CUSTOMIZED HAZARD RATIOS

As we have seen, for each predictor variable PROC PHREG reports a hazard ratio (HR), which is just the exponentiated value of its coefficient. And if we further calculate 100(HR-1), we get the percentage change in the hazard of the event for a 1-unit increase in that particular variable. Two problems can arise, however. First, a 1-unit change may be either too small or too large to be usefully interpreted. If a person's income is measured in dollars, for example, a $1 increase will most likely produce a very tiny percentage change in the hazard. On the other hand, if a lab measurement varies only between 0 and 0.1, a 1-unit increase (from 0 to 1) will be 10 times the observed range of the variable. Although you can do hand calculations to get the hazard ratio for different units (or modify the units of the variables before estimating the model), the HAZARDRATIO statement (available in SAS 9.2 and later) makes things much easier.

Let's apply these options to the recidivism data. In Output 5.1, we saw a hazard ratio of .944 for AGE, which we interpreted to mean that each 1-year increase in age was associated with a 5.6 percent reduction in the hazard of arrest. Suppose, instead, that we want the hazard ratios for a 5- year increase and a 10-year increase in age. We can get that with the following code: