CHAPTER 23 Survival Regression 339

Testing the validity of the assumptions

When you’re analyzing data using PH regression, you’re assuming that your data

are consistent with the idea of flexing a baseline survival curve by raising all the

points in the entire curve to the same power (shown as h in Figures 23-1b and 

23-2b). You’re not allowed to twist the curve so that it goes higher than the base-

line curve (h

1) for small time values and lower than baseline (h

1) for large

time values. That would be a non-PH flexing of the curve.

One quick check to see whether a predictor is affecting your data in a non-PH way

is to take the following steps:

1.

Split your data into two groups, based on the predictor.

2.

Plot the Kaplan-Meier survival curve for each group (see Chapter 22).

If the two survival curves for a particular predictor display the slanted figure-

eight pattern shown in Figure 23-5, either don’t use PH regression on those

data, or don’t use that predictor in your PH regression model. That’s because it

violates the assumption of proportional hazards underlying PH regression.

Your statistical software may offer several options to test the hazard-

proportionality assumption. Check your software’s documentation to see what

it offers and how to interpret the output. It may offer the following:»

» ^{Graphs of the hazard functions versus time, which let you see the extent to}

which the hazards are proportional.»

» ^{A statistical test for significant hazard non-proportionality. R provides a}

function called cox.zph for this purpose, and other packages may offer

a comparable option.

FIGURE 23-5:

Don’t try PH

regression on this

kind of data

because it

violates the PH

assumption.

© John Wiley & Sons, Inc.