# Sample Size for Independent Case-control Studies

Menu location: **Analysis_Sample Size_Independent Case-Control**.

This function gives the minimum number of case subjects required to detect a real odds ratio or case exposure rate with power POWER and two sided type I error probability ALPHA. This sample size is also given as a continuity-corrected value intended for use with corrected chi-square and Fisher's exact tests (Schlesselman, 1982; Casagrande et al. 1978; Dupont, 1990).

__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).
- P0: probability of exposure in controls.
- *: Input either P1 or OR.
- P1: probability of exposure in case subjects.
- OR: odds ratio of exposures between cases and controls.
- M: number of control subjects per case 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.
- P0 can be estimated as the population prevalence of exposure.
- If possible, choose a range of odds ratios that you want have the statistical power to detect.

__Technical validation__

The estimated sample size n is calculated as:

- where α = alpha, β = 1 - power, ψ = odds ratio, n_{c} is the continuity corrected sample size, m is the number of control subjects per case, and z_{p} is the standard normal deviate for probability p. n is rounded up to the closest integer.