The response variable in medical data is often in the form of counts. Examples include visits to the doctor, cases of stroke or heart attacks, and number of deaths due to various causes. Two common distributions used to model counts that arise in situations such as these are the Poisson and negative binomial distributions. In this entry, the important aspects of Poisson and negative binomial regression are covered along with an example to illustrate basic inference for these models.

Perhaps the most common realization of Poisson data is that of “rare-event” data, which are events that occur relatively few times in a large population. In this case, the Poisson distribution is seen as a limiting form of the binomial distribution when the sample size, n, grows ...