In longitudinal studies for analyze change, we recomend to use the observation plan called Event History Data. The proportional hazard model allows to study the effect of a set of explicatives variables about the hazard function. In this context, we introduce the partial likelihood method that permits to estimate the parameters of the Cox regression model. We distinguish between three situation which are possible depending on the type of data: complete, incomplete and tie. A simple example will permit to follow in a numerical and exhaustive way, all the steps present at the parameters estimation process, their signification and interpretation.