THE PIECEWISE EXPONENTIAL MODEL

All the AFT models we have considered so far assume that the hazard is a smooth, relatively simple function of time. The Cox model (estimated with the PHREG procedure) is much less restrictive in this regard, but it lacks the facility to test hypotheses about the shape of the hazard function. One way to get some of the flexibility of the Cox model without losing the hypothesis testing capability is to employ the piecewise exponential model, a method that is widely used in several fields. We can easily estimate it with PROC LIFEREG, although it requires some preliminary restructuring of the data. A bonus of this method is the ability to incorporate time-dependent covariates.

The basic idea is simple. Divide the time scale into intervals. Assume that the hazard is constant within each interval but can vary across intervals. In symbols, we define a set of J intervals, with cut points a₀, a₁, ... , a_j, where a₀ = 0, and a_j = ∞. Thus, interval j is given by [a_j-1, a_j).