respondeR re-expresses meta-analyses of continuous trial outcomes in terms of responders. Clinicians and patients reason about "how many people get better", not about standardized mean differences. It uses only the summary statistics that trials usually report: the mean change, standard deviation and sample size in each arm. From these respondeR estimates the proportion of patients whose change crosses a minimal important difference (MID) threshold, and contrasts the arms as a risk difference (RD), risk ratio (RR), odds ratio (OR) or number needed to treat (NNT).
It follows the interpretability tutorial of Thorlund, Walter, Johnston, Furukawa & Guyatt (2011), implementing the cut-point ("dichotomization") and standardized-mean-difference conversions it reviews, and adds a threshold-free common-language effect size. The estimation methods were evaluated in a simulation study (Sofi-Mahmudi, 2024).
Try it in the browser (no install): https://choxos.github.io/respondeR/app/ (a separate implementation; the R package is the reference)
Documentation: https://choxos.github.io/respondeR/
# From CRAN
install.packages("respondeR")
# Development version from GitHub
# install.packages("remotes")
remotes::install_github("choxos/respondeR")library(respondeR)
# Built-in example: three trials of a continuous change score
sample_responder_data
#> study change_e sd_e n_e change_c sd_c n_c
#> 1 Study 1 0.9581395 1.257593 43 0.217777778 1.195501 45
#> 2 Study 2 0.7920863 1.281364 139 0.003448276 1.324629 145
#> 3 Study 3 1.0230769 1.341201 156 -0.041975309 1.263178 162
# Proportion of responders (change > MID of 1) and between-arm contrasts
responder_analysis(sample_responder_data, mid = 1)
#> Responder analysis (respondeR)
#> MID = 1 (a higher change is a response); k = 3 studies; fixed
#> effects; delta per-study variance
#> Percentages; 95% confidence intervals.
#>
#> Method PE PC RD RR
#> Individual - - 25.5 (20.0 to 31.0) 2.15 (1.79 to 2.58)
#> Weighted mean 47.6 22.1 25.5 (20.0 to 31.0) 2.16 (1.80 to 2.59)
#> Unweighted mean 47.7 22.8 24.9 2.09
#> Median 48.7 21.5 27.2 2.26
#> OR NNT
#> 3.20 (2.45 to 4.18) NNTB 3.9 (3.2 to 5.0)
#> 3.21 (2.46 to 4.19) NNTB 3.9 (3.2 to 5.0)
#> 3.09 NNTB 4.0
#> 3.46 NNTB 3.7The result is a data frame (res$rd, as.data.frame(res) for every column) with
summary() and plot() (forest plot) methods. Proportions and risk differences
are stored on the [0, 1] scale.
# Random effects with the small-k Hartung-Knapp-Sidik-Jonkman interval
res <- responder_analysis(sample_responder_data, mid = 1, method = "individual",
pooling = "random", ci_method = "hksj_adhoc")
# How the result depends on the MID
plot(responder_curve(sample_responder_data, mids = seq(0, 2, by = 0.25)), at = 1)
# GRADE summary-of-findings rows per 1000 patients
responder_sof(res, control_risk = c(0.1, 0.3))
# Threshold-free: how often does a treated patient do better than a control?
responder_cles(sample_responder_data)One row per study, with these columns (the experimental arm is _e, the control
arm _c):
| Column | Meaning |
|---|---|
study |
Study (comparison) label |
change_e |
Mean change in the experimental arm |
sd_e |
SD of change in the experimental arm |
n_e |
Experimental arm sample size |
change_c |
Mean change in the control arm |
sd_c |
SD of change in the control arm |
n_c |
Control arm sample size |
trial |
Optional: trial label shared by the comparisons of a multi-arm trial |
Comparisons of one multi-arm trial that reuse a control arm are marked by a
shared trial value; respondeR then splits that control arm among them so its
patients are not counted twice. Missing change-score SDs can be reconstructed
with impute_change_sd().
Two datasets ship with the package: sample_responder_data (a small toy
example) and vas_pain, a real meta-analysis of 20 exercise-versus-control
comparisons for spinal health pooled on the VAS pain scale (Li et al., 2025,
reproduced under CC BY 4.0). Because VAS change is negative when pain improves,
analyze it with direction = "lower":
# Proportion reaching a 1.5 cm VAS reduction, exercise vs control
responder_analysis(vas_pain, mid = -1.5, direction = "lower",
pooling = "random", ci_method = "hksj_adhoc")A responder is a patient whose change crosses the MID. Under a Normal model an
arm's responder probability is p = Phi((mu - mid) / sigma) (for
direction = "higher"). The methods differ in how the per-arm summaries are
pooled across studies before, or after, dichotomizing.
| Method | What it pools | Variance / CI | Notes |
|---|---|---|---|
individual |
Per-study contrasts (fixed or random effects) | Yes | Recommended; comparisons stay within trials |
weighted |
Pooled control mean plus pooled within-study mean difference | Delta method | Pool-then-dichotomize, randomization kept |
unweighted |
Arithmetic mean of study means and SDs | None | Descriptive (point estimate) |
median |
Median of study means and SDs | None | Descriptive (point estimate) |
smd |
Standardized mean difference to odds ratio | Yes | Logistic bridge; opt-in |
Responder probabilities are evaluated on the log scale, so risk and odds ratios
stay exact even in the far tails. With fixed effects the risk difference uses
sample-size weights, which a study with probabilities near 0 or 1 cannot
dominate, and a warning flags any study that holds more than half of the weight.
control = "median" takes the baseline risk from the median control arm, as in
the simulation study of Sofi-Mahmudi (2024); the result is then a point estimate.
Effect measures. Every method reports the absolute risk difference, the
relative risk ratio and odds ratio, and the number needed to treat in
the Altman form (NNTB for benefit, NNTH for harm). responder_cles() adds the
threshold-free common-language effect size.
Options. pooling = "random" (DerSimonian-Laird or REML) with
ci_method = "wald", "hksj" or "hksj_adhoc"; se_method ("delta" or
"binomial"); rd_weights; control for the baseline-risk rule;
ci_type = "logit" for bounded MOVER intervals; mid_sd to propagate MID
uncertainty (added once, after pooling); and dist = "lognormal" or "t" for
non-Normal change scores.
Version 0.2.0 corrects several methods, so its numbers differ from 0.1.0; see
NEWS.md.
Already have a continuous meta-analysis saved in an R object? Pass it straight to
responder_analysis(). A meta::metacont object carries both arms, so the full
analysis runs; a metafor::rma fit carries only the pooled effect, so you give a
baseline control responder risk. respondeR reads the object with base R, so the
source package need not be attached, and it adds no new dependencies.
# meta::metacont object: full analysis
responder_analysis(metacont_fit, mid = 1)
# metafor::rma object (SMD or MD): pooled effect + a named baseline control risk
responder_analysis(rma_fit, baseline = 0.22)
responder_analysis(rma_fit, baseline = 0.22, direction = "lower") # e.g. pain
# Just a pooled estimate from a paper:
responder_from_effect(0.5, se = 0.1, measure = "SMD", baseline = 0.25)The fit's own choices carry over: excluded studies are dropped, random-effects and
Hartung-Knapp settings are reused, and an rma fit's interval and confidence
level are kept. See vignette("meta-analysis-objects"). Support for netmeta
and multinma objects is planned for a later release.
| Function | Purpose |
|---|---|
responder_analysis() |
Pooled responder proportions and effect measures (data frame or fitted MA object) |
responder_from_effect() |
Convert a pooled SMD/MD + baseline to responder measures |
as_responder_data() |
Extract the arm-summary data frame from an MA object |
responder_curve() |
The analysis across a range of MID thresholds |
responder_sof() |
GRADE summary-of-findings rows per 1000 patients |
impute_change_sd() |
Reconstruct change-score SDs (Cochrane Handbook) |
responder_rd_individual() |
Per-study risk differences (forest-plot input) |
responder_proportions() |
Per-arm responder probabilities with variances |
responder_cles() |
Threshold-free common-language effect size |
format_responder_results() |
Display-ready formatting |
launch_responder_analysis() |
Launch the Shiny application |
The package bundles a point-and-click app: upload a CSV or use the bundled example, set the MID and direction, choose methods and options, and view the results table, per-study forest plot and CLES, with CSV downloads. Notes and warnings from the analysis are listed under the results.
launch_responder_analysis()A browser version (no R, no install) runs at https://choxos.github.io/respondeR/app/; it is a separate implementation that does not yet include the 0.2.0 changes.
vignette("respondeR"): getting started; data format, a worked example, and interpreting the output.vignette("methodology"): the statistics in full; the cut-point approach, each method and its variance, the relative measures, CLES, the SMD bridge, heterogeneity, MID uncertainty, multi-arm trials, assumptions and a method-choice guide.vignette("meta-analysis-objects"): responder analysis from a fittedmetaormetaformeta-analysis, or from a single pooled estimate.
Sofi-Mahmudi, A. (2024). Identifying an optimal strategy for converting pain as a continuous outcome to a responder analysis [Master's thesis, McMaster University]. MacSphere. https://hdl.handle.net/11375/30210
Thorlund, K., Walter, S. D., Johnston, B. C., Furukawa, T. A., & Guyatt, G. H. (2011). Pooling health-related quality of life outcomes in meta-analysis: a tutorial and review of methods for enhancing interpretability. Research Synthesis Methods, 2(3), 188 to 203. doi:10.1002/jrsm.46
Anzures-Cabrera, J., Sarpatwari, A., & Higgins, J. P. T. (2011). Expressing findings from meta-analyses of continuous outcomes in terms of risks. Statistics in Medicine, 30(25), 2967 to 2985. doi:10.1002/sim.4298
McGraw, K. O., & Wong, S. P. (1992). A common language effect size statistic. Psychological Bulletin, 111(2), 361 to 365.
Chinn, S. (2000). A simple method for converting an odds ratio to effect size for use in meta-analysis. Statistics in Medicine, 19(22), 3127 to 3131.
Bundled data:
Li, Z., Bao, Z., Wang, S., & Zhao, M. (2025). Meta-analysis of the best exercise mode and dose study for improving spinal health. Frontiers in Sports and Active Living, 7, 1614906. doi:10.3389/fspor.2025.1614906 (the
vas_paindataset, Figure 3, reproduced under CC BY 4.0).
citation("respondeR")The hex logo shows two Normal change-score distributions, control and experimental, split by a dashed MID cut-point. The shaded tails beyond the cut are the responder proportions in each arm; their contrast is the risk difference. That is responder analysis in one picture.
GPL-3. See https://www.gnu.org/licenses/gpl-3.0 for the full license text.