Unmatched Cohort/RCT

Calculation for Unmatched Cohort Studies, Randomized Controlled Trials (RCTs) etc comparing two groups.

Formula Used (Sample Size per Group, n_g):

$$n_g = \frac{[Z_{1-\alpha/2}\sqrt{2\bar{\pi}(1-\bar{\pi})} + Z_{1-\beta}\sqrt{\pi_1(1-\pi_1)+\pi_2(1-\pi_2)}]^2}{(\pi_1-\pi_2)^2}$$

Where Z_α and Z_β are Z-scores for significance (α) and power (1-β), π₁ and π₂ are the expected proportions, and π̅ = (π₁ + π₂)/2.

1. Expected Proportion in Group 1 (π₁):

Expected proportion in the control/unexposed group (e.g., 0.20).

2. Expected Proportion in Group 2 (π₂):

Expected proportion in the intervention/exposed group (e.g., 0.40).

3. Significance Level (α):

Probability of a Type I error (False Positive).

4. Power (1-β):

Probability of correctly rejecting the null hypothesis.

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