Graphs of the hazard functions versus time, which let you see the extent to which the hazards are

proportional.

A statistical test for significant hazard non-proportionality. R provides a function called cox.zph

for this purpose, and other packages may offer a comparable option.

Checking out the table of regression coefficients

A regression coefficients table in a survival regression looks very much like the tables produced by

almost all kinds of regression: ordinary least-squares, logistic, Poisson, and so on. The survival

regression table has a row for every predictor variable, usually containing the following items:

The value of the regression coefficient. This says how much the log of the HR increases when

the predictor variable increases by exactly 1.0 unit. It’s hard to interpret unless you exponentiate it

into a HR. In Figure 23-4, the coefficient for CenterCD is 0.4522, indicating that every increase of

1 in CenterCD (which literally means comparing everyone at Centers A and B to those at Centers

C and D), there is an increase the logarithm of the hazard by 0.4522. When exponentiated, this

translates into a HR of 1.57 (listed on the output under exp(coef)). As predicted from looking at

Figure 24-3, this indicates that those at Centers C and D together are associated with a higher

hazard compared with those at Centers A and B together. For indicator variables, there will be a

row in the table for each non-reference level, so in this case, you see a row for Radiation. The

coefficient for Radiation is –0.4323, which when exponentiated, translates to an HR of 0.65 (again

listed under exp(coef)). The negative sign indicates that in this study, radiation treatment is

associated with less hazard and better survival than the comparison treatment, which is

chemotherapy. Interpreting the HRs and their confidence intervals is described in the next section

“Homing in on hazard ratios and their confidence intervals.”

The coefficient’s standard error (SE), which is a measure of the precision of the regression

coefficient. The SE of the CenterCD coefficient is 0.1013, so you would express the CenterCD

coefficient as 0.45 ± 0.10.

The coefficient divided by its SE often labeled t or Wald, but designated as z in Figure 23-4.

The p value. Under the assumption that α = 0.05, if the p value is less than 0.05, it indicates that

the coefficient is statistically significantly different from 0 after adjusting for the effects of all the

other variables that may appear the model. In other words, a p value of less than 0.05 means that

the corresponding predictor variable is statistically significantly associated with survival. The p

value for CenterCD is shown as 8.09e–06, which is scientific notation for 0.000008, indicating

that CenterCD is very significantly associated with survival.

The HR and its confidence limits, which we describe in the next section.

You may be surprised that no intercept (or constant) row is in the coefficient table in the output

shown in Figure 23-4. PH regression doesn’t include an intercept in the linear part of the model

because the intercept is absorbed into the baseline survival function.

Homing in on hazard ratios and their confidence intervals