324 PART 6 Analyzing Survival Data

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 regres-

sion in Chapter 23.

Estimating the Sample Size Needed for

Survival 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