Causal inference in RCTs

This repository contains code examples for several methods in a Causal Inference in RCTs short course. Novartis associates and external collaborators presented the short course at the following conferences:

• ICSA 2023 Applied Statistics Symposium
• Joint Statistical Meetings 2023
• ASA Biopharmaceutical Section Regulatory-Industry Statistics Workshop 2023
• CEN 2023
• Australian Pharmaceutical Biostatistics Group 2024
• International Society for Biopharmaceutical Statistics 2024
• PSI 2024
• Joint Statistical Meetings 2024
• International Biometric Conference 2024
• Joint Statistical Meetings 2025

For data privacy reasons, the numerical results in the hypothetical_estimand folder are based on simulated toy datasets and will not match the results from the short courses. The numerical results in the heart_transplant and conditional_marginal folders will match the results from the short courses.

Repository contents

Conditional and marginal effects (conditional_marginal)

This folder contains example code for the "conditional and marginal treatment effect" lecture of the short course.

In this repository, we implemented the following approaches:

• Conditional treatment effect point estimates and SEs using Huber-White robust "sandwich" estimator.

• Marginal treatment effect point estimates and SEs using Ye et al. (2023) semiparametric approaches implemented in RobinCar2 package

• Functions from previous lectures, available in conditional_marginal/funs/old_funs.R estimate the SE of the marginal treatment effect via the following approaches:

  • Nonparametric bootstrap method (Efron and Tibshirani, 1994)
  • Delta method
  • Parametric bootstrap method (Aalen et al., 1998).

How to run the scripts

To run the demo, first run conditional_marginal/src/01_gen_data.R, which will generate the toy dataset using the benchtm package. The toy dataset has 500 samples randomized to placebo (0) or treatment (1) arm with 10 covariates. The binary response is generated from the model logit(p) = 1*(X1=='Y') + 0.3*X2 + 0.3*trt. Therefore, there are two prognostic covariates, X1 and X2. This script saves the generated data to conditional_marginal/data/toy_data.rds. The data are also stored in the repository to ensure reproducibility.

Second, conditional_marginal/src/02_analysis.R estimates the marginal and conditional treatment effects on both the risk difference and odds ratio scales. This script compares treatment effects under the following adjustment models:

• unadjusted, Y ~ trt

• adjusted with one prognostic factor Y ~ trt + X1

• adjusted with two prognostic factors Y ~ trt + X1 + X2.

Heart transplant example (heart_transplant)

This folder contains two approaches to estimate the average causal effect on the risk difference scale (E[Y(1) - Y(0)]) for a binary treatment Z, a binary covariate X, and a binary outcome Y. The data example in these scripts is modified from the heart transplant example in Chapter 1 of Hernán and Robins (2020).

• gcomp.R: Example of G-computation to estimate E[Y(1) - Y(0)] and bootstrapping to construct a confidence interval.

• ipw.R: Example of inverse probability weighting to estimate E[Y(1) - Y(0)] and bootstrapping to construct a confidence interval.

Hypothetical estimand example (hypothetical_estimand)

This folder contains two approaches to estimate a hypothetical estimand. Suppose Y is an outcome, Z_0 indicates initial treatment assignment, and Z_1 indicates a switch to rescue medication. Let Y(z_0, z_1) represent the potential outcome under treatment assignment Z_0 = z_0 and rescue medication use indicated by Z_1 = z_1. These examples estimate E[Y(1,0) - Y(0,0)], which represents the average treatment effect in a hypothetical trial without the possibility of switching to rescue medication. This approach uses methods from Parra, Daniel, and Bartlett (2022).

• hypothetical_gcomp.R: Example of G-computation to estimate E[Y(1,0) - Y(0,0)] and bootstrapping to construct a confidence interval.

• hypothetical_ipw.R: Example of inverse probability weighting to estimate E[Y(1,0) - Y(0,0)] and bootstrapping to construct a confidence interval.

Required packages

We list all packages that are required to run scripts within this repository. Unless otherwise specified, packages can be installed from CRAN by using install.packages().

• benchtm: Install by running devtools::install_github("Sophie-Sun/benchtm").
• data.table
• future.apply
• lmtest
• mgcv
• progress
• sandwich
• tidyverse

External links

• Markdown document with code examples for the principal stratum estimation approaches from Bornkamp et al. (2021). Created by Björn Bornkamp and Kaspar Rufibach.

Code authors

• Robin Dunn, robin.dunn@novartis.com
• Jiarui Lu, jiarui.lu@novartis.com
• Tianmeng Lyu, tianmeng.lyu@novartis.com
• Tobias Muetze, tobias.muetze@novartis.com
• Cong Zhang, cong.zhang@novartis.com