A power series beta Weibull regression model for predicting breast carcinoma

Abstract

The postmastectomy survival rates are often based on previous outcomes of large numbers of women who had adisease, but they do not accurately predict what will happen in any particular patient’s case. Pathologic explana-tory variables such as disease multifocality, tumor size, tumor grade, lymphovascular invasion, and enhancedlymph node staining are prognostically signicant to predict these survival rates. We propose a new cure ratesurvival regression model for predicting breast carcinoma survival in women who underwent mastectomy. Weassume that the unknown number of competing causes that can inuence the survival time is given by a powerseries distribution and that the time of the tumor cells left active after the mastectomy for metastasizing follows thebeta Weibull distribution. The new compounding regression model includes as special cases several well-knowncure rate models discussed in the literature. The model parameters are estimated by maximum likelihood. Fur-ther, for different parameter settings, sample sizes, and censoring percentages, some simulations are performed.We derive the appropriate matrices for assessing local inuences on the parameter estimates under different per-turbation schemes and present some ways to assess local inuences. The potentiality of the new regression modelto predict accurately breast carcinoma mortality is illustrated by means of real data. Copyright © 2015 JohnWiley & Sons, Ltd.