Harmonized Standardized Mean Differences

Computes traditional standardized mean differences (SMDs) and harmonized standardized mean differences (HSMDs) by replacing observed group standard deviations with common coefficient-of-variation benchmarks. Pooled summaries are estimated with mars(), allowing the harmonized effect sizes to be analyzed with univariate, multivariate, or multilevel model structures.

Usage

hsmd(
  data,
  mT,
  sdT,
  nT,
  mC,
  sdC,
  nC,
  study = NULL,
  probs = c(0.25, 0.5, 0.75),
  measure = c("d", "g"),
  structure = "univariate",
  formula = NULL,
  effectID = NULL,
  sample_size = NULL,
  varcov_type = NULL,
  variance = NULL,
  cv_by = NULL,
  cv_benchmarks = NULL,
  estimation_method = "REML",
  ...
)

# S3 method for class 'hsmd'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

data: A data frame containing treatment and control summary statistics.
mT, sdT, nT: Unquoted column names for treatment-group mean, standard deviation, and sample size.
mC, sdC, nC: Unquoted column names for control-group mean, standard deviation, and sample size.
study: Optional unquoted column name identifying studies. If omitted, a sequential study identifier is created.
probs: Numeric vector of coefficient-of-variation quantiles to use for harmonization. Defaults to c(0.25, 0.50, 0.75).
measure: Effect-size estimate used in the fitted mars() models, either "d" for Cohen's d or "g" for Hedges' g. Both estimates are returned.
structure: Model structure passed to mars(). Use "univariate", "multivariate"/"UN"/"DIAG1"/"DIAG2", or "multilevel".
formula: Optional model formula for univariate or multilevel models. The left-hand side is replaced internally with each SMD/HSMD effect-size column, so callers may supply either a one-sided formula (for example ~ 1 + (1 | district/study)) or a two-sided formula.
effectID: Optional column identifying dependent effect sizes for multivariate models.
sample_size: Optional sample-size column passed to mars() for multivariate SMD workflows.
varcov_type: Within-study variance-covariance type passed to mars(). Defaults to "univariate", "outcome", or "multilevel" depending on structure.
variance: Optional variance column used when the selected varcov_type requires an explicit variance argument.
cv_by: Optional unquoted column used to compute coefficient-of-variation benchmarks within subgroups, such as outcomes or domains.
cv_benchmarks: Optional named list with elements treatment and control, each a numeric vector of benchmark CVs aligned with probs.
estimation_method: Estimation method passed to mars(), either "REML" or "MLE".
...: Additional arguments passed to downstream print methods.
x: An object of class "hsmd".
digits: Number of digits used when printing numeric results.

Value

A list with class "hsmd" containing:

summary: Data frame of pooled SMD and HSMD model summaries.
effect_sizes: Data frame of study-level effect sizes and variances.
data: Original input data with added coefficient-of-variation and harmonized SD columns.
models: Named list of fitted mars model objects.
quantiles: Named numeric vector of the requested harmonization quantiles.

Examples

ex1 <- hsmd(
  data = hsmd_example_1,
  mT = mT, sdT = sdT, nT = nT,
  mC = mC, sdC = sdC, nC = nC,
  study = Study
)
ex1$summary
#>    method   component        est         se      ci.lb       ci.ub       tau2
#> 1     SMD (Intercept) -0.3060830 0.10640132 -0.5146258 -0.09754029 0.11743966
#> 2 HSMD_25 (Intercept) -0.4778418 0.22512747 -0.9190835 -0.03660002 0.72841275
#> 3 HSMD_50 (Intercept) -0.1789429 0.10868797 -0.3919674  0.03408160 0.12560800
#> 4 HSMD_75 (Intercept) -0.1105698 0.08000593 -0.2673785  0.04623900 0.04819645
#>         avwW       I2
#> 1 0.04191511 60.01581
#> 2 0.04546883 89.56395
#> 3 0.04186181 61.64808
#> 4 0.04132897 38.45138

ex2 <- hsmd(
  data = hsmd_example_2,
  mT = mT, sdT = sdT, nT = nT,
  mC = mC, sdC = sdC, nC = nC,
  study = Study
)
head(ex2$effect_sizes)
#>            d         vd          g         vg        d25       vd25        g25
#> 1 0.01961060 0.05128452 0.01941643 0.05027401 0.05640465 0.05130245 0.05584619
#> 2 0.25148710 0.01472472 0.25089351 0.01465529 0.22236365 0.01470316 0.22183880
#> 3 0.58686206 0.03247340 0.58346979 0.03209907 0.44725231 0.03192654 0.44466704
#> 4 0.75744489 0.13001630 0.73897062 0.12375138 0.98211539 0.13593793 0.95816136
#> 5 0.63954509 0.07257364 0.63094134 0.07063412 1.11658753 0.07979562 1.10156617
#> 6 0.07976613 0.03004166 0.07931205 0.02970061 0.11808903 0.03006995 0.11741680
#>         vg25        d50       vd50        g50       vg50        d75       vd75
#> 1 0.05029158 0.03853757 0.05129157 0.03815601 0.05028092 0.02160971 0.05128504
#> 2 0.01463383 0.15556823 0.01466371 0.15520103 0.01459457 0.09376783 0.01463964
#> 3 0.03155851 0.31282141 0.03153950 0.31101319 0.03117594 0.18838641 0.03130326
#> 4 0.12938768 0.69670406 0.12867802 0.67971128 0.12247759 0.44131633 0.12427444
#> 5 0.07766309 0.79372367 0.07447863 0.78304578 0.07248820 0.50675967 0.07126146
#> 6 0.02972858 0.08116724 0.03004250 0.08070519 0.02970144 0.04629415 0.03002592
#>          g75       vg75
#> 1 0.02139575 0.05027453
#> 2 0.09354650 0.01457061
#> 3 0.18729747 0.03094242
#> 4 0.43055252 0.11828620
#> 5 0.49994227 0.06935701
#> 6 0.04603062 0.02968504