Radiotherapy toxicity prediction using knowledge-constrained generalized linear model

Abstract

Radiation therapy (RT) is a frontline approach to treating cancer. While the target of radiation dose delivery is the tumor, there is an inevitable spill of dose to nearby normal organs causing complications. This phenomenon is known as radiotherapy toxicity. To predict the outcome of the toxicity, statistical models can be built based on dosimetric variables received by the normal organ at risk (OAR), known as Normal Tissue Complication Probability (NTCP) models. To tackle the challenge of the high dimensionality of dosimetric variables and limited clinical sample sizes, statistical models with variable selection techniques are viable choices. However, existing variable selection techniques are data-driven and do not integrate medical domain knowledge into the model formulation. We propose a knowledge-constrained generalized linear model (KC-GLM). KC-GLM includes a new mathematical formulation to translate three pieces of domain knowledge into non-negativity, monotonicity, and adjacent similarity constraints on the model coefficients. We further propose an equivalent transformation of the KC-GLM formulation, which makes it possible to solve the model coefficients using existing optimization solvers. Furthermore, we compare KC-GLM and several well-known variable selection techniques via a simulation study and on two real datasets of prostate cancer and lung cancer, respectively. These experiments show that KC-GLM selects variables with better interpretability, avoids producing counter-intuitive and misleading results, and has better prediction accuracy.

Keywords: Statistical modeling; generalized linear models; radiation toxicity prediction; variable selection techniques.

Figure 1.

Workflow of building a DVH-based NTCP model using rectal complication prediction of prostate cancer patients as an example.

Figure 2.

MAE between the true and estimated coefficients on a simulation dataset of 100 patients. The simulation is repeated 200 times to get the distribution of MAE for each method, which is represented by a bar chart. KC-GLM has a significantly lower MAE than all others with adjusted $p<0.0003$ after correction for multiple comparisons.

Figure 3.

AUC on the validation set of 20 patients (left) and on a unseen test set of 50 patients (right) under four methods. The simulation is repeated 200 times to get the distribution of MAE for each method, which is represented by a bar chart. KC-GLM has a significantly higher AUC than all others on the test set with adjusted $p<0.03$ after correction for multiple comparisons.

Figure 4.

Zero/non-zero coefficients estimated by KC-GLM (red dash) and fused lasso (blue dash) compared with true coefficients (black solid) in three simulation runs.

Figure 5.

Coefficient estimates by the four methods under (a) the dense feature setting and (b) the sparse feature setting.

Figure 6.

Coefficient estimates by the four methods under (a) the dense feature setting and (b) the sparse feature setting.

Figure 7.

Predicted survival probability curves by four methods for a deceased patient.