Zero-inflated generalized extreme value regression model for binary response data and application in health study

Binary responses are often present in medical studies. When the dependent variable Y represents a rare event, the logistic regression model shows relevant drawbacks. To overcome these drawbacks, we propose the quantile function of the generalized extreme value regression distribution as a link function and focus our attention on values close to one. One problem arising in the presence of cure fraction is that, it is usually unknown who are the cured and the susceptible subjects, unless the outcome of interest has been observed. In these settings, a logistic regression analysis is no more straightforward. We develop a maximum likelihood estimation procedure, based on the joint modeling of the binary response of interest and the cure status. We investigate the identifiability of the resulting model and establish the asymptotic properties. We conduct a simulation study to investigate its finite-sample behaviour, and application to real data.