Cohort Sample Size Formula

Cohort Sample Size Formula:

\[ n = \frac{Z^2 (p_1(1-p_1) + p_2(1-p_2))}{(p_1 - p_2)^2} \times (1 + \frac{1}{k}) \]

Z-score:

unitless

Proportion 1 (p1):

proportion

Proportion 2 (p2):

proportion

Ratio (k):

ratio

Sample Size (n):

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1. What is the Cohort Sample Size Formula?

The Cohort Sample Size Formula is used to determine the required sample size for comparing outcomes between two cohorts in epidemiological and clinical studies. It ensures studies have adequate statistical power to detect meaningful differences.

2. How Does the Calculator Work?

The calculator uses the cohort sample size formula:

\[ n = \frac{Z^2 (p_1(1-p_1) + p_2(1-p_2))}{(p_1 - p_2)^2} \times (1 + \frac{1}{k}) \]

Where:

\( Z \) — Z-score for desired confidence level (typically 1.96 for 95% confidence)
\( p_1 \) — Expected proportion in group 1
\( p_2 \) — Expected proportion in group 2
\( k \) — Ratio of sample sizes between groups
\( n \) — Required sample size for group 1

Explanation: This formula accounts for the variance in proportions between two groups and adjusts for unequal group sizes using the k ratio parameter.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is essential for study validity, ensuring adequate statistical power to detect true effects while minimizing the risk of type I and type II errors.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), expected proportions for both groups (between 0 and 1), and the ratio between group sizes. All values must be valid and proportions must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What Z-score should I use?
A: For 95% confidence level, use 1.96; for 90% confidence, use 1.645; for 99% confidence, use 2.576.

Q2: How do I determine expected proportions?
A: Use data from previous studies, pilot studies, or clinical expertise to estimate the expected event rates in each group.

Q3: What does the k ratio represent?
A: k represents the ratio of sample sizes between groups (e.g., k=1 for equal groups, k=2 if one group is twice as large as the other).

Q4: When is this formula appropriate?
A: This formula is suitable for cohort studies comparing binary outcomes between two groups with known or estimated proportions.

Q5: What if I need to account for dropout?
A: Increase the calculated sample size by your expected dropout rate (e.g., multiply by 1/(1-dropout_rate)).