340 PART 6 Analyzing Survival Data

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 correspond-

ing 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.