We have so far considered situations where the outcome variable is numeric and Normally distributed, or binary. In clinical work one often encounters situations where the outcome variable is numeric, but in the form of counts. Often it is a count of rare events such as the number of new cases of lung cancer occurring in a population over a certain period of time. The aim of regression analysis in such instances is to model the dependent variable Y as the estimate of outcome using some or all of the explanatory variables (in mathematical terminology estimating the outcome as a function of some explanatory variables.
Poisson regression is appropriate when the dependent variable is a count, for instance of events such as the arrival of a telephone call at a call centre. The events must be independent in the sense that the arrival of one call will not make another more or less likely, but the probability per unit time of events is understood to be related to covariates such as time of day.