# Sample size: Survival analysis (logrank test)

## Description

Calculates the required sample size for the comparison of survival rates in two independent groups.

## Required input

- Type I error - alpha: the probability of making a Type I error (α-level, two-sided), i.e. the probability of rejecting the null hypothesis when in fact it is true.
- Type II error - beta: the probability of making a Type II error (β-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
- Survival rate Group 1: the hypothesized survival rate in the first group.
- Survival rate Group 2: the hypothesized survival rate in the second group.
- Ratio of sample sizes in Group 1 / Group 2: the ratio of the sample sizes in group 1 and 2. Enter 1 for equal sample sizes in both groups. Enter 2 if the number of cases in group 1 must be double of the number of cases in group 2.

## Example

You are interested in detecting a difference between survival rates of 0.4 and 0.6. You plan to have the same number of cases in both groups.

Enter the values 0.4 and 0.6 for the Survival rates in Group 1 and Group 2, and enter 1 for the Ratio of sample sizes.

For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).

## Results

After you click the OK button the program will display the required sample size (196 in the example, meaning that you will need a total of 196 cases or 98 cases in each group).

A table shows the required total sample size for different Type I and Type II Error levels.

## Reference

- Machin D, Campbell MJ, Tan SB, Tan SH (2009) Sample size tables for clinical studies. 3
^{rd}ed. Chichester: Wiley-Blackwell.