# Sample Size for Matched Case-control Studies

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

This function gives you the minimum sample size necessary to detect a true odds ratio OR with power POWER and a two sided type I error probability ALPHA. If you are using more than one control per case then this function also provides the reduction in sample size relative to a paired study that you can obtain using your number of controls per case (Dupont, 1988).

__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).
- r: correlation coefficient (ϕ) for exposure between matched cases and controls.
- P0: probability of exposure in the control group.
- m: number of control subjects matched to each case subject.
- OR: odds ratio (ψ).

__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.
- r can be estimated from previous studies - note that r is the phi (correlation) coefficient that is given for a two by two table if you enter it into the StatsDirect r by c chi-square function. When r is not known from previous studies, some authors state that it is better to use a small arbitrary value for r, say 0.2, than it is to assume independence (a value of 0) (Dupont, 1988).
- P0 can be estimated as the population prevalence of exposure. Note, however, that due to matching, the control sample is not a random sample from the population therefore population prevalence of exposure can be a poor estimate of P0 (especially if confounders are strongly associated with exposure, Dupont, 1988).
- 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 (Dupont, 1990):

- where α = alpha, β = 1 - power, ψ = odds ratio, ϕ is the correlation coefficient for exposure between matched cases and controls, and Zp is the standard normal deviate for probability p. n is rounded up to the closest integer.