ABSTRACT
This chapter examines two parametric approaches that are specific to the analysis of time-to-event data. The first parametric approach is probably the oldest, exponential regression. The second method is a generalization of the first. The exponential distribution is a special case of the gamma distribution. The chapter argues that each observation follows an exponential distribution but that the log of the expected value follows a linear model. It suggests that each observation follows a gamma distribution but that the log of the expected value follows a linear model. The chapter also argues that the least important assumption one typically makes in a data analysis is the distributional assumption. A generalization of exponential regression involves using the gamma distribution. The gamma distribution has two parameters, like a normal distribution, and deviances in gamma regression are used like sums of squares error in normal theory models.
