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Estimate a meta-analytic Cohen's d1 across multiple studies

Source: R/meta_d1.R
meta_d1.Rd

meta_d1 is suitable for synthesizing across multiple single-group studies with a continuous outcome variable, but where the outcome is not measured on the same scale in all studies

Usage

meta_d1(
  data,
  ds,
  ns,
  labels = NULL,
  moderator = NULL,
  contrast = NULL,
  effect_label = "My effect",
  random_effects = TRUE,
  conf_level = 0.95
)

Arguments

data

A data frame or tibble

ds

Set of bias-adjusted cohen's d1 values, 1 for each study

ns

Set of sample sizes, positive integers, 1 for each study

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

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 d1: (mean - reference) / sd.

And the d1 values should all be corrected for bias. The function CI_smd_one() can assist with converting raw data from each study to d1_unbiased.

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

# example code
  original_7 <- data.frame(
study_name = c(
  "Aden (1993)"  ,
  "Buggs (1995)"  ,
  "Crazed (1999)"  ,
  "Dudley (2003)"  ,
  "Evers (2005)"  ,
  "Fox (2009)",
  "Mine (2011)"
),
rt_mean = c(
  454  ,
  317  ,
  430  ,
  525  ,
  479  ,
  387,
  531
),
rt_sd = c(
  142  ,
  158  ,
  137  ,
  260  ,
  144  ,
  165,
  233
),
rt_n = c(
  24  ,
  7  ,
  20  ,
  8  ,
 14  ,
 13,
  18
),
subset = as.factor(
  c(
    "90s",
   "90s",
    "90s",
    "00s",
    "00s",
    "00s",
    "00s"
  )
),
d1_unbiased = c(
  3.091587,
  1.742751,
  3.012857,
  1.793487,
  3.130074,
  2.195209,
  2.17667
)
)


# Fixed effect, 95% CI
estimate <- esci::meta_d1(
  original_7,
  d1_unbiased,
  rt_n,
  study_name,
  random_effects = FALSE
)

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


# Add a moderator
estimate_moderator <- esci::meta_d1(
  data = original_7,
  ds = d1_unbiased,
  ns = rt_n,
  moderator = subset,
  labels = study_name,
  random_effects = FALSE
)

# 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.