Matched Case-Control

Calculation for comparing proportions in a $1:1$ matched case-control study, using the anticipated Odds Ratio (OR).

Formula Used (Number of Matched Pairs, n):

$$n = \frac{(Z_{1-\alpha/2} + Z_{1-\beta})^2 [P_{10} + P_{01}]}{[P_{10} - P_{01}]^2}$$

Where $P_{10}$ and $P_{01}$ are the discordant proportions derived from OR and $P_{exp}$. The result $n$ is the number of **pairs**.

1. Anticipated Odds Ratio (OR):

Expected association between exposure and disease (e.g., OR = 2.5).

2. Proportion Exposed in Population ($P_{exp}$):

Overall exposure prevalence in the source population (e.g., 0.30).

3. Significance Level ($\alpha$):

Probability of a Type I error.

4. Desired Power (1-$\beta$):

Probability of correctly detecting the OR.

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