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https://github.com/Novartis/Causal-inference-in-RCTs

This repository contains code examples for several methods in a Causal Inference in RCTs short course.
https://github.com/Novartis/Causal-inference-in-RCTs

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This repository contains code examples for several methods in a Causal Inference in RCTs short course.

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README 

        
# 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](https://www.icsa.org/icsa-2023-applied-statistics-symposium/)

- [Joint Statistical Meetings 2023](https://ww2.amstat.org/meetings/jsm/2023/)

- [ASA Biopharmaceutical Section Regulatory-Industry Statistics Workshop 2023](https://ww2.amstat.org/meetings/biop/2023/)

- [CEN 2023](https://cen2023.github.io/home/)

- [Australian Pharmaceutical Biostatistics Group 2024](https://apbg.org.au/apbg-events/)

- [International Society for Biopharmaceutical Statistics 2024](https://www.isbiostat.org/)

- [PSI 2024](https://www.psiweb.org/conferences/about-the-conference)

- [Joint Statistical Meetings 2024](https://ww2.amstat.org/meetings/jsm/2024/)



For data privacy reasons, 

the numerical results in the [`conditional_marginal`](conditional_marginal)

and [`hypothetical_estimand`](hypothetical_estimand) folders are based on simulated toy datasets and will not

match the results from the short courses. 

The numerical results in the [`heart_transplant`](heart_transplant) folder

will match the results from the short courses.



# Repository contents



## Conditional and marginal effects ([`conditional_marginal`](conditional_marginal))



This folder contains example code for the 

"conditional and marginal treatment effect" lecture of the short course.



In this repo, we implemented the following approaches:



  * Conditional treatment effect point estimate and SE using Huber-White robust “sandwich” estimator

  * Marginal treatment effect point estimate using standardization

  * SE of marginal treatment effect using

    

      * Nonparametric bootstrap method ([Efron and Tibshirani, 1994](https://www.taylorfrancis.com/books/mono/10.1201/9780429246593/introduction-bootstrap-bradley-efron-tibshirani)) 

      * Delta method

      * Parametric bootstrap method ([Aalen et al., 1998](https://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0258(19971015)16:19%3C2191::AID-SIM645%3E3.0.CO;2-5))



### How to run the scripts



The utilized functions to calculated the conditional and marginal estimates are 

in [`conditional_marginal/funs/funs.R`](conditional_marginal/funs/funs.R).

A wrapper function `summary_Estimate` could be used to obtain the conditional and marginal estimates with corresponding SE calculated in different ways. It can be called by `summary_Estimate(data=data, formula = as.formula("y ~ trt + X1"), nsim = 1000, trt.var = "trt", type = "OR")`, where



* `data` is the data frame including treatment factor and covariates of used samples



* `formula` specifies the response, treatment variable and adjusted covariates



* `nsim` is the number of bootstrap replicates when calculating SE for marginal estimate



* `trt.var` is the name of treatment variable



* `type` is the used estimator, "OR" for odds ratio and "RD" for risk difference.



To run the demo, first run `source("conditional_marginal/src/01_gen_data.R")`, which will generate the toy dataset using `benchtm` package.

The toy dataset has 500 samples randomised to pbo (`0`) or treatment (`1`) arm with 10 covariates. And the response is generated using `logit(p) = 0.5*(X1=='Y') + 1*X3 + 0.3*trt`. Therefore, there are two prognostic covariates, `X1` and `X3`.



Then `source("conditional_marginal/src/02_analysis.R")` gives the conditional and marginal estimates. And here we compare



* unadjusted, `Y ~ trt`



* adjusted with one moderate prognostic factor `Y ~ trt + X1`



* adjusted with one moderate and one strong prognostic factor `Y ~ trt + X1 + X3`



* adjusted with both prognostic factors and an unrelated factor `Y ~ trt + X1 + X3 + X8`



Both odds ratio and risk difference estimates will be calculated and saved in

`conditional_marginal/output/Result_condi_margin_OR.csv` and `conditional_marginal/output/Result_condi_margin_RD.csv` respectively.



## Heart transplant example ([`heart_transplant`](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)](https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/).



- [`gcomp.R`](heart_transplant/gcomp.R): Example of G-computation to estimate

E[Y(1) - Y(0)] and bootstrapping to construct a confidence interval.



- [`ipw.R`](heart_transplant/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`](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)](https://www.tandfonline.com/doi/full/10.1080/19466315.2022.2081599).



- [`hypothetical_gcomp.R`](hypothetical_estimand/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`](hypothetical_estimand/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`](https://github.com/Sophie-Sun/benchtm): 

Install by running `devtools::install_github("Sophie-Sun/benchtm")`.

- [`data.table`](https://cran.r-project.org/web/packages/data.table/index.html)

- [`future.apply`](https://cran.r-project.org/web/packages/future.apply/index.html)

- [`lmtest`](https://cran.r-project.org/web/packages/lmtest/index.html)

- [`mgcv`](https://cran.r-project.org/web/packages/mgcv/index.html)

- [`progress`](https://cran.r-project.org/web/packages/progress/index.html)

- [`sandwich`](https://cran.r-project.org/web/packages/sandwich/index.html)

- [`tidyverse`](https://cran.r-project.org/web/packages/tidyverse/index.html)



# External links



- [Markdown document](https://oncoestimand.github.io/princ_strat_drug_dev/princ_strat_example.html) with code examples for the principal stratum estimation approaches from [Bornkamp et al. (2021)](https://onlinelibrary.wiley.com/doi/10.1002/pst.2104). Created by Björn Bornkamp and Kaspar Rufibach.



# Code authors



- Robin Dunn, [email protected]

- Jiarui Lu, [email protected]

- Tianmeng Lyu, [email protected]

- Tobias Muetze, [email protected]

- Cong Zhang, [email protected]