The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

Disparities in female breast cancer mortality rates in Brazil between 1980 and 2009

OBJECTIVE: To describe the temporal trends in female breast cancer mortality rates in Brazil in its macro-regions and states between 1980 and 2009. METHODS: This was an ecological time-series study using data on breast cancer deaths registered in the Mortality Data System (SIM/WHO) and census data on the resident population collected by the Brazilian Institute of Geography and Statistics (IBGE/WHO). Joinpoint regression analyses were used to identify the significant changes in trends and to estimate the annual percentage change (APC) in mortality rates. RESULTS: Female breast cancer mortality rates in Brazil tended to stabilize from 1994 onward (APC = 0.4%). Considering the Brazilian macro-regions, the annual mortality rates decreased in the Southeast, stabilized in the South and increased in the Northeast, North, and Midwest. Only the states of Sao Paulo (APC = -1.9%), Rio Grande do Sul (APC = -0.8%) and Rio de Janeiro (APC = -0.6%) presented a significant decline in mortality rates. The greatest increases were found in Maranhao (APC = 12%), Paraiba (APC = 11.9%), and Piaui (APC = 10.9%). CONCLUSION: Although there has been a trend toward stabilization in female breast cancer mortality rates in Brazil, when the mortality rate of each macro-region and state is analyzed individually, considerable inequalities are found, with rate decline or stabilization in states with higher socioeconomic levels and a substantial increase in those with lower socioeconomic levels.