International Journal of Radiation Oncology*Biology*Physics
Biology contributionIs α/β for prostate tumors really low?
Introduction
The analysis in 1999 by Brenner and Hall (1) of clinical results from external beam radiotherapy for prostatic carcinoma compared with results from permanent implants of iodine-125 yielded an estimated α/β ratio of 1.5 Gy (95% CI 0.8–2.2). This low value, in contrast to values of about 10 Gy or higher for most other types of tumor, has generated much discussion about the possible use of hypofractionation and/or high-dose, high-dose-rate boost doses for the treatment of prostatic carcinomas 2, 3, 4, 5. Such a low value of α/β is indeed consistent with the uniquely slow proliferation rates of prostatic cancer, with a median Tpot of 42 days, range 15–170 days (6).
We have carried out a review of clinical outcome in patients treated with external beam radiotherapy only, I-125 implants only, and Pd-103 implants only, to update the comparison and analysis of Brenner and Hall (1). We have used a generalization of their model that allows us to estimate the rate constant of intracellular repair of the tumors, μ, rather than assuming it to be zero as they did. Nevertheless, our conclusions are remarkably similar to theirs. Their result was criticized by King and Mayo (3) on the grounds that different (larger) values of α/β are found if heterogeneity of the parameters is assumed, although this argument has apparently recently been settled in favor of small α/β values (See end of “Discussion”). However, we consider that this criticism can be answered by using actual iso-effect doses obtained from clinical data, without assuming numbers of cells or intrinsic radiosensitivities. We suggest that these results have already inevitably taken full account of heterogeneity, including variations in tumors, patients, dose delivery, and different centers. The resulting dose–response curves are relatively shallow, γ ≈ 2.0, which was the central point of the original criticism of the simple probabilistic modeling 7, 8.
Further suggestion of a low value of α/β comes from early clinical results where high-dose and high-dose-rate boost doses have already been used for a number of years in the treatment of prostatic carcinoma (Martinez et al. [9]), as discussed below.
Section snippets
Methods and materials
Three methods were used in this paper to estimate values for α/β in prostate tumors. They are based on 5-year results for bNED (no biochemical evidence of disease) that have recently become available from all three types of radiation employed. We repeat the caution that 5-year bNED values do not necessarily relate proportionally to ultimate long-term local control. Although there is no reason to assume that they would decline at different rates with the three types of radiation, the concern
First method
Figure 1 shows the updated dose–response curve for 5-year actuarial bNED obtained by logit regression through the 10 points for external beam treatments from five centers in Table 1, published no earlier than 1997 11, 12, 13, 14, 15, 16. The slightly different curves were obtained from the different assumptions about α/β used for correction of mean total doses to NTD (at a dose per fraction of 2 Gy). Differences were less than 1% over the region of interest between 70% and 75%. The slope of the
Discussion
The present estimates of α/β are in remarkable agreement with that of Brenner and Hall (1) of 1.5 Gy (95% CI 0.8–2.2). There seems to be little doubt that the extremely different total doses required by the external beams at 2 Gy per fraction and the low dose-rates from I-125 and Pd-103 to give equal biochemical control at 5 years indicate a low α/β ratio. If we accept the median estimate of T as being close to 2 h, the low dose-rates can be estimated to be biologically equivalent to
Conclusions
The alpha/beta ratio for prostatic cancer appears to be low, with a best estimate by Direct Analysis of 1.49 Gy (95% CI 1.25–1.76). Sensitivity tests confirmed the stability of this estimate to small variations of iso-effect dose and the omission of any one center’s data. A two-step graphical method yielded 1.7 Gy, with a slightly larger confidence range, overlapping the Direct Analysis value. These results are supported by preliminary data from treatments using high-dose and high-dose-rate
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