Overview
mlumr implements multilevel unanchored meta-regression (ML-UMR) for indirect treatment comparisons using individual patient data (IPD) and aggregate data (AgD). It supports binary, continuous (normal), and count (Poisson) outcomes. It provides:
-
ML-UMR (Bayesian): SPFA and Relaxed SPFA models via
Stan (
rstanby default, with optionalcmdstanr) - STC: Simulated treatment comparison via parametric G-computation
- Naive: Unadjusted comparison as a benchmark
Version 0.1.0 is a two-treatment package: one treatment is represented by IPD (the index treatment) and one by AgD (the comparator treatment). Multi-treatment unanchored networks are outside the current package scope.
When to use mlumr
Use mlumr when you need to compare two treatments that have never been directly compared in the same trial (disconnected network), and you have:
- IPD from one trial (index treatment)
- AgD from another trial (comparator treatment)
- Shared covariates between populations
- Binary, continuous, or count outcomes
Installation
# From GitHub (development version)
# install.packages("remotes")
remotes::install_github("choxos/mlumr")Quick start
The pipeline below runs on toy data so every chunk is self-contained.
For a more detailed worked analysis, see
vignette("worked-example").
library(mlumr)
set.seed(2026)
# Toy IPD: trial A (index treatment, binary outcome)
n_a <- 300
trial_a_data <- data.frame(
trt = "Drug_A",
response = rbinom(n_a, 1, 0.55),
age_cat = rbinom(n_a, 1, 0.40),
sex = rbinom(n_a, 1, 0.55)
)
# Toy AgD: trial B (comparator treatment)
trial_b_data <- data.frame(
trt = "Drug_B",
n_total = 400,
n_events = 160,
age_cat_mean = 0.35,
sex_mean = 0.50
)
# 1. Prepare IPD
ipd <- set_ipd(
data = trial_a_data,
treatment = "trt",
outcome = "response",
covariates = c("age_cat", "sex")
)
# 2. Prepare AgD
agd <- set_agd(
data = trial_b_data,
treatment = "trt",
outcome_n = "n_total",
outcome_r = "n_events",
cov_means = c("age_cat_mean", "sex_mean"),
cov_types = c("binary", "binary")
)
# 3. Combine
dat <- combine_data(ipd, agd)
# 4. Add integration points (needed for ML-UMR)
dat <- add_integration(
dat,
n_int = 64,
age_cat = distr(qbern, prob = age_cat_mean),
sex = distr(qbern, prob = sex_mean)
)
# 5. Fit ML-UMR
fit_spfa <- mlumr(
dat, model = "spfa",
chains = 2, iter = 500, warmup = 250,
seed = 42, refresh = 0, verbose = FALSE
)
fit_relaxed <- mlumr(
dat, model = "relaxed",
chains = 2, iter = 500, warmup = 250,
seed = 43, refresh = 0, verbose = FALSE
)
# 6. Compare
summary(fit_spfa)
#> ML-UMR Model Summary
#> ====================
#>
#> Model: SPFA
#> Family: Binary
#> Link: logit
#> Engine: rstan
#> Treatments: Drug_A (IPD) vs Drug_B (AgD)
#>
#> MCMC Diagnostics:
#> Divergent transitions: 0
#> Max treedepth hits: 0
#> Max Rhat: 1.016
#> Min ESS: 149
#>
#> Intercepts (logit scale):
#> variable mean sd 2.5% 97.5% Rhat
#> mu_index 0.01040724 0.1915921 -0.3307466 0.3815756 1.007205
#> mu_comparator -0.63607867 0.1700693 -0.9595353 -0.3209510 1.015403
#>
#> Regression Coefficients:
#> variable mean sd 2.5% 97.5% Rhat
#> beta[1] -0.1538366 0.2480568 -0.6437745 0.3240322 0.9976325
#> beta[2] 0.5748965 0.2306527 0.1285506 1.0311792 1.0164810
#>
#> Marginal Treatment Effects:
#> Log Odds Ratios:
#> variable mean sd 2.5% 97.5%
#> lor_index 0.6293387 0.1529275 0.3198898 0.9268537
#> lor_comparator 0.6296880 0.1530364 0.3199753 0.9284606
#> Risk Differences:
#> variable mean sd 2.5% 97.5%
#> rd_index 0.1553421 0.03716764 0.07954897 0.2274495
#> rd_comparator 0.1553186 0.03719440 0.07955894 0.2276036
#> Risk Ratios:
#> variable mean sd 2.5% 97.5%
#> rr_index 1.390010 0.1108687 1.182237 1.622135
#> rr_comparator 1.394113 0.1115285 1.182954 1.627734
compare_models(fit_spfa, fit_relaxed)
#>
#> Model Comparison (DIC)
#> ======================
#>
#> Model DIC pD Delta_DIC
#> Relaxed SPFA 419.68 3.88 0.00
#> SPFA 420.17 4.05 0.48
#>
#> Lower DIC = better fit. Delta_DIC > 5 is a rough heuristic for
#> meaningful difference, not a formally calibrated threshold.
#> DIC should not be the sole basis for model selection.
# 7. Frequentist benchmarks
naive_result <- naive(dat)
stc_result <- stc(dat)
print(naive_result)
#> Naive Unadjusted Indirect Comparison
#> =====================================
#>
#> Treatments: Drug_A vs Drug_B
#>
#> Event rates:
#> Index (IPD): 0.560 (168/300)
#> Comparator (AgD): 0.400 (160/400)
#>
#> Log Odds Ratio: 0.6466 (SE: 0.1547)
#> 95% CI: [0.3433, 0.9499]
print(stc_result)
#> Simulated Treatment Comparison (G-computation)
#> ===============================================
#>
#> Treatments: Drug_A vs Drug_B
#>
#> Marginalized P(Y=1|index trt, comp pop): 0.5555
#> Observed P(Y=1|comp trt, comp pop): 0.4000
#>
#> Log Odds Ratio: 0.6285 (SE: 0.1549)
#> 95% CI: [0.3250, 0.9321]
#>
#> Outcome model coefficients:
#> (Intercept) age_cat sex
#> 0.0133 -0.1527 0.5697Before using results in a real analysis, inspect integration quality and posterior diagnostics:
check_integration(
dat,
age_cat = distr(qbern, prob = age_cat_mean),
sex = distr(qbern, prob = sex_mean)
)
#> Integration check: n_int = 64 vs 128
#> Marginals -- max relative difference: 0.0476
#> CAUTION: 1-5%% marginal relative difference. Consider increasing n_int.
#> Joint -- max |cor(current) - cor(doubled)|: 0.0012
#> OK joint: pairwise correlations agree within 0.05.
prior_summary(fit_spfa)
#> Priors for ML-UMR Fit
#> =====================
#>
#> Intercepts (mu_index, mu_comparator):
#> normal(0, 10)
#> (package default, mlumr 0.1.0)
#>
#> Regression coefficients (beta):
#> normal(0, 2.5) applied to all 2 covariate(s)
#> (package default, mlumr 0.1.0)
fit_spfa$diagnostics
#> $n_divergent
#> [1] 0
#>
#> $n_max_treedepth
#> [1] 0
max(fit_spfa$summary$Rhat, na.rm = TRUE)
#> [1] 1.016481
min(fit_spfa$summary$n_eff, na.rm = TRUE)
#> [1] 148.6844Choosing a method
| Method | Adjusts for covariates? | Effect modification? | Inference |
|---|---|---|---|
| ML-UMR SPFA | Yes | No (shared betas) | Bayesian |
| ML-UMR Relaxed | Yes | Yes (treatment-specific betas) | Bayesian |
| STC | Yes (outcome model only) | No | Frequentist |
| Naive | No | N/A | Frequentist |
- ML-UMR SPFA is appropriate when prognostic factors affect both treatments equally.
- ML-UMR Relaxed is appropriate when you suspect treatment-by-covariate interactions (effect modification).
- STC adjusts for imbalances through an outcome model and uses integration points when available; best when treatment effects do not vary with covariates.
- Naive serves as a benchmark only; do not use for inference in the presence of cross-trial differences.