HRs from survival and other time-to-event data are used extensively as safety and efficacy outcomes

of clinical trials, as well as in large-scale epidemiological studies. Depending on how the output is

formatted, it may show the HR for each predictor in a separate column in the regression table, or it

may create a separate table just for the HRs and their confidence intervals (CIs).

If the software doesn’t output HRs or their CIs, you can calculate them from the regression

coefficients and standard errors (SEs) as follows:

Hazard ratio

Lower 95 percent confidence limit

Upper 95 percent confidence limit

In Figure 23-4, the coefficients are listed under coef, and the SEs are listed under se(coef). HRs are

useful and meaningful measures of the extent to which a variable influences survival.

A HR of 1 corresponds to a regression coefficient of 0, and indicates that the variable has no effect

on survival.

The CI around the HR estimated from your sample indicates the range in which the true HR of the

population from which your sample was drawn probably lies.

In Figure 23-4, the HR for CenterCD is

, with a 95 percent CI of 1.29 to 1.92. This

means that an increase of 1 in CenterCD (meaning being a participant at Centers A or B compared to

being one at Centers C or D) is statistically significantly associated with a 57 percent increase in

hazard. This is because multiplying by 1.57 is equivalent to a 57 percent increase. Similarly, the HR

for Radiation (relative to the comparison, which is chemotherapy) is 0.649, with a 95 percent CI of

0.43 to 0.98. This means that those undergoing radiation had only 65 percent the hazard of those

undergoing chemotherapy, and the relationship is statistically significant.

Risk factors, or predictors associated with increased risk of the outcome, have HRs greater

than 1. Protective factors, or predictors associated with decreased risk of the outcome, have HRs

less than 1. In the example, CenterCD is a risk factor, and Radiation is a protective factor.

Assessing goodness-of-fit and predictive ability of the model

There are several measures of how well a regression model fits the survival data. These measures can

be useful when you’re choosing among several different models:

Should you include a possible predictor variable (like age) in the model?

Should you include the squares or cubes of predictor variables in the model (meaning including

age² or age³ in addition to age)?

Should you include a term for the interaction between two predictors?