CHAPTER 23 Survival Regression 329

»

» ^{Quantify the extent to which a predictor variable influences survival, including}

testing whether survival is statistically significantly different between groups»

» ^{Adjust for the effects of confounding variables that also influence survival»}

» ^{Generate a predicted survival curve called a prognosis curve that is customized}

for any particular set of values of the predictor variables

Grasping the Concepts behind

Survival Regression

Note: Our explanation of survival regression has a little math in it, but nothing

beyond high school algebra. In laying out these concepts, we focus on multiple

survival regression, which is survival regression with more than one predictor. But

everything we say is also true when you have only one predictor variable.

Most kinds of regression require you to write a formula to fit to your data. The

formula is easiest to understand and work with when the predictors appear in the

function as a linear combination in which each predictor variable is multiplied by a

coefficient, and these terms are all added together (perhaps with another coeffi-

cient, called an intercept, thrown in). Here is an example of a typical regression

formula: y

c

c x

c x

c x

0

1

1

2

2

3

3

. Linear combinations (such as c2x2 from the

example formula) can also have terms with higher powers  — like squares or

cubes — attached to the predictor variables. Linear combinations can also have

interaction terms, which are products of two or more predictors, or the same pre-

dictor with itself.

Survival regression takes the linear combination and uses it to predict survival.

But survival data presents some special challenges:»

» ^{Censoring: Censoring happens when the event doesn’t occur during the}

observation time of the study (which, in human studies, means during

follow-up). Before considering using survival regression on your data, you

need to evaluate the impact censoring may have on the results. You can do

this using life tables, the Kaplan-Meier method, and the log-rank test, as

described in Chapters 21 and 22.»

» ^{Survival curve shapes: Some business disciplines develop models for}

estimating time to failure of mechanical or electronic devices. They estimate

the times to certain kinds of events, like a computer’s motherboard wearing

out or the transmission of a car going kaput, and find that they follow