# Sample Size for Survival Analysis

Menu location: **Analysis_Sample Size_Survival Times**.

This function gives you the minimum number of subjects that you require to detect a true ratio of median survival times (hr) with power POWER and two sided type I error probability ALPHA (Dupont, 1990; Schoenfeld and Richter, 1982).

The method used here is suitable for calculating sample sizes for studies that will be analysed by the log-rank test.

__Information required__

- POWER: probability of detecting a real effect.
- ALPHA: probability of detecting a false effect (two sided: double this if you need one sided).
- A: accrual time during which subjects are recruited to the study.
- F: additional follow-up time after the end of recruitment.
- *: input either (C and r) or (C and E), where r=E/C.
- C: median survival time for control group.
- E: median survival time for experimental group.
- r: hazard ratio or ratio of median survival times.
- M: number of controls per experimental subject.

__Practical issues__

- Usual values for POWER are 80%, 85% and 90%; try several in order to explore/scope.
- 5% is the usual choice for ALPHA.
- C is usually estimated from previous studies.
- If possible, choose a range of hazard ratios that you want have the statistical power to detect.

__Technical validation__

The estimated sample size per group n is calculated as:

- where α = alpha, β = 1 - power and z_{p} is the standard normal deviate for probability p. n is rounded up to the closest integer. (1+1/m)/p is equivalent to 2/p in the first equation if the experimental and control group sizes are unequal.