Estimation of α/β for late rectal toxicity based on RTOG 94-06

Abstract

Purpose: To estimate α/β, the parameter ratio from the linear-quadratic (LQ) model, for Grade ≥2 late rectal toxicity among patients treated on Radiation Therapy Oncology Group (RTOG) protocol 94-06; and to determine whether correcting the rectal dose-volume histogram (DVH) for differences in dose per fraction, based on the LQ model, significantly improves the fit to these data of the Lyman-Kutcher-Burman (LKB) normal-tissue complication probability (NTCP) model.

Methods and materials: The generalized LKB model was fitted to the Grade ≥2 late rectal toxicity data in two ways: by using DVHs representing physical dose to rectum, and by using a modified approach in which dose bins in the rectal DVH were corrected for differences in dose per fraction using the LQ model, with α/β estimated as an additional unknown parameter. The analysis included only patients treated with the same treatment plan throughout radiotherapy, so that the dose per fraction to each voxel of rectum could be determined from the DVH. The likelihood ratio test was used to assess whether the fit of the LQ-corrected model was significantly better than the fit of the LKB model based on physical doses to rectum.

Results: The analysis included 509 of the 1,084 patients enrolled on RTOG 94-06. The estimate of α/β from the LQ-corrected LKB model was 4.8 Gy, with 68% confidence interval 0.6 Gy to 46 Gy. The fit was not significantly different from the fit of the LKB model based on physical dose to rectum (p = 0.236).

Conclusions: The estimated fractionation sensitivity for Grade ≥2 late rectal toxicity is consistent with values of α/β for rectum found previously in human beings and in rodents. However, the confidence interval is large, and there is no evidence that LQ correction of the rectal DVH significantly changes the fit or predictions of the LKB model for this endpoint.

Figure 1

Solid curve: Profile log-likelihood (LL) from the fit of the generalized LQ-corrected Lyman-Kutcher-Burman model (Eqs. 1, 2, 4, 5), plotted as a function of the parameter ratio α/β from the LQ model. The maximum LL occurs at α/β =4.8 Gy, representing the best estimate of α/β, as indicated by the location of the vertical stippled line. The 68% profile-likelihood confidence interval for α/β = 4.8 Gy is represented by the range of α/β values between the points of intersection of the solid curve with the horizontal dashed line, and ranges from 0.6 Gy to 46 Gy.