A Two-Parameter Model for the Survival Curve of Treated Cancer Patients

Abstract A two-parameter model for representing the survival curve of treated cancer patients is described. If PT is the proportion of the treated patients surviving to time T, and PtildeT is the proportion of a normal population surviving to time T then the survival curve may be represented by: — PT/PtildeT = c.e-loge c,e-βT , where c is the proportion cured and β is the asymptotic value as T approaches ∞ of the instantaneous risk of dying from cancer in the uncured group. The model stems from the observation that, in the whole series, the conditional probability of dying from cancer in an interval calculated by the usual actuarial method, tends to decrease exponentially with time, and the model has been designated ‘extrapolated actuarial’ to distinguish it from the lognormal model of Boag 2, and the exponential model of Berkson and Gage 1. The parameters c and β may be estimated from crude survival data and a knowledge of the expected mortality in a normal population of the same age and sex as the treated group. Examples are given of its application to three series of patients.