title: 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 a disease, but they do not accurately predict what will happen in any particular patient's case. Pathologic explanatory variables such as disease multifocality, tumor size, tumor grade, lymphovascular invasion, and enhanced lymph node staining are prognostically significant to predict these survival rates. We propose a new cure rate survival regression model for predicting breast carcinoma survival in women who underwent mastectomy. We assume that the unknown number of competing causes that can influence the survival time is given by a power series distribution and that the time of the tumor cells left active after the mastectomy for metastasizing follows the beta Weibull distribution. The new compounding regression model includes as special cases several well-known cure rate models discussed in the literature. The model parameters are estimated by maximum likelihood. Further, for different parameter settings, sample sizes, and censoring percentages, some simulations are performed. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess local influences. The potentiality of the new regression model to predict accurately breast carcinoma mortality is illustrated by means of real data.
authors.affiliation: Department of Exact Sciences, University of São Paulo, Piracicaba, Brazil.
authors.forename: Edwin M M
authors.initials: EM
authors.lastname: Ortega
authors.forename: Gauss M
authors.initials: GM
authors.lastname: Cordeiro
authors.forename: Ana K
authors.initials: AK
authors.lastname: Campelo
authors.forename: Michael W
authors.initials: MW
authors.lastname: Kattan
authors.forename: Vicente G
authors.initials: VG
authors.lastname: Cancho
mesh_terms: D017677:Age Distribution; D001943:Breast Neoplasms / Q000401:mortality* / Q000473:pathology / Q000601:surgery; D003198:Computer Simulation; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008198:Lymph Nodes / Q000473:pathology; D008207:Lymphatic Metastasis; D008408:Mastectomy / Q000706:statistics & numerical data*; D008954:Models, Biological; D060787:Neoplasm Grading; D011379:Prognosis; D016016:Proportional Hazards Models; D012044:Regression Analysis; D016008:Statistical Distributions; D015996:Survival Rate; D013997:Time Factors
keywords: beta Weibull distribution; breast cancer; cure fraction; likelihood function; long-term survivor; mastectomy; power series distribution