CHAPTER 22 Comparing Survival Times 319

Comparing Survival between Two Groups

with the Log-Rank Test

The log-rank test can be performed using individual-level data, or on data that

has been summarized into a life-table format. In this section, we describe how to

run a log-rank test with statistical software, which is how it is usually done. Next,

to help you understand the underlying calculations, we describe the log-rank test

calculations in detail using the life-table as you might carry them out manually

using spreadsheet software such as Microsoft Excel.

Understanding what the log-rank

test is doing

A two-group log-rank test asks whether events  — which are deaths in our

example — are split between the two groups in the same proportion as the num-

ber of at-risk individuals in the two groups. The computer selects a group and

sums the difference between the observed and expected number of deaths in each

time slice over all the time slices to get the total excess deaths for that group. The

excess death sum is then scaled down, meaning it is divided by an estimate of its

standard deviation. (Later in this chapter we describe how to calculate that stan-

dard deviation estimate.) The scaled-down excess deaths sum is a number whose

random sampling fluctuations should follow a normal distribution, and from

which a p value can be easily calculated. The null hypothesis of the log-rank test

is that there is no difference in survival between the two groups, so a p value less

than your selected α (usually 0.05) indicates a statistically significant difference.

FIGURE 22-1:

Survival curves

for two groups of

laboratory

animals.

© John Wiley & Sons, Inc.