CHAPTER 23 Survival Regression 341

Homing in on hazard ratios and their

confidence intervals

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 eCoef»}

» ^{Lower 95 percent confidence limit eCoef 1.96}

SE»

» ^{Upper 95 percent confidence limit e}

SE

Coef 1.96

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 e

1.57

0.4522

, 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 signifi-

cantly 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 (rela-

tive 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 Radi-

ation is a protective factor.