A parametric regression model of tumor recurrence: An application to the analysis of clinical data on breast cancer

Abstract

A new parametric model is proposed for the regression analysis of relapse-free time data. It offers a natural classification of covariates in terms of their predominant effect either on the expected number of clonogens in a treated tumor or on the time of tumor progression. Within the framework of the model, the probability of local control is uniquely determined by the mean number of surviving clonogenic cells. Two versions of the model are considered; in one of them every mode of treatment is represented by indicator variables while in the other version the linear-quadratic model of radiation cell survival is used to describe the effect of radiotherapy. Maximum likelihood estimation of the model parameters is provided by a nonlinear programming procedure which has been shown to be computationally tractable. The results are reported of the analysis of relevant data on breast cancer recurrence after conservative treatment of the primary tumor. The most striking finding is that age of a patient exerts a very strong effect on the mean number of surviving clonogens in the ipsilateral breast, or equivalently, the probability of tumor cure, while its effect on the progression time appears to be negligible. On the other hand, the primary tumor size contributes significantly to both characteristics of tumor latency. No significant covariate effects emerged from the analysis of the contralateral breast cancer recurrence.