Novel Influence Diagnostics in Multistate Models for Breast Cancer

Multistate models were developed to model survival data where several midpoints and endpoints are of interest; and they have been particular successful in modeling dynamics of cancer. As in any statistical model, identification of influential observations is an essential task, as they can significantly affect the validity of inferred parameters and conclusions drawn from the data. The local influence approach is a set of methods designed to detect the effect of small perturbations of the model or data on the inference, allowing for deeper data analysis. In this paper, we derive local influence methods for multistate models and illustrate their use with a breast cancer dataset. In particular, we develop and implement local influence diagnostic techniques based on a suitable estimation equation. For simplicity, we restrict our consideration to the Multistate Proportional Hazards model, using different case-weight perturbation strategies.