Fitting Bayesian Marginal Structural Models for Longitudinal Observational Data

Implements Bayesian marginal structural models for causal effect estimation with time-varying treatment and confounding. It includes an extension to handle informative right censoring. The Bayesian importance sampling weights are estimated using JAGS. See Saarela (2015) for methodological details.

bayesmsm

Overview

bayesmsm is an R package that implements the Bayesian marginal structural models to estimate average treatment effect for drawing causal inference with time-varying treatment assignment and confounding with extension to handle informative right-censoring. The Bayesian marginal structural models is a semi-parametric approach and features a two-step estimation process. The first step involves Bayesian parametric estimation of the time-varying treatment assignment models and the second step involves non-parametric Bayesian bootstrap to estimate the average treatment effect between two distinct treatment sequences of interest.

Reference paper on Bayesian marginal structural models:

• Saarela, O., Stephens, D. A., Moodie, E. E., & Klein, M. B. (2015). On Bayesian estimation of marginal structural models. Biometrics, 71(2), 279-288.

• Liu, K., Saarela, O., Feldman, B. M., & Pullenayegum, E. (2020). Estimation of causal effects with repeatedly measured outcomes in a Bayesian framework. Statistical methods in medical research, 29(9), 2507-2519.

Installation

Install using devtools package:

## install.packages(devtools) ## make sure to have devtools installed 
devtools::install_github("Kuan-Liu-Lab/bayesmsm")
library(bayesmsm)

Dependency

This package depends on the following R packages:

• MCMCpack
• doParallel
• foreach
• parallel
• R2jags
• coda

Quick Start

Here are some examples demonstrating how to use the bayesmsm package:

# Simulating longitudinal causal data without right-censoring
# 1) Define coefficient lists for 2 visits
amodel <- list(
  # Visit 1: logit P(A1=1) = -0.3 + 0.4*L1_1 - 0.2*L2_1
  c("(Intercept)" = -0.3, "L1_1" = 0.4, "L2_1" = -0.2),
  # Visit 2: logit P(A2=1) = -0.1 + 0.3*L1_2 - 0.1*L2_2 + 0.5*A_prev
  c("(Intercept)" = -0.1, "L1_2" = 0.3, "L2_2" = -0.1, "A_prev" = 0.5)
)

# 2) Define binary outcome model: logistic on treatments and last covariates
ymodel <- c(
  "(Intercept)" = -0.8,
  "A1"          = 0.2,
  "A2"          = 0.4,
  "L1_2"        = 0.3,
  "L2_2"        = -0.3
)

# 3) Load package and simulate data without censoring
testdata <- simData(
  n                = 100,
  n_visits         = 2,
  covariate_counts = c(2, 2),
  amodel           = amodel,
  ymodel           = ymodel,
  y_type           = "binary",
  right_censor     = FALSE,
  seed             = 123
)


# Calculate Bayesian weights
weights <- bayesweight(
  trtmodel.list = list(
    A1 ~ L1_1 + L2_1,
    A2 ~ L1_2 + L2_2 + A1),
  data = simdat,
  n.chains = 1,
  n.iter = 200,
  n.burnin = 100,
  n.thin = 1,
  seed = 890123,
  parallel = FALSE)

# Perform Bayesian non-parametric bootstrap
model <- bayesmsm(ymodel = Y ~ A1 + A2,
  nvisit = 2,
  reference = c(rep(0,2)),
  comparator = c(rep(1,2)),
  family = "binomial",
  data = simdat,
  wmean = weights$weights,
  nboot = 50,
  optim_method = "BFGS",
  parallel = TRUE,
  seed = 890123,
  ncore = 2)

# View model summary
summary_bayesmsm(model)

License

This package is licensed under the MIT License. See the LICENSE file for details.

Citation

Please cite our software using:

@Manual{,
  title = {bayesmsm: An R package for longitudinal causal analysis using Bayesian Marginal Structural Models},
  author = {Xiao Yan and Martin Urner and Kuan Liu},
  year = {2025},
  note = {https://github.com/Kuan-Liu-Lab/bayesmsm},
  url = {https://kuan-liu-lab.github.io/bayesmsm/},
}

Contact

• e-mail: [email protected], [email protected]
• Please report bugs by opening an issue.