Steepness of the Clinical Dose–control Curve and Variation in the in Vitro Radiosensitivity of Head and Neck Squamous Cell Carcinoma

Abstract

Inter-tumour heterogeneity in radiobiological parameters has been proposed as an explanation for the quite shallow dose–response curves for local tumour control after radiotherapy observed in clinical data. Variability in the intrinsic radiosensitivity is potentially a very strong source of variation in local control. A method is presented for forcing such variability into a direct analysis (maximum-likelihood estimation) of tumour control data. The method is used to reanalyse a series of local tumour control data in 181 patients with squamous cell carcinoma of the oropharynx taking the distribution of in vitro radiosensitivities from an independent series of patients into account. It is concluded that direct application of the in vitro radiosensitivities leads to an unrealistically high estimate for the number of target cells per cm³. A more realistic fit is obtained after including a dose-modifying factor to correct for the apparent difference between in vitro and clinical radiosensitivities. The value of this factor is estimated at 2·4 with approximate 95% confidence interval (CI) (1·3, 5·9). It is suggested that hypoxia plays a role in reducing the radiosensitivity of tumours in clinical radiotherapy. Using this method provides more biologically reasonable estimates of other radiobiological parameters. The target-cell doubling time during treatment is estimated at 3·2 days with 95% CI (1·7, 8·7) days. Estimates of the target cell density in typical patients vary between 1·8 × 10⁻⁶ and 6·6 × 10⁻⁴ when the delay before accelerated tumour growth is assumed to vary between 0 and 28 days. Using the method presented here, the shallow clinical dose–control curve is interpreted as a superposition of quite steep dose–response relationships in individual patients. The steepness of the dose–control curve for a typical patient is characterized by a normalized dose–response gradient (the percentage change in tumour control for a 1% change in total dose) of 7·3 after stratification for intrinsic radiosensitivity as compared with 1·6 if such stratification is not performed.