Basic Statistics

ADDITIONAL ANALYSES USING SURVIVAL DATA 215

of time falls into. The last five columns of Table 14.2 are arithmetic manipulations of

previous columns. Spreadsheet programs often provide the capability to perform the

calculations to obtain these columns from the previous ones. When the sample size is

large, the intervals can be made quite small and the difference in appearance of a plot

of the estimated survival function from a clinical life table or from the Kaplan-Meier

method is negligible.

14.5 ADDITIONAL ANALYSES USING SURVIVAL DATA

In this section we briefly mention two other types of analyses that can be performed

using survival data that include censored observations. References are given to texts

that provide additional information.

14.5.1 Comparing the Equality of Survival Functions

In addition to examining survival for a single group of patients, we often wish to
compare survival for two or more treatment groups. Visually examining the estimated
survival function or hazard rate is often done in order to compare a standard to an
experimental treatment. If one survival curve is appreciably above the other, the
treatment with the higher curve is usually preferred. One difficulty in looking for
differences in estimated survival functions is that minor differences in estimated
survival functions sometime look larger than they are. For example, if there is a
minor difference soon after entry to the study and if after that the survival functions
are similar, the treatment that did better initially will tend to have a higher survival
function throughout. This may exaggerate minor differences. It is useful to examine
both the survival function and the hazard function to get a better idea of what happens
over time.
Survival statistical programs may also offer the option of several tests for the null
hypothesis that two or more survival functions are equal. These tests were not derived
to test for equality of the means as the tests described in Chapter 8 were. If the null
hypothesis is rejected, we can conclude that the survival functions are not equal.
For any of these tests, the test results should be treated with caution if the sample
size is small. Also, the pattern of censoring should be examined to look for major
differences between the treatment groups. For example, if the experimental group
had a much higher rate of patients refusing treatment or being lost to follow-up, it may
not be better than the standard treatment even though the few patients who remain on
the experimental treatment do somewhat better than the larger proportion remaining
on the standard treatment. It is always recommended that a plot be examined of time
versus the number or proportion censored for both groups to see if there are major
differences.
Two of the more commonly used tests are the log-rank test (also called the Muntel-
Cox test) and the Peto test (also called the Peto-Breslow test). Statistical programs are
commonly used to perform the tests, but a description of the calculations is beyond
the scope of this book (see Kleinbaum and Klein [2005] for a very understandable
explanation). In considering these tests it should be kept in mind that the log-rank test