_two is suitable for synthesizing across multiple two-group studies (paired or independent) with a continuous outcome measure. It takes in raw data from each study. If all studies used the same measurement scale, a meta-analytic raw-score difference can be returned. If studies used different scales, a standardized mean difference can be returned. Studies can be all paired, all independent, or a mix. Equal variance can be assumed, or not. If standardized mean difference is the output, it is d_s when equal variance is assumed and d_avg when equal variance is not assumed.

Usage

meta_mdiff_two(
  data,
  comparison_means,
  comparison_sds,
  comparison_ns,
  reference_means,
  reference_sds,
  reference_ns,
  r = NULL,
  labels = NULL,
  moderator = NULL,
  contrast = NULL,
  effect_label = "My effect",
  reported_effect_size = c("mean_difference", "smd_unbiased", "smd"),
  assume_equal_variance = FALSE,
  random_effects = TRUE,
  conf_level = 0.95
)

Arguments

data: A data frame or tibble
comparison_means: Set of comparison_group means, 1 per study
comparison_sds: Set of comparison_group standard deviations, 1 per study, all > 0
comparison_ns: Set of comparison_group sample sizes, positive integers, 1 for each study
reference_means: Set of reference_group means, 1 per study
reference_sds: Set of comparison_group standard deviations, 1 per study, all > 0
reference_ns: Set of reference_group sample sizes, positive integers, 1 for each study
r: Optional correlation between measures for w-s studies, NA otherwise
labels: An optional collection of study labels
moderator: An optional factor to analyze as a categorical moderator, must have k > 2 per groups
contrast: An optional contrast to estimate between moderator levels; express as a vector of contrast weights with 1 weight per moderator level.
effect_label: Optional character giving a human-friendly name of the effect being synthesized
reported_effect_size: Character specifying effect size to return: Must be one of 'mean_difference', 'smd_unbiased' (to return an unbiased Cohen's d_s or d_avg) or 'smd' (to return d_s or d_avg without correction for bias). Defaults to mean_difference.
assume_equal_variance: Defaults to FALSE
random_effects: TRUE for random effect model; FALSE for 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().

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().

If reported_effect_size is smd_unbiased or smd the conversion to Cohen's d is handled by CI_smd_ind_contrast().

Examples

# Data set -- see Introduction to the New Statistics, 2nd edition
data("data_mccabemichael_brain")

# Meta-analysis: random effects, no moderator
estimate <- esci::meta_mdiff_two(
  data = esci::data_mccabemichael_brain,
  comparison_means = "M Brain",
  comparison_sds = "s Brain",
  comparison_ns = "n Brain",
  reference_means = "M No Brain",
  reference_sds = "s No Brain",
  reference_ns = "n No Brain",
  labels = "Study name",
  effect_label = "Brain Photo Rating - No Brain Photo Rating",
  assume_equal_variance = TRUE,
  random_effects = TRUE
)
# Forest plot
myplot_forest <- esci::plot_meta(estimate)


# Meta-analysis: random effects, moderator
estimate_moderator <- esci::meta_mdiff_two(
  data = esci::data_mccabemichael_brain,
  comparison_means = "M Brain",
  comparison_sds = "s Brain",
  comparison_ns = "n Brain",
  reference_means = "M No Brain",
  reference_sds = "s No Brain",
  reference_ns = "n No Brain",
  labels = "Study name",
  moderator = "Research group",
  effect_label = "Brain Photo Rating - No Brain Photo Rating",
  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.


# Meta-analysis: random effects, moderator, output d_s
estimate_moderator_d <- esci::meta_mdiff_two(
  data = esci::data_mccabemichael_brain,
  comparison_means = "M Brain",
  comparison_sds = "s Brain",
  comparison_ns = "n Brain",
  reference_means = "M No Brain",
  reference_sds = "s No Brain",
  reference_ns = "n No Brain",
  labels = "Study name",
  moderator = "Research group",
  effect_label = "Brain Photo Rating - No Brain Photo Rating",
  assume_equal_variance = TRUE,
  random_effects = TRUE
)
# Forest plot
myplot_forest_moderator_d <- esci::plot_meta(estimate_moderator_d)
#> 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.