This repository contains simulation studies comparing causal inference estimators for the Average Treatment Effect (ATE) under observational data settings — where treatment is not randomly assigned and confounding must be carefully accounted for.

The work is motivated by real challenges in healthcare and genomic research: how do we reliably estimate the causal effect of a treatment or exposure when we cannot run a randomised controlled trial, and when the data is high-dimensional and messy?

This simulation study benchmarks four estimators across scenarios of increasing complexity, from low-dimensional correlated covariates to high-dimensional sparse settings with up to 100 covariates.

Context: This work forms part of my PhD research in Statistics at the University of Edinburgh, where I apply these methods to large-scale observational healthcare and genomic data (UK Biobank). The simulations here use fully synthetic data — no real patient data is used or shared.

In observational studies — clinical registries, electronic health records, genomic cohorts — we observe who received a treatment and what happened to them, but we cannot control who got treated. Patients who receive a particular drug may systematically differ from those who don't, in ways that also affect their outcomes. This is confounding, and naively comparing treated and untreated groups gives a biased estimate of the true causal effect.

Causal inference methods address this by explicitly modelling:

1. The outcome mechanism Q(A, W): how the outcome Y depends on treatment A and covariates W
2. The treatment mechanism g(W): the probability of receiving treatment given covariates (the propensity score)

Getting both right — especially in high-dimensional settings — is the central challenge this project addresses.

All estimators use influence function-based inference for standard errors and confidence intervals, which provides valid uncertainty quantification without relying on parametric assumptions.

In high-dimensional settings (glmnet_update.R), outcome and propensity score models are estimated using cross-validated LASSO/elastic net (glmnet), replacing standard GLMs to handle the curse of dimensionality.

Key metrics evaluated across Monte Carlo replications:

• Mean bias
• Empirical variance and mean squared error (MSE)
• 95% confidence interval coverage
• Bias-to-standard-error ratio

Three data generating processes (DGPs) of increasing complexity:

Two correlated Gaussian covariates (ρ = 0.5). Three variants:

• 1a: Nonlinear outcome mechanism Q₀ = 1 + A − 0.7W₁ + 0.3·exp(−W₁W₂)
• 1b: Interaction in treatment mechanism g₀ = expit(0.5 − 1.5W₁W₂)
• 1c: Randomised treatment (benchmark — all estimators should perform well)

Eight binary covariates with a structured dependency chain (W4 depends on W1, W5 depends on W1–W4, etc.), mimicking the kind of correlated binary data common in clinical settings.

• p = 100 covariates, Toeplitz covariance structure with ρ = 0.5–0.9
• Only k = 10–20 covariates are truly predictive (sparse signal)
• Separate sparse signals for outcome and treatment mechanisms
• True ATE = 2

This is the most challenging setting and the primary focus of the glmnet-based estimators.

causal-inference-simulation/ │ ├── README.md │ ├── scripts/ │ ├── 01_data_generating_processes.R # DGP functions for all simulation studies │ ├── 02_utilities.R # Helper functions, MC evaluation, plotting │ ├── 03_estimators.R # Core estimators: DM, OLS, IPW, TMLE, C-TMLE │ └── 04_estimators_highdim.R # glmnet-based estimators for high-dim settings │ ├── notebooks/ │ └── simulation_study.Rmd # Main analysis notebook (rendered below) │ └── results/ └── ctmle_glmnet.csv # Saved Monte Carlo results (k=100, n=5000) 

Monte Carlo results based on k = 100 replications, n = 5,000 observations, high-dimensional sparse setting (Study 3):

All four estimators recover the true ATE = 2. The C-TMLE variants demonstrate improved bias-variance trade-off compared to standard TMLE in the high-dimensional sparse setting, consistent with the theoretical motivation for collaborative estimation. Full results including coverage rates and CI distributions are in notebooks/simulation_study.Rmd.

install.packages(c( "tidyverse", "MASS", "survey", "boot", "ggplot2", "skimr", "glm2", "glmnet", "randomForest", "SuperLearner" ))

# 1. Clone the repository # 2. Open simulation_study.Rmd in RStudio # 3. Set your working directory to the repo root # 4. Knit or run chunks sequentially # To run a quick single-dataset test: source("scripts/01_data_generating_processes.R") source("scripts/02_utilities.R") source("scripts/04_estimators_highdim.R") data_test <- sim3(n = 1000, p = 100) estimate_TMLE_glmnet(data_test, true_value = 2)

Note: The full Monte Carlo study (k = 100, n = 5000) is computationally intensive (~180-300 min). Pre-computed results are saved in results/ctmle_glmnet.csv for immediate exploration.

• Language: R (≥ 4.0)
• Core packages: glmnet, SuperLearner, survey, glm2, tidyverse
• Estimation: LASSO / elastic net via cross-validated glmnet for high-dimensional nuisance models
• Inference: Influence function-based standard errors (semiparametric efficiency theory)
• Evaluation: Monte Carlo simulation with empirical bias, variance, MSE, and coverage

This repository is part of my PhD research at the University of Edinburgh, School of Mathematics. My thesis focuses on estimating causal effects from observational healthcare data in the presence of non-ignorable missingness, applying C-TMLE methodology to identify genetic variants with causal effects on disease outcomes using UK Biobank data.

The simulation work here serves to validate and compare the performance of these estimators under controlled conditions before applying them to real data.

Related areas of application:

• Pharmacoepidemiology and clinical trials emulation
• Genomics / Mendelian randomisation
• Health technology assessment
• Any domain where RCTs are infeasible and high-quality causal estimates from observational data are needed

Juliet Asantewaa Sarpong
PhD Candidate, Statistics — University of Edinburgh
📧 asantewaahsarpong@gmail.com
🐙 github.com/Asantewaah
💼 linkedin.com/in/asantewaah-sarpong

Feedback, questions, and collaboration enquiries welcome.