Unmatched Case-Control
BioScale Report: Unmatched Case-Control
Calculation for comparing exposure proportion ($P_1$) in cases to exposure proportion ($P_2$) in controls, using the anticipated Odds Ratio (OR).
Formula Used (Sample Size per Group, n):
$$n = \frac{[Z_{1-\alpha/2}\sqrt{2\bar{P}(1-\bar{P})} + Z_{1-\beta}\sqrt{P_1(1-P_1)+P_2(1-P_2)}]^2}{(P_1 - P_2)^2}$$
P1 is the proportion exposed in cases, P2 is the proportion exposed in controls. P1 is derived from the {OR} and P2:
$$P_1 = \frac{\text{OR} \cdot P_2}{1 + P_2(\text{OR}-1)} \quad \text{and} \quad \bar{P} = \frac{P_1 + P_2}{2}$$
Expected association between exposure and disease (e.g., OR = 2.5).
Exposure prevalence in the non-diseased (control) population (e.g., 0.30).
Probability of a Type I error.
Probability of correctly detecting the OR.