Comparisons

We introduce power and sample size in Chapter 3. Calculating the sample size for survival

comparisons is complicated by several factors:

The need to specify an alternative hypothesis: This hypothesis can take the form of a hazard

ratio, described in Chapter 23, where the null hypothesis is that the hazard ratio = 1. Or, you can

hypothesize the difference between two median survival times.

The impact of censoring: How censoring impacts sample size needed depends on the accrual

rate, dropout rate, and the length of follow-up.

The shape of the survival curves: For sample-size calculations, it is often assumed that the

survival curve is exponential, but that may not be realistic.

In Chapter 4, we recommend using free software G*Power for your sample-size calculations.

However, because G*Power does not offer a survival sample-size estimator, for this, we

recommend you use another free software package called PS (Power and Sample Size

Calculation), which is available from Vanderbilt University Medical Center

(https://biostat.app.vumc.org/wiki/Main/PowerSampleSize).

After opening the PS program, choose the Survival tab, fill in the form, and click Calculate. The

median survival times for the two groups are labeled m1 and m2, the accrual interval is labeled A, the

post-accrual follow-up period is labeled F, and the group allocation proportion is labeled m. Note that

the time variables must always be entered in the same units (days, in this example). You will also need

to enter your chosen α and power.

Here is an example. Suppose that you’re planning a study to compare an experimental drug for keeping

cancer remission to placebo in two equal-sized groups of cancer patients whose cancer is in

remission. You expect to observe participants for a total of three years to see whether their cancer

returns (which is the outcome). From existing studies, you expect the median placebo time to be 20

months, and you think the drug should extend this to 30 months. If it truly does extend survival (time to

remission) that much, you want to be able to detect this. You set α = 0.05 and power at 80 percent so

that you have an 80 percent chance of getting a p value of less than 0.05 when you compare drug to

placebo using the log-rank test. If you fill in the PS form with these estimates and select Calculate,

under Sample Size the software will say you need 170 participants in each group (a total of 340

participants).