Clinical Investigation
Confirmation of a Low α/β Ratio for Prostate Cancer Treated by External Beam Radiation Therapy Alone Using a Post-Treatment Repeated-Measures Model for PSA Dynamics

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Purpose

To estimate the α/β ratio of prostate cancer treated with external beam radiation only by use of a model of long-term prostate-specific antigen (PSA) dynamics.

Methods and Materials

Repeated measures of PSA from 5,093 patients from 6 institutions treated for localized prostate cancer by external beam radiation therapy (EBRT) without planned androgen deprivation were analyzed. A biphasic linear mixed model described the post-treatment evolution of PSA, rather than a conventional model of time to biochemical recurrence. The model was adjusted for standard prognostic factors (T stage, initial PSA level, and Gleason score) and cohort-specific effects. The radiation dose fractionation effect was estimated from the long-term rate of rise of PSA level.

Results

Adjusted for other factors, total dose of EBRT and sum of squared doses per fraction were associated with long-term rate of change of PSA level (p = 0.0017 and p = 0.0003, respectively), an increase of each being associated with a lower rate of rise. The α/β ratio was estimated at 1.55 Gy (95% confidence band, 0.46–4.52 Gy). This estimate was robust to adjustment of the linear mixed model.

Conclusions

By analysis of a large EBRT-only cohort along with a method that uses all the repeated measures of PSA after the end of treatment, a low and precise α/β was estimated. These data support the use of hypofractionation at fractional doses up to 2.8 Gy but cannot presently be assumed to accurately represent higher doses per fraction.

Introduction

The radiation oncology literature is permeated with suggestions that the apparent sensitivity of prostate cancer to hypofractionated radiotherapy is a valuable therapeutic target 1, 2, 3, 4. When quantifying the dose and dose-per-fraction (DPF) relationship with a linear–quadratic biological model, the consensus is that the derived α/β ratio is substantially lower in prostate cancer than in most cancers, with typical purported values between 1 and 3 Gy 3, 5, 6, 7. Although no prospective controlled studies have confirmed these observational data to date, the hypothesis generated by them is that larger DPF therapies may be optimal therapy in patients with this type of cancer, which has been incorporated into several clinical techniques 8, 9, 10.

In applying the available radiobiology knowledge to clinical protocols in prostate cancer, α/β ratio estimates that have displayed the tightest estimates are, quite understandably, those that clinicians have relied on. These estimates have unfailingly used external beam radiation therapy (EBRT) in combination with brachytherapy data to date. From a modeling viewpoint, these combined data are required because they enable one either to theoretically eliminate the β component from calculations involving the low–dose-rate brachytherapy (LDRB) data 3, 6, 11 or to have access to large enough DPF variation to successfully model both the α and β components by use of hypofractionated high–dose-rate brachytherapy (HDRB) data 5, 7. Each of these approaches can be criticized on a number of fronts, such as including, yet not accounting for, uncertainties associated with comparing the relatively homogeneous dose of EBRT with highly inhomogeneous brachytherapy dose distributions (12). Inherently, these combined-modality data should not be extrapolated to the design of EBRT-only fractionation strategies.

A more acceptable approach would be to derive the α/β ratio from fractionation studies incorporating EBRT only. Unfortunately, the largest randomized study to date comparing conventional DPF and hypofractionation (13) has failed to provide precise estimates (14), whereas data from observational models are similarly imprecise when using only EBRT data (7). One constant throughout all the previous studies has been the use of a conventional binary failure endpoint to assess outcome, such as a time-to-recurrence endpoint (biochemical or clinical). Yet, we have access to repeated measures of prostate-specific antigen (PSA) collected after therapy, the evolution of which can be described by use of a linear mixed model. We have previously provided a framework for evaluating prognostic and other factors that may be associated with disease progression in such a model of prostate cancer (15). By incorporating the complete PSA history, rather than reducing it to a somewhat arbitrary single point, such as biochemical recurrence, this complex multivariable modeling approach can greatly increase the power with which prognostic variables can be interpreted. A finding from previous validation work using this mixed modeling strategy was that the dose of radiation was associated with the pattern of post-treatment PSA values (15). Furthermore, after accounting for the pattern of PSA, the dose of radiation provided no further significant information about the risk of subsequent clinical recurrence, suggesting that clinical outcomes related to radiation dose effects can be largely described via PSA dynamics. This provides a rationale for the approach in this article, where we are investigating the effect of the radiation fractionation schedule on disease progression, and this can be achieved by use of just the linear mixed model approach focusing on the PSA values after treatment and not considering clinical recurrence. This study's aim is to use this modeling strategy to attempt to describe the α/β ratio using data from a large number of men treated with EBRT containing little dose inhomogeneity, in whom this was not able to be done previously with adequate precision.

Section snippets

Patient cohorts

The analysis included all patients treated for prostate cancer by EBRT from 6 different cohorts: University of Michigan, Ann Arbor, Michigan (UM) (16); Radiation Therapy Oncology Group (RTOG) 9406 (17); Peter MacCallum Cancer Center, Melbourne, Australia (PMCC) (18); William Beaumont Hospital, Detroit, Michigan (WBH) (19); Royal Brisbane Hospital, Brisbane, Australia (RBH) (20); and British Columbia Cancer Agency, Vancouver, British Columbia, Canada (BCCA) (21). Locoregional and systemic

Description of cohorts

Summary variables for the six cohorts are described in Table 1. The median follow-up was 4.7 years, with a relatively shorter time of follow-up for UM and WBH (median of 4.1 and 3.7 years, respectively) and longer time for RBH, with a median of 5.3 years. The prognostic factor distribution differed significantly over cohorts (p < 0.0001 for each factor). The Radiation Therapy Oncology Group included more T 1 cases and fewer T 3 and 4 cases, whereas PMCC and BCCA had a converse distribution. The

Discussion

The design of optimal radiation fractionation schedules to treat prostate cancer is an active area of clinical research presently. The consensus for a low α/β ratio in prostate cancer via a number of modeling studies 3, 5, 6, 7 has produced a groundswell of support for schedules incorporating large DPFs, with considerable early implementation by use of HDRB in particular (10). External beam radiation therapy techniques have also been designed to meet these theoretic benefits (28), despite

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Supported by grant CA110518 from the US National Cancer Institute.

Conflict of interest: none.

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