Parametric Regression Models
In the previous chapters, we focused on the use of either nonparametric or semi-parametric models for the analysis of censored survival time data. The rationale for using these techniques, in particular the semiparametric proportional hazards regression model, was to avoid having to specify the hazard function completely. The utility of the proportional hazards model stems from the fact that a reduced set of assumptions is needed to provide hazard ratios that are easily interpreted and clinically meaningful. However, there may be settings in which the distribution of survival time, through previous research, has a known parametric form that justifies use of a fully parametric model to address the goals of the analysis better. A fully parametric model has some advantages: (1) full maximum likelihood may be used to estimate the parameters, (2) the estimated coefficients or transformations of them can provide clinically meaningful estimates of effect, (3) fitted values from the model can provide estimates of survival time, and (4) residuals can be computed as differences between observed and predicted values of time. An analysis of censored time-to-event data using a fully parametric model can almost have the look and feel of a normal-errors linear regression analysis.
In this chapter, we begin by considering a class of models called accelerated failure time models and discuss in detail three specific examples: the exponential, ...