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 experience 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.

© John Wiley & Sons, Inc.

FIGURE 22-4: Proportional (a) and nonproportional (b) hazards relationships between two survival curves.

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 generally 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.

Considering More Complicated Comparisons

The log-rank test is good for comparing survival between two or more groups. But it doesn’t extend

well to more complicated situations. What if you want to do one of the following?

Test whether survival depends on age or some other continuous variable

Test the simultaneous effect of several variables, or their interactions, on survival

Correct for the presence of confounding variables or other covariates

In other areas of statistical testing, such situations are handled by regression techniques. Survival

analysis regression uses survival outcomes with censored observations, and can accommodate these

analyses. We describe survival regression in Chapter 23.

Estimating the Sample Size Needed for Survival