Multilevel Unanchored Meta-Regression for Indirect Treatment Comparisons • mlumr

mlumr implements Multilevel Unanchored Meta-Regression (ML-UMR), a population-adjusted indirect treatment comparison method for disconnected evidence networks. ML-UMR extends Multilevel Network Meta-Regression (ML-NMR; Phillippo et al., 2020) to the unanchored setting, where individual patient data (IPD) are available for one treatment and only aggregate data (AgD) are available for the comparator, with no common reference arm (e.g. comparison of single arm studies). In this setting, mlumr estimates treatment effects while adjusting for cross-trial differences in prognostic factors.

In terms of the software, mlumr is an adaptation of the GPL-3 licensed multinma package, which provides functionality for conducting ML-NMR and NMAs. mlumr uses similar Sobol quasi-Monte Carlo and Gaussian-copula integration machinery to marginalize over the comparator-population covariate distribution, and extends the implementation with Stan likelihoods for the unanchored two-treatment problem, including SPFA and relaxed-SPFA models for binomial, normal, and Poisson outcomes.

The package provides three complementary methods within a unified interface:

ML-UMR (Bayesian): SPFA and Relaxed SPFA models via Stan, with quasi-Monte Carlo integration and Gaussian copula for population adjustment
STC (Frequentist): Simulated treatment comparison via parametric G-computation with delta-method standard errors
Naive (Benchmark): Unadjusted comparison of crude outcome summaries

Supported outcome families and link functions

Family	Outcome type	Link functions
Binomial	Binary (0/1)	logit (default), probit, cloglog
Normal	Continuous	identity (default), log
Poisson	Count + exposure	log (default)

Installation

Development version

# install.packages("remotes")
remotes::install_github("choxos/mlumr")

Prerequisites

mlumr uses Stan for Bayesian model fitting. The default backend is rstan, with Stan model C++ code generated by rstantools and compiled during package installation. A C++ toolchain is required:

macOS: Install Xcode Command Line Tools (xcode-select --install)
Windows: Install Rtools
Linux: Install g++ and make (usually available by default)

Optional: cmdstanr backend

Users who prefer cmdstanr can switch backends after installation:

# Switch to cmdstanr (will offer to install cmdstanr + CmdStan if needed)
mlumr_engine("cmdstanr")

# Switch back to rstan
mlumr_engine("rstan")

# Check current engine
mlumr_engine()

The engine preference persists for the current session. To set a permanent default, add to your .Rprofile:

options(mlumr.stan_engine = "cmdstanr")

You can also override the engine for a single model fit:

fit <- mlumr(dat, model = "spfa", engine = "cmdstanr")

When the package is attached with library(mlumr), it prints a short startup message with the installed version and GitHub repository.

Using mlumr alongside multinma

A subset of mlumr’s exported functions perform similar actions to their multinma counterparts and intentionally retain the same name (set_ipd(), set_agd(), add_integration(), unnest_integration(), distr(), marginal_effects(), qbern()/pbern()/dbern()). mlumr also exports several functions that are not available in multinma (mlumr(), naive(), stc(), combine_data(), check_integration(), conditional_effects(), conditional_predict(), prior_sensitivity(), calculate_dic()/loo()/waic(), compare_models()).

If both packages are attached in the same R session, R issues masking warnings on the shared names. The cleanest practice is to use only one package per session for any given analysis, matched to the network type (anchored connected → multinma; unanchored disconnected → mlumr). When you do need both attached (e.g. a methods-comparison sensitivity analysis), use the namespace prefix to disambiguate:

library(multinma)
library(mlumr)

# mlumr fits ML-UMR (disconnected, two-trial)
ipd_umr <- mlumr::set_ipd(ipd_df, treatment = "trt", outcome = "outcome",
                          covariates = c("age_group", "sex"))
fit_umr <- mlumr::mlumr(dat, model = "spfa")

# multinma fits ML-NMR (connected network)
net_nmr <- multinma::set_ipd(pso_ipd, study = studyc, trt = trtc, r = pasi75)
fit_nmr <- multinma::nma(net_nmr, regression = ~ age:.trt)

Quick start

library(mlumr)
set.seed(2026)

# --- Prepare IPD (index treatment) ---
n_A <- 500
ipd_df <- data.frame(
  trt = "Drug_A",
  outcome = rbinom(n_A, 1, 0.55),
  age_group = rbinom(n_A, 1, 0.40),
  sex = rbinom(n_A, 1, 0.55)
)

ipd <- set_ipd(ipd_df, treatment = "trt", outcome = "outcome",
                     covariates = c("age_group", "sex"))

# --- Prepare AgD (comparator) ---
agd_df <- data.frame(
  trt = "Drug_B", n_total = 400, n_events = 148,
  age_group_mean = 0.35, sex_mean = 0.50
)

agd <- set_agd(agd_df, treatment = "trt",
                     outcome_n = "n_total", outcome_r = "n_events",
                     cov_means = c("age_group_mean", "sex_mean"),
                     cov_types = c("binary", "binary"))

# --- Combine and add integration points ---
dat <- combine_data(ipd, agd)
dat <- add_integration(dat, n_int = 64,
  age_group = distr(qbern, prob = age_group_mean),
  sex = distr(qbern, prob = sex_mean)
)

# --- Run all three methods ---
# Naive (instant)
naive_result <- naive(dat)

# STC (instant)
stc_result <- stc(dat)

# ML-UMR SPFA (Bayesian, takes a few minutes)
fit <- mlumr(dat, model = "spfa",
             prior_intercept = prior_normal(0, 10),
             prior_beta = prior_normal(0, 2.5),
             chains = 4, iter = 4000, warmup = 2000, seed = 42)

summary(fit)
marginal_effects(fit, effect = "lor")

Methods overview

Feature	ML-UMR SPFA	ML-UMR Relaxed	STC	Naive
Covariate adjustment	Joint model	Joint model	Outcome regression	None
Effect modification	Assumed absent	Estimated	Not captured	N/A
Uncertainty	Posterior	Posterior	Delta method	Delta method
Population weighting	QMC integration	QMC integration	G-computation	None
Speed	Minutes	Minutes	Sub-second	Sub-second
Integration points required	Yes	Yes	Optional	No

Key functions

Function	Purpose
`set_ipd()`, `set_agd()`	Prepare IPD and AgD with outcome and covariate specification
`combine_data()`	Combine IPD and AgD into a unified dataset
`add_integration()`	Generate QMC integration points with Gaussian copula
`mlumr()`	Fit ML-UMR SPFA or Relaxed model via Stan
`mlumr_engine()`	Get or set the Stan backend (rstan or cmdstanr)
`naive()`, `stc()`	Frequentist benchmark methods
`predict()`	Population-specific predicted outcomes
`marginal_effects()`	Posterior treatment effect summaries
`conditional_effects()`	Covariate-conditional treatment effects
`conditional_predict()`	Predictions at specific covariate values
`calculate_loo()`, `calculate_waic()`, `calculate_dic()`, `compare_models()`	Bayesian model comparison (LOO-CV, WAIC, DIC)

When to use ML-UMR

Method	Data required	Type of ITC	Pairwise only	Type of treatment effect	Target population
MAIC	IPD + AgD	Anchored or unanchored	Yes	Marginal	Comparator
STC	IPD + AgD	Anchored or unanchored	Yes	Marginal	Comparator
ML-NMR	IPD + AgD	Anchored	No	Marginal or conditional	Any pre-specified target
ML-UMR	IPD + AgD	Unanchored	No	Marginal or conditional	Any pre-specified target

ML-UMR is most appropriate when:

You have IPD for one treatment and AgD for the comparator
No common reference arm connects the evidence (unanchored)
Binary, continuous, or count outcomes are of interest
Covariate distributions differ between trial populations

Vignettes

Detailed tutorials are available as package vignettes:

vignette("introduction") – Package overview, installation, and quick start
vignette("data-preparation") – IPD/AgD setup, integration points, and correlation handling
vignette("mlumr-models") – SPFA vs Relaxed models, priors, diagnostics, and LOO/WAIC/DIC model comparison
vignette("stc-and-naive") – STC and naive methods with delta-method details
vignette("model-comparison") – Side-by-side comparison of all methods with interpretation guidance
vignette("worked-example") – Complete end-to-end analysis from simulated data

References

The ML-UMR methodology extends the ML-NMR framework:

Phillippo, D. M., Dias, S., Ades, A. E., Belger, M., Brnabic, A., Schacht, A., Saure, D., Kadziola, Z., & Welton, N. J. (2020). “Multilevel Network Meta-Regression for population-adjusted treatment comparisons.” Journal of the Royal Statistical Society: Series A, 183(3), 1189–1210. doi:10.1111/rssa.12579

Chandler, C. & Ishak, J. (2025). “Anchors Away: Navigating Unanchored Indirect Comparisons With Multilevel Unanchored Meta-Regression (ML-UMR).” ISPOR Europe 2025, MSR28. Value in Health, 28, S498. https://www.valueinhealthjournal.com/article/S1098-3015(25)05944-3/abstract

Chandler, C. & Ishak, J. (2026). “Surviving Unanchored Indirect Comparisons: An Extension of Multilevel Unanchored Meta-Regression (ML-UMR) for Survival Analyses.” ISPOR 2026, MSR131. Value in Health, 29(S6). https://www.ispor.org/heor-resources/presentations-database/presentation-cti/ispor-2026/poster-session-3-3/surviving-unanchored-indirect-comparisons-an-extension-of-multilevel-unanchored-meta-regression-ml-umr-for-survival-analyses

Citing mlumr

citation("mlumr")

Authors

Ahmad Sofi-Mahmudi (author, maintainer)
Conor Chandler (author)

Acknowledgments

Portions of the package code, documentation, and Stan models were drafted and audited with the assistance of large language models: Anthropic’s Claude Opus 4.6 and 4.7 (via Claude Code) and OpenAI’s ChatGPT 5.4 and 5.5 (via Codex). All methodological choices, design decisions, and the final review and validation were performed by the named authors, who take responsibility for the package’s contents.

License

GPL-3. See https://www.gnu.org/licenses/gpl-3.0 for the full license text.

mlumr: Multilevel Unanchored Meta-Regression