Meta-analysis of the alpha/beta ratio for prostate cancer in the presence of an overall time factor: bad news, good news, or no news?

Abstract

Purpose: To present a novel method for meta-analysis of the fractionation sensitivity of tumors as applied to prostate cancer in the presence of an overall time factor.

Methods and materials: A systematic search for radiation dose-fractionation trials in prostate cancer was performed using PubMed and by manual search. Published trials comparing standard fractionated external beam radiation therapy with alternative fractionation were eligible. For each trial the α/β ratio and its 95% confidence interval (CI) were extracted, and the data were synthesized with each study weighted by the inverse variance. An overall time factor was included in the analysis, and its influence on α/β was investigated.

Results: Five studies involving 1965 patients were included in the meta-analysis of α/β. The synthesized α/β assuming no effect of overall treatment time was -0.07 Gy (95% CI -0.73-0.59), which was increased to 0.47 Gy (95% CI -0.55-1.50) if a single highly weighted study was excluded. In a separate analysis, 2 studies based on 10,808 patients in total allowed extraction of a synthesized estimate of a time factor of 0.31 Gy/d (95% CI 0.20-0.42). The time factor increased the α/β estimate to 0.58 Gy (95% CI -0.53-1.69)/1.93 Gy (95% CI -0.27-4.14) with/without the heavily weighted study. An analysis of the uncertainty of the α/β estimate showed a loss of information when the hypofractionated arm was underdosed compared with the normo-fractionated arm.

Conclusions: The current external beam fractionation studies are consistent with a very low α/β ratio for prostate cancer, although the CIs include α/β ratios up to 4.14 Gy in the presence of a time factor. Details of the dose fractionation in the 2 trial arms have critical influence on the information that can be extracted from a study. Studies with unfortunate designs will supply little or no information about α/β regardless of the number of subjects enrolled.

Fig. 1

A synthesis of the observed time factors of Thames et al (5) and Miralbell et al (10). It should be noted that a formal systematic search and meta-analysis was not possible, and several studies discuss the effect of overall treatment time without providing data amenable for synthesis in the present analysis (see, eg, reference 4). IV = inverse variance weighted; fixed = fixed-effects model; CI = confidence interval.

Fig. 2

Meta-analysis of the α/β ratio including all studies (A and C) and excluding the heavily weighted study by Arcangeli et al (12) (B and D). Assuming no effect of overall treatment time (A and B) and assuming δ_prolif = 0.31 Gy/d (C and D). IV = inverse variance weighted; Fixed = fixed-effects model; CI = confidence interval.

Fig. 3

The standard error of the α/β ratio vs. the time factor, δ_prolif. A singularity, where the uncertainty of the estimate explodes, exists for all studies except Valdagni et al (15), which is insensitive to δ_prolif because both arms have same overall treatment time. The large number of patients in the study by Lukka et al (14) results in a narrower peak, but the standard error of the α/β estimate is still larger than in Arcangeli et al (12) for a wide range of δ_prolif, including δ_prolif = 0.