Design-Indexed Location-Scale Meta-Analysis

Fits constrained and unrestricted meta-analytic location-scale models in which residual between-study heterogeneity is modeled as an exponential function of a prespecified design-robustness score. The package supports maximum-likelihood (ML) and restricted maximum-likelihood (REML) estimation, location moderators, the conventional random-effects model as a nested special case, exact estimation at the nonnegative scale-gradient boundary, design-indexed heterogeneity summaries, scale-attenuation measures, prediction of fitted heterogeneity, leave-one-out influence diagnostics, and parametric-bootstrap inference for the scale gradient. A grouped scale diagnostic checks whether a monotone curve misses an interior peak or trough. Because the scale-gradient null lies on the boundary of the constrained parameter space, standard chi-square likelihood-ratio references do not apply (Self and Liang, 1987, ). The general location-scale parent model is described in Viechtbauer and Lopez-Lopez (2022, ). A scale model reweights studies and does not adjust the mean for design-linked bias.

drmeta

Design-Indexed Location-Scale Meta-Analysis

drmeta fits meta-analytic location-scale models in which residual between-study heterogeneity is an exponential function of a prespecified design-robustness index:

y_i ~ N( x_i'beta ,  v_i + tau0^2 * exp(-gamma * DR_i) )

The constrained form imposes gamma >= 0, encoding the directional hypothesis that unexplained heterogeneity does not increase as design robustness improves. Setting gamma = 0 recovers the conventional random-effects model exactly.

What this model does and does not do

A scale model changes how precision is allocated across studies. It does not identify or remove a systematic design-linked shift in the conditional mean. If the mean varies with design robustness, the scale-only pooled estimate is a model-dependent weighted average, not the effect of a hypothetical perfectly designed study. Supply location moderators via mods when design-linked mean differences are plausible, and do not describe scale reweighting as confounding adjustment.

Installation

install.packages("drmeta")

# Development version
# remotes::install_github("subirhait/drmeta")

Quick start

library(drmeta)

bcg <- utils::read.csv(
  system.file("extdata", "bcg_design_robustness.csv", package = "drmeta")
)

# Constrained fit
fit <- drmeta(yi = bcg[["yi"]], vi = bcg[["vi"]], dr = bcg[["dr"]])
summary(fit)

# Minimum comparison set
re  <- drmeta(bcg[["yi"]], bcg[["vi"]], bcg[["dr"]], gamma_fixed = 0)  # random effects
ls  <- drmeta(bcg[["yi"]], bcg[["vi"]], bcg[["dr"]], constrained = FALSE)
jls <- drmeta(bcg[["yi"]], bcg[["vi"]], bcg[["dr"]], mods = 1 - bcg[["dr"]])

# Interpretation over observed support, not extrapolated to [0,1]
dr_scale_attenuation(fit)
dr_plot_vfun(fit)

# Boundary-aware inference and influence
drmeta_bootstrap_gamma(fit, B = 999, seed = 1)
dr_loo(fit)

Reporting

Report gamma together with the observed range of the design index, the convergence and boundary status, and the fitted variance ratio or attenuation over a prespecified contrast within observed support. The magnitude of gamma alone depends on the scaling of the index and is not an invariant measure of design sensitivity.

For a primary analysis, construct the design index without using the realized effect estimate, its standard error, its p-value, its confidence interval, or any outcome-dependent diagnostic. Scores that use such information define an exploratory analysis.

Status

Current development version 0.2.3. NEWS.md documents the breaking changes from 0.1.0, including the functions removed and the withdrawal of the design-explained variance decomposition, and the 0.2.1 change to drmeta_bootstrap_gamma(), which now short-circuits when the constrained scale gradient is estimated at the boundary.

License

MIT