Sample Size for Matched Case-control Studies

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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.