Biologically Equivalent Dose in Construction of Tumor Control Probability Curve for Hepatocellular Carcinoma Treated by Radiotherapy
Abstract
Background: The incorporation of biologically effective dose (BED) or equivalent total dose in 2 Gy fraction (EQD2) in tumor control probability (TCP) equation allows the fitting of clinical data to yield a mathematical function useful for predicting outcome of dose-fractionation. Purpose: To establish a logistic function describing the dependence of TCP on BED or EQD2 for hepatocellular carcinoma (HCC) treated by radiation and to evaluate the validity BED- and EQD2-derived functions in predicting effects of dose-fractionations particularly those relevant to stereotactic body radiotherapy (SBRT). Methods and Materials: Eight clinical papers published during 2000 and 2008 were selected for fitting. Dose and dose per fraction were converted to BED and EQD2 with an α/β of 10 Gy for HCC. These biologically equivalent doses and their associated survival rate at 2 years were fitted to a logit-transformed equation. The difference between slopes of logit-regression lines was analyzed by t-test. The parameters of fit were used for defining the logistic functions which were used to calculate TCPs for dosefractionation schemes typically used in SBRT. Results: Two significant logit-transformed regression lines were established (P = 0.0119) and enabled the construction of two TCP curves described by following logistic functions: The r2 for the curve fitting was 0.83. The established functions were used to calculate TCP for series of fractionation schemes relevant to SBRT and this allowed paperbased study of dose escalation and pre-clinical evaluation of the chosen scheme for treatment of HCC with SBRT. Neither slopes of two curves nor TCPs calculated by BED and EQD2 were statistically different (P > 0.5). Validity of TCP prediction was supported by published data on treatment of HCC with SBRT. Conclusion: BED- or EQD2-derived logistic function is equally reliable in predicting effects of dose-fractionations for HCC particularly those typically used in SBRT.
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