CHAPTER 22 Comparing Survival Times 323

Assessing the assumptions

Like all statistical tests, the log-rank test assumes that you studied an unbiased

sample from the population about which you’re trying to draw conclusions. It also

assumes that any censoring that occurred was due to circumstances unrelated to

the treatment being tested (for example, individuals didn’t drop out of the study

because the drug made them sick).

Also, the log-rank test looks for differences in overall survival time. In other

words, it’s not good at detecting differences in shape between two survival curves

with similar overall survival time, like the two curves shown in Figure 22-4. These

two curves actually have the same median survival time, but the survival experi-

ence is different, as shown in the graph. When two survival curves cross over each

other, as shown in Figure 22-4b, the excess deaths are positive for some time

slices and negative for others. This leads them to cancel out when they’re added

up, producing a smaller z value as a test statistic z value, which translates to

larger, non-statistically significant p value.

Therefore, one very important assumption of the log-rank test is that the two

groups have proportional hazards, which means the two groups must have gener-

ally similar survival shapes, as shown in Figure 22-4a. Flip to Chapter 21 for more

about survival curves, and read about hazards in more detail in Chapter 23.

FIGURE 22-4:

Proportional (a)

and nonpropor-

tional (b) hazards

relationships

between two

survival curves.

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