318 PART 6 Analyzing Survival Data

In this chapter, as in Chapters 21 and 23, we use the term survival in reference to

the outcome of death. However, all the calculations pertain to any type of outcome

event being studied, including good ones, such as cancer going into remission.

There is some ambiguity associated with the name log-rank test. It has also been

called different names (such as the Mantel-Cox test), and has been extended into

variants such as the Gehan-Breslow test. You may also observe that different

software may calculates the log-rank test slightly differently. In this chapter, we

describe the most commonly used form of the log-rank test.

If have no censored observations in your data, you can skip most of this chapter.

This may happen if, for example, death is your outcome and at the end of your

study period no individuals are alive anymore — they all have died in your study.

As you may guess, this situation is much more common in animal studies than

human studies. But if you have followed all the individuals in your data until they

all experienced the outcome, and you have two or more groups of numbers indi-

cating survival times that you want to compare, you can use approaches described

in Chapter 11. One option is to use an unpaired Student t test to test whether one

group has a statistically significantly longer mean survival time than the other. If

you have three or more groups, you would use an ANOVA instead. But because

survival times are very likely to be non-normally distributed, you may prefer to

use a nonparametric test, such as the Wilcoxon Sum-of-Ranks test or Mann-

Whitney U test, to compare the median survival time between two groups. With

more than two groups, you would use the nonparametric Kruskal-Wallis test.

Suppose that you conduct a toxicity study with laboratory animals of a potential

cancer drug. You obtain 90 experimental mice. The mice are randomly placed in

groups such that 60 receive the drug in their food, and 30 are given control food

with no drug. A laboratory worker observes them and records their vital status

every day after the experiment starts, taking note of when each animal dies or is

censored, meaning they are taken out of the study for another reason (such as not

eating). You perform a life-table analysis on each group of mice — the drug com-

pared to control — as described in Chapter 21, and graph the results. The graph

displays the survival curves shown in Figure 22-1. As a bonus, the two life tables

generated to support this display also provide the summary information needed

the log-rank test.

The two survival curves in Figure 22-1 look different. The drug group seems to be

showing better survival than the control group. But is this apparent difference

real, or could it be the result of random fluctuations only? The log-rank test

answers this question.