PREDICTING THE RADIATION CONTROL PROBABILITY OF HETEROGENEOUS TUMOR ENSEMBLES - DATA-ANALYSIS AND PARAMETER-ESTIMATION USING A CLOSED-FORM EXPRESSION

A closed-form formula describing the tumour control probability (tcp) of a heterogeneous collection of rumours has been obtained by analytic ally averaging the homogeneous double-exponential tcp formula over int er-tumour distributions of clonogen radiosensitivity, density and repo pulation rate, tumour volume and dose. The formula can be straightforw ardly and relatively quickly fitted to clinical data, yielding radiobi ological parameter values for use in rep modelling. The formula was fi tted to published tcp data which catalogued tumour control records gro uped by dose and tumour volume, and treatment duration. Fitted paramet er values, confidence intervals and goodness-of-fit statistics were de termined. The sets of parameter values obtained are unique only to wit hin a scaling factor. The formula provides non-rejectable fits to data which grouped tcp by dose and volume when radiosensitivity parameters take values close to laboratory estimates, the fitted volume dependen ce parameter, however, taking rather high values. Good fits are obtain able with the intuitively reasonable volume parameter value of one, bu t with radiosensitivity values around one-third of their laboratory es timates. Non-rejectable fits to data which grouped rep by dose and tre atment duration may be obtained with radiosensitivity and repopulation rate parameters lying close to laboratory estimates.