320 PART 6 Analyzing Survival Data

Don’t worry if the preceding paragraph makes your head spin. It is only meant to

give you a general sense behind the calculations in the log-rank test.

Running the log-rank test on software

Most commercial statistical software packages (like those described in Chapter 4)

can perform a log-rank test. You first organize your data into a table that has one

row per individual, and these three columns:»

» ^{Group: The group variable contains a code indicating the individual’s group. In}

this example, we could use the code Drug = 1 and Control = 2.»

» ^{Time: A numerical variable containing the individual’s survival time. For}

individuals experiencing the event during the study, it represents time to

event. For censored individuals, it is time to the end of observation.»

» ^{Event status: A variable that indicates the individual’s status at the end of}

observation. If they got the event, it is usually coded as 1, and if not or they

are censored, it is coded as 0.

To run the log-rank test, you tell your computer program which variable repre-

sents the group variable, which one means time, and which one contains the

event status. The program should produce a p value for the log-rank test. If you

set α = 0.05 and the p value is less than that, you reject the null and conclude that

the two groups have statistically significantly different survival curves.

In addition to the p value, the program may output median survival time for each

group along with confidence intervals, and difference in median times between

groups. If possible, you will also want to request graphs that show whether your

data are consistent with the hazard proportionality assumption that we describe

later in “Assessing the assumptions.”

Looking at the calculations

The log-rank test should not be done manually because it is an error-prone task.

But we believe you’ll have a better appreciation of the log-rank test if you under-

stand how it works, so we describe how the calculations could theoretically be

carried out using a Microsoft Excel spreadsheet.

The log-rank test utilizes information from the life tables needed to produce the

graph shown earlier in Figure 22-1. Figure 22-2 shows a portion of the life tables

that produced the curves shown in Figure 22-1, with the data for the two groups

displayed side by side.