Voxel Forecast for Precision Oncology: Predicting Spatially Variant and Multiscale Cancer Therapy Response on Longitudinal Quantitative Molecular Imaging

Abstract

Purpose: Prediction of spatially variant response to cancer therapies can inform risk-adaptive management within precision oncology. We developed the "Voxel Forecast" multiscale regression framework for predicting spatially variant tumor response to chemoradiotherapy on fluorodeoxyglucose (FDG) positron emission tomography/computed tomography (PET/CT) imaging.

Experimental design: Twenty-five patients with locally advanced non-small cell lung cancer, enrolled on the FLARE-RT phase II trial (NCT02773238), underwent FDG PET/CT imaging prior to (PETpre) and during week 3 (PETmid) of concurrent chemoradiotherapy. Voxel Forecast was designed to predict tumor voxel standardized uptake value (SUV) on PETmid from baseline patient-level and voxel-level covariates using a custom generalized least squares (GLS) algorithm. Matérn covariance matrices were fit to patient- specific empirical variograms of distance-dependent intervoxel correlation. Regression coefficients from variogram-based weights and corresponding standard errors were estimated using the jackknife technique. The framework was validated using statistical simulations of known spatially variant tumor response. Mean absolute prediction errors (MAEs) of Voxel Forecast models were calculated under leave-one-patient-out cross-validation.

Results: Patient-level forecasts resulted in tumor voxel SUV MAE on PETmid of 1.5 g/mL while combined patient- and voxel-level forecasts achieved lower MAE of 1.0 g/mL (P < 0.0001). PETpre voxel SUV was the most important predictor of PETmid voxel SUV. Patients with a greater percentage of under-responding tumor voxels were classified as PETmid nonresponders (P = 0.030) with worse overall survival prognosis (P < 0.001).

Conclusions: Voxel Forecast multiscale regression provides a statistical framework to predict voxel-wise response patterns during therapy. Voxel Forecast can be extended to predict spatially variant response on multimodal quantitative imaging and may eventually guide optimized spatial-temporal dose distributions for precision cancer therapy.

©2019 American Association for Cancer Research.

Figures

Figure 1.

Baseline (Pre-RT, upper row) and Week 3 response (Mid-RT, lower row) FDG PET/CT imaging during chemoradiotherapy in 2 example FLARE-RT protocol patients. FDG-PET imaging standardized uptake value (SUV) hot-metal colorscale is overlaid on treatment planning CT imaging with rainbow colorscale planned isodose lines between the Pre-RT and Mid-RT time points. Pre-RT metabolic tumor volume (MTV) is displayed as a khaki contour. Patient (A) presents with large spatially heterogeneous response, while patient (B) presents with modest spatially homogeneous response that preserves the baseline ring uptake pattern.

Figure 2.

Schematic of Voxel Forecast variogram-weighted multiscale regression framework to predict tumor voxel response. Multiscale patient- and voxel-level predictors generate ordinary least squares (OLS) residuals to initialize iterative OLS-GLS (generalized least squares) hybrid regression with Matérn variogram to account for spatial auto-correlation of voxels under leave-1-out cross validation. Regression coefficient standard errors (SE) are estimated using the jack-knife technique.

Figure 3.

Standard errors (top row) and coverage of 95% confidence intervals (CIs) (bottom row) for regression coefficients across different sample sizes and methods (naïve OLS, GLS, OLS-GLS hybrid) using simulated data. The horizontal dashed line in the low panels indicates the nominal 95% coverage. The margin-of-error for differences between different points on the 95% CI coverage curves for the naïve and GLS/hybrid methods are approximately ±5% (for both) for the intercept, ±5% and ±4% for G, ±8% and ±5% for X1, and ±4% and ±5% for X4, respectively.

Figure 4.

Estimated variogram based on Matérn function for an example FLARE-RT patient (A, black curve) and patient population (B, black curve). The sill represents the dynamic range of spatial variance, normalized to 1 for the population estimate. The range represents the inter-voxel distance over which data remain correlated. Gray curves show leave-one-patient-out cross-validation (LOOCV) estimates. Each patient has an individualized variogram with common range and smoothness but patient-specific sill.

Figure 5.

Voxel Forecast model prediction errors. Leave-one-patient-out cross-validation (LOOCV) mean absolute error from OLS-GLS hybrid model of patient-level predictors only compared to OLS-GLS hybrid model of patient- and voxel-level predictors. Median (line), quartiles (box), and 1.5 IQR (whisker) are shown. Non-parametric pairwise comparisons were performed by Wilcoxon signed-rank testing.

Figure 6.

Comparison of Voxel Forecast predicted (black markers) vs. observed (gray markers) Week 3 mid-treatment FDG PET voxel SUV in two example FLARE-RT protocol patients blinded to model training (A, B). Patient A presents with homogeneous response over moderate SUV range, resulting in mean absolute prediction error of 1.1 SUV [g/cm3], with most voxels over-responding to conventionally fractionated RT dose relative to prediction. Patient B presents with low response over large SUV range, resulting in biased prediction at high SUV and high mean absolute prediction error of 3.3 SUV [g/cm3]. SUV voxels in Patient B that under-responded to conventionally fractionated RT doses compared to prediction may define high-risk regions.

Figure 7.

Comparison of Voxel Forecast predicted (A, D) vs. observed (B, E) Week 3 mid-treatment FDG PET tumor images in the same blinded FLARE-RT protocol patients as Figure 6. The first patient (top row) shows regions of over-response (C, ΔSUV = SUVpredicted – SUVobserved > 0) with low systematic bias in spatially variant prediction. The second patient (bottom row) shows systematic under-response (F, ΔSUV = SUVpredicted – SUVobserved

Figure 8.

Kaplan-Meier estimated overall survival stratified by mid-treatment PET response status according to the FLARE-RT protocol (log rank p<0.001).