The analysis of rates and of survivorship using log-linear models

Models are considered in which the underlying rate at which events occur has a log-linear relationship with covariates. It is shown that the estimation of parameters involves the solution of identical systems of equations for data from either a Poisson process, an exponential distribution, a survival model or a generalized log-linear model. This enables one to use algorithms for fitting log-linear models, such as iterative proportional fitting (IPF), for the analysis of rates or survivorship.