Survival Analysis Using SAS®: A Practical Guide

Tied Data

The formula for the partial likelihood in equation (5.10) is valid only for data in which no two events occur at the same time. It’s quite common for data to contain tied event times, however, so we need an alternative formula to handle those situations. Most partial likelihood programs use a technique called Breslow’s approximation, which works well when ties are relatively few. But when data are heavily tied, the approximation can be quite poor (Farewell and Prentice 1980; Hsieh 1995). Although PROC PHREG uses Breslow’s approximation as the default, it is unique in providing a somewhat better approximation proposed by Efron (1977) as well as two exact methods.

This section explains the background, rationale, and implementation of ...