Robust Inference for Zero-Inflated Models with Outliers Applied to the Number of Involved Lymph Nodes in Patients with Breast Cancer

Abstract Objective: The aim of this study is to investigate the factors that influencing the number of axillary lymph nodes in women diagnosed with early breast cancer by choosing a strong model to evaluate the excess of zeros and outliers usually present in these data. Methods: The study based on a retrospective analysis of hospital records of 669 breast cancer patients in Iran. Zero-inflated, robust zero-inflated and Bayesian modelling techniques were used to assess the association between factors studied and the number of involved lymph nodes in breast cancer patients. Count data models, including zero-inflated models (zero-inflated Poisson and zero-inflated negative binomial), robust zero-inflated models (robust zero-inflated Poisson and robust zero-inflated negative binomial) and Bayesian models (Bayesian zero-inflated Poisson and Bayesian zero-inflated negative binomial) were applied. Performance evaluation of models was compared using AIC and BIC. Results: According to the AIC and BIC, the robust zero-inflated negative binomial model is the best model. Findings indicate that women who had a larger tumor had a greater number of axillary lymph nodes, hormone receptor status was associated with the number of lymph nodes, tumor grades II and III also contributed to a higher number of lymph nodes. Women who were older had a higher risk of having lymph nodes. Conclusions: Our analysis showed that the robust zero-inflated negative binomial is the best model for predicting and describing the number of nodes involved in primary breast cancer when overdispersion and outliers occurs.