Estimates of Alpha/Beta (α/β) Ratios for Individual Late Rectal Toxicity Endpoints: An Analysis of the CHHiP Trial

Abstract

Purpose: Changes in fraction size of external beam radiation therapy exert nonlinear effects on subsequent toxicity. Commonly described by the linear-quadratic model, fraction size sensitivity of normal tissues is expressed by the α/β ratio. We sought to study individual α/β ratios for different late rectal effects after prostate external beam radiation therapy.

Methods and materials: The CHHiP trial (ISRCTN97182923) randomized men with nonmetastatic prostate cancer 1:1:1 to 74 Gy/37 fractions (Fr), 60 Gy/20 Fr, or 57 Gy/19 Fr. Patients in the study had full dosimetric data and zero baseline toxicity. Toxicity scales were amalgamated to 6 bowel endpoints: bleeding, diarrhea, pain, proctitis, sphincter control, and stricture. Lyman-Kutcher-Burman models with or without equivalent dose in 2 Gy/Fr correction were log-likelihood fitted by endpoint, estimating α/β ratios. The α/β ratio estimate sensitivity was assessed using sequential inclusion of dose modifying factors (DMFs): age, diabetes, hypertension, inflammatory bowel or diverticular disease (IBD/diverticular), and hemorrhoids. 95% confidence intervals (CIs) were bootstrapped. Likelihood ratio testing of 632 estimator log-likelihoods compared the models.

Results: Late rectal α/β ratio estimates (without DMF) ranged from bleeding (G1 + α/β = 1.6 Gy; 95% CI, 0.9-2.5 Gy) to sphincter control (G1 + α/β = 3.1 Gy; 95% CI, 1.4-9.1 Gy). Bowel pain modelled poorly (α/β, 3.6 Gy; 95% CI, 0.0-840 Gy). Inclusion of IBD/diverticular disease as a DMF significantly improved fits for stool frequency G2+ (P = .00041) and proctitis G1+ (P = .00046). However, the α/β ratios were similar in these no-DMF versus DMF models for both stool frequency G2+ (α/β 2.7 Gy vs 2.5 Gy) and proctitis G1+ (α/β 2.7 Gy vs 2.6 Gy). Frequency-weighted averaging of endpoint α/β ratios produced: G1 + α/β ratio = 2.4 Gy; G2 + α/β ratio = 2.3 Gy.

Conclusions: We estimated α/β ratios for several common late adverse effects of rectal radiation therapy. When comparing dose-fractionation schedules, we suggest using late a rectal α/β ratio ≤ 3 Gy.

Fig. 1

Patient flow diagram showing any reasons for exclusion of all patients originally randomized into the CHHiP trial. Abbreviations: DICOM = Digital Imaging and Communications in Medicine; ID = Identity; OAR = organ at risk.

Fig. 2

Calibration plots for rectal bleeding G1 + LKB-EQD2 model. (A) The fit of the model calibration (blue line) compared against optimal calibration (orange line), demonstrating a good overall fit. The lower histogram shows the predicted NTCP for patients, separated by toxicity (red, above line) or no toxicity (blue, below line). (B) Patients grouped into deciles by predicted NTCP, showing this against observed toxicity within each decile. Bin ordering is generally appropriate. (A color version of this figure is available at https://doi.org/10.1016/j.ijrobp.2020.12.041).