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

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.

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).

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.

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.

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.