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.

The odd log-logistic logarithmic generated family of distributions with applications in different areas

“…Some proposals have been made recently in the literature by more long term survival to model lifetimes with covariates. For example, Ortega et al (2012) considered the problem of assessing local influence in the negative binomial beta Weibull regression model to predict the cure of prostate cancer, Hashimoto et al (2013) derived curvature quantities under various perturbation schemes in Neyman type A beta-Weibull model for long-term survivors, Fachini et al (2014) adapted local influence methods to a bivariate regression model with cure fraction and, recently, Ortega et al (2015) used local influence methods to the power series beta-Weibull regression model for predicting breast carcinoma. The MMs allow simultaneously estimating whether the event of interest will occur, which is called incidence, and when it will occur, given that it can occur, which is called latency.…”

A new extended Birnbaum-Saunders model with cure fraction: classical and Bayesian approach

“…Further, Peng and Dear (2000) investigated a nonparametric MM for cure estimation, Sy and Taylor (2000) considered estimation in a proportional hazards cure model and Yu and Peng (2008) extended MMs to bivariate survival data by modeling marginal distributions. Fachini et al (2014) recently proposed a scale model for bivariate survival times based on the copula that model the dependence of bivariate survival data with cure fraction, Hashimoto et al (2015) introduced the new long-term survival model with interval-censored data, Ortega et al (2015) proposed the power series beta Weibull regression model to predict breast carcinoma, Lanjoni et al (2016) conducted extended Burr XII regression models and Ortega et al (2017) proposed regression models generated by gamma random variables with long-term survivors.…”

Regression models generated by gamma random variables with long-term survivors

“…Several authors have applied the local influence methodology in regression analysis with censoring. Ortega et al (2012) considered the problem of assessing local influence in the negative binomial beta Weibull regression model to predict a cure rate for prostate cancer, Hashimoto et al (2013) derived curvature quantities under various perturbation schemes in Neyman type A beta Weibull model for long-term survivors, Fachini et al (2014) used local influence methods to a bivariate regression model with cure fraction and Ortega et al (2015) adapted local influence methods to model a power series beta Weibull regression model to predict breast carcinoma. We propose a similar methodology to detect influential subjects in the PG-G family with cure rate.…”