ABSTRACT
This chapter examines the Poisson distribution and the connection to Cox regression and tabular lifetime data. The Poisson distribution is represented by four functions, dpois, ppois, qpois, and rpois, representing the probability density function; the cumulative distribution function; the quantile function; and random number generation, respectively. Fertility data is over-dispersed compared to the Poisson distribution. A simple way to check that is to calculate the sample mean and variance of the data. If data come from a Poisson distribution, these numbers should be equal. The data set is summarized around each observed failure time. That is, a snapshot of the risk set at each failure time is created by the function to Binary. In the Poisson regression to follow, the factor riskset must be included as a cluster. This is equivalent to including it as a factor covariate, but for data set with many distinct failure times, the number of levels will be too large to be run by glm.
