α/β for Hepatocellular Carcinoma Tumors Treated With Radiation Therapy

Primary hepatocellular carcinoma lesions are frequently treated with fractionated radiation therapy. The linear-quadratic (LQ) model can be used to compare different fractionation schemes for their effect on the local recurrence rate of the hepatocellular carcinoma tumors. In this paper, we seek to find the value of the α/β ratio in the LQ model, which gives the best prediction of the recurrence rate.

Two separate data sets were analyzed. The first data set contains the time to recurrence of 390 lesions, treated at 2 institutions between 2008 and 2021. Factors considered were the gross tumor volume (GTV), the fractionation scheme, the dose-volume histogram (DVH) of GTV, and the elapsed time between the first and last dose of radiation. Four different ways of summarizing the DVH, based on the LQ model, were used and combined with the Cox proportional hazards model to estimate the α/β ratio. The second data set contains the recurrence rate at 1, 2, 3, 4, and 5 years, for 46 different fractionation schemes, derived from the results presented in 41 publications, based on a total of 4313 lesions. For this meta-analysis, a linear model of a transformed recurrence rate, assuming an autoregressive covariance structure, was used to estimate the α/β ratio.

From the lesion-level data, the best estimate of α/β was in the range 37.5 to 52 Gy, with a wide confidence interval (3.4 to ∞). A combined model of how the radiation was delivered, based on the fraction regimen and elapsed time, was strongly associated with the hazard of recurrence (P < .001). However, the elapsed time alone was not significantly associated with the hazard of recurrence (hazard ratio for a 1 day increase, 1.01; P = .33). The analysis also suggested that larger GTV may lead to a higher hazard of recurrence, but was not statistically significant [hazard ratio of log(GTV) = 1.12, P = .21]. Lower doses in the DVH were better predictors of the outcome than the mean DVH dose. The meta-analysis of the published data gave the best estimate of the α/β ratio of 161.4 Gy, but with a wide confidence interval (4.7 to ∞).

Both analyses suggested a high value of α/β of at least 37.5 Gy, but neither could provide precise estimates, and only very small values could be excluded. From a practical perspective, any value of the α/β ratio of greater than about 20 Gy would give a similar ranking of the merits of different fractionation schemes. To obtain more precise estimates of α/β, the data sets would need to include more patients who received fractionated radiation with doses per fraction in the range of 2.0 to 2.9 Gy.