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.