Voxel-Based Causal Inference in Radiotherapy: A Simulation Study

  • Alexander Jenkins

Student thesis: Master of Philosophy


Radiotherapy is the most common treatment for cancer, delivering 3D, personalised radiation dose to the tumour. Radiotherapy planning requires considering a high-dimensional continuous optimisation space to achieve tumour control while limiting the probability of treatment complications. However, estimating the Average Treatment Effect (ATE) of radiation dose on complications across the anatomy is difficult; mainly because of confounding in observational data. Under certain assumptions, developing a causal framework provides methods to adjust for confounding. The aim of this work is to use simulated data to investigate if unbiased and consistent voxel-based causal inference is possible, how, under what circumstances, and with what accuracy. I simulate radiotherapy treatment plans from a simplified, yet realistic, data generating process. Patients have a single tumour (random location) where dose is maximal and a single Organ at Risk (OAR) (fixed location) where dose is minimal. Variables control fall-off of dose around the tumour, fall-off and magnitude of dose at the organ, and a covariate that confounds the treatment plan. I simulate realistic treatment uncertainties: random shifts in x- and y-directions of the entire planned dose distribution, spatially correlated noise sampled from a Gaussian process prior, and independent noise at each pixel. A continuous complication is generated via a linear function of the delivered dose to a spatially inhomogeneous set of pixels (ATE estimand), a covariate that also affects the delivered dose distribution, and a spatially inhomogeneous interaction between delivered dose and the covariate. Three methods based in causal inference are used to estimate the ATE at each pixel: 1) pixel-wise sparse causal regression, 2) sparse causal regression and 3) a causal regression. The sparse estimator used is the Adaptive Lasso. These are compared to methods currently used in radiotherapy. I found that all methods based in causal inference performed with lower total Mean Squared Error (MSE), across all parameterisations tested in the simulation compared to the currently used voxel-based statistical methods in radiotherapy. Exploiting the oracle property of the Adaptive Lasso to simultaneously identify important pixels with dose-response and estimate ATE, was in general a successful technique over all parameterisations of the simulation tested. The only method capable of unbiased estimation was the causal regression, however, multicollinearity hinders accurate ATE estimation at specific regions of parameter space and at a high resolution. The estimation method that scored a consistently low total MSE over all parameterisations was the sparse causal regression. This method was able to assign a near zero effect to unimportant pixels, and whilst estimates elsewhere were biased, they were accurate and efficient; especially at lower resolutions.
Date of Award1 Aug 2022
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorEliana Vasquez Osorio (Supervisor), Andrew Green (Supervisor), Alan Mcwilliam (Supervisor), David Thomson (Supervisor), Matthew Sperrin (Supervisor) & Mike Merchant (Supervisor)

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