mlumr: Multilevel Unanchored Meta-Regression

The mlumr package implements Multilevel Unanchored Meta-Regression (ML-UMR) for population-adjusted indirect comparisons in disconnected networks. This method extends the ML-NMR framework (Phillippo et al. 2020) to handle situations where individual patient data (IPD) is available for one treatment and only aggregate data (AgD) is available for the comparator, with no common comparator linking the two studies. Models are estimated in a Bayesian framework using Stan via cmdstanr.

Key Features

• Multiple outcome types: Binary (binomial), continuous (normal), and count (Poisson) outcomes
• Population adjustment: Account for differences in prognostic factors between study populations using quasi-Monte Carlo integration with Gaussian copula
• Shared Prognostic Factor Assumption (SPFA): Fit models with shared or treatment-specific regression coefficients to test for effect modification
• Multiple estimands: Marginal treatment effects in index, comparator, or external target populations
• Model comparison: DIC-based model comparison and comprehensive diagnostics
• Simulation: Built-in data generation for testing and validation

Installation

Prerequisites

Install cmdstanr and CmdStan:

install.packages("cmdstanr", repos = c("https://stan-dev.r-universe.dev", getOption("repos")))
cmdstanr::install_cmdstan()

Install mlumr

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

Getting Started

A good place to start is with the package vignettes which walk through example analyses:

• Introduction to ML-UMR - Complete tutorial covering the full analysis workflow
• Continuous Outcomes - Mean difference analysis
• Count/Rate Outcomes - Rate ratio analysis
• Effect Modification - Testing and relaxing the SPFA
• Model Diagnostics - Convergence, DIC, and sensitivity analysis

Full function documentation is available at https://choxos.github.io/mlumr/reference/.

The methodology is described in:

Chandler, C. & Ishak, J. (2025). "Anchors Away: Navigating Unanchored Indirect Comparisons With Multilevel Unanchored Meta-Regression (ML-UMR)." ISPOR Europe 2025.

Phillippo, D. M. et al. (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.

Quick Start

library(mlumr)

# Generate example data (binary outcome)
data <- generate_simulation_data(
  n_index = 200,
  n_comparator = 150,
  n_covariates = 2,
  effect_modification = "none"
)

# Set up unanchored comparison
ipd <- set_ipd_unanchored(
  data = data$ipd,
  treatment = "treatment",
  outcome = "outcome",
  covariates = c("x1", "x2")
)

agd <- set_agd_unanchored(
  data = data$agd,
  treatment = "treatment",
  outcome_n = "n_total",
  outcome_r = "n_events",
  cov_means = c("x1_mean", "x2_mean"),
  cov_sds = c("x1_sd", "x2_sd")
)

# Combine and add integration points
network <- combine_unanchored(ipd, agd)
network <- add_integration_unanchored(
  network,
  n_int = 64,
  x1 = distr(qnorm, mean = x1_mean, sd = x1_sd),
  x2 = distr(qnorm, mean = x2_mean, sd = x2_sd)
)

# Fit ML-UMR model with SPFA
fit <- mlumr(
  data = network,
  spfa = TRUE,
  iter_warmup = 1000,
  iter_sampling = 2000,
  chains = 4
)

# Summary and marginal effects
summary(fit)
marginal_effects(fit, population = "both")

When to Use ML-UMR

Method	Data Required	Network Type	Population Adjustment	Effect Modification
MAIC	IPD + AgD	Disconnected	Yes (reweighting)	Limited
STC	IPD + AgD	Disconnected	Yes (regression)	Yes
ML-NMR	IPD + AgD	Connected	Yes (integration)	Yes
ML-UMR	IPD + AgD	Disconnected	Yes (integration)	Yes

Citing mlumr

citation("mlumr")

Sofi-Mahmudi, A. (2026). mlumr: Multilevel Unanchored Meta-Regression for Indirect Comparisons. R package version 0.1.0. https://choxos.github.io/mlumr/

When using ML-UMR, please also cite the methodology papers listed above.

Author

Ahmad Sofi-Mahmudi (ORCID)

License

MIT License. See LICENSE file for details.