Survival time analysis in women with breast cancer using distributional regression models

Cancer is a global public health concern due to its high mortality rates. In Brazil, breast cancer is one of the leading causes of disease and death among women in all regions of the country, with higher mortality rates in less developed regions. Hence, this study analyzes variables associated with survival time in breast cancer patients in Campina Grande, Paraíba State, Brazil. Distributional regression models, also known as generalized additive models for location, scale, and shape (GAMLSS), were used due to their flexibility in explaining complex behaviors of a given response (for example, survival time) based on other variables. Tumor site, age, number of hormone therapy, radiotherapy and chemotherapy sessions, and molecular markers such as estrogen receptor, progesterone receptor, Ki-67 protein, p53, HER2 mutation and molecular subtype were examined. Two different GAMLSS were fitted considering Weibull and log-normal distributions, the former of which is more appropriate per the Akaike information criterion. Using a variable selection procedure specific to GAMLSS, we identified four covariates that directly affect average survival time: number of hormone therapy and chemotherapy sessions, p53 status, and estrogen receptor status. Excepting estrogen receptor status, the other covariates selected to explain average survival time were also used to explicitly explain the variability of these times.