2. Estimate how your hypothesized predictor variables may impact the bends in this curve — in

other words, in what ways your predictors may affect survival.

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 calculated 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 biostatisticians, 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

.