CHAPTER 23 Survival Regression 331

3.

Create a PH regression model that fits your data the best it can, and

interpret the values of the regression coefficients so you can calculate

predicted survival times.

Determining the baseline in time-to-event

analyses

Your software may define the baseline survival function in one of two ways:»

» ^{The survival curve of an average participant: This curve is calculated as if}

the value of each predictor is equal to the group average value for that

variable. The average-participant baseline is like the overall survival curve you

get from a Kaplan-Meier calculation by using all the available participants.»

» ^{The survival curve of a hypothetical zero participant: This curve is calcu-}

lated assuming the value of each predictor is equal to 0. Some mathematicians

prefer to use the zero-participant baseline because can make formulas simpler,

but biostatisticians don’t like it because it corresponds to a hypothetical

participant who can’t possibly exist in the real world. No actual person has an

age equal to 0 years, or weighs 0 kilograms, and so on. The survival curve for

this impossible person doesn’t look like a regular survival curve, so as biostatis-

ticians, we can’t really use the zero-participant baseline survival function.

Luckily, the way your software defines its baseline function doesn’t affect any of

the calculated measures on your output, so you don’t have to worry about it. But

you should be aware of these definitions if you plan to generate prognosis curves,

because the formulas to generate these are slightly different depending upon the

way the computer calculates the baseline survival function.

Bending the baseline

Now for the tricky part. How do you bend or flex this baseline curve to express how

survival may increase or decrease for different predictor values? Survival curves

always start at 1.0 at time 0, meaning 100 percent of the sample do not have the

event at time 0. The bending process must preserve that time starts at 0, and

maximum survival is 1.0. If you raise 0 or 1 to any power, you will find that they

stay the same — 0 stays 0, and 1 stays 1. But, exponentiating any number between

0 and 1 smoothly raises or lowers all the values between 0 and 1.

We will demonstrate what we mean by imagining our baseline function was a

straight line (even though no actual biological survival curve would ever be exactly

a straight line). Look at Figure 23-1a, which is a graph of the equation y

x

1

.