Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors X. The binary response may represent, for example, the occurrence of some outcome of interest (Y=1 if the outcome occurred and Y=0 otherwise). When the dependent variable Y represents a rare event, the logistic regression model shows relevant drawbacks. In order to overcome these drawbacks we propose the Generalized Extreme Value (GEV) regression model. In particularly, we suggest the quantile function of the GEV distribution as link function. Strokes are a serious pathology and a neurological emergency involving the vital prognosis and the functional prognosis. In Senegal, strokes account for more than 30% of hospitalizations and are responsible for nearly two thirds of mortality. In this work, we use the GVE regression model for binary data to determine the risk factors leading to stroke and to develop a predictive model of life-threatening outcomes in central Sénégal.