Methods of causal effect estimation for high-dimensional treatments: A radiotherapy simulation study

Abstract

Background

Radiotherapy, the use of high-energy radiation to treat cancer, presents a challenge in determining treatment outcome relationships due to its complex nature. These challenges include its continuous, spatial, high-dimensional, multi-collinear treatment, and personalized nature, which introduces confounding bias.

Purpose

Existing voxel based estimators may lead to biased estimates as they do not use a causal inference framework. We propose a novel estimator using sparsity via Adaptive Lasso within Pearl's causal framework, the Causal Adaptive Lasso (CAL).

Methods

First, simplified 2-dimensional treatment plans were simulated on $10\times 10$ and $25\times 25$ grids. Each simulation had an organ at risk placed in a consistent location where dose was minimized and a randomly placed target volume where dose was maximized. Treatment uncertainties were simulated to emulated a fractionated delivery. A directed acyclic graph was devised which captured the causal relationship between our outcome, including confounding.

The estimand was set to the associated dose-outcome response for each simulated delivery ($n=500$). We compared our proposed estimator the CAL against established voxel based regression estimators using planned and delivered simulated doses. Three variations on the causal inference-based estimators were implemented: causal regression without sparsity, CAL, and pixel-wise CAL. Variables were chosen based on Pearl's Back-Door Criterion. Model performance was evaluated using Mean Squared Error (MSE) and assessing bias of the recovered estimand.

Results

CAL is tested on simulated radiotherapy treatment outcome data with a spatially embedded dose response function. All tested CAL estimators outperformed voxel-based estimators, resulting in significantly lower total MSE, ${\text{MSE}}_{tot}$, and bias, yielding up to a four order of magnitude improvement in ${\text{MSE}}_{tot}$ compared to current voxel-based estimators ( compared to ${\text{MSE}}_{tot}\approx 1\times {10}^6$). CAL also showed minimal bias in pixels with no dose response.

Conclusions

This work shows that leveraging sparse causal inference methods can benefit both the identification of regions of given dose-response and the estimation of treatment effects. Causal inference methodologies provide a powerful approach to account for limitations in voxel-based analysis. Adapting causal inference methodologies to the analysis of clinical radiotherapy treatment-outcome data could lead to new and impactful insights on the causes of treatment complications.