Sample Size Calculation in Clinical Research

Sample Size Formula for Comparing Proportions:

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

Sample Size per Group (n):

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1. What is Sample Size Calculation?

Sample size calculation is a crucial step in clinical research design that determines the number of participants needed to detect a statistically significant effect. Proper sample size ensures study validity and adequate power to answer research questions.

2. How Does the Calculator Work?

The calculator uses the formula for comparing two proportions:

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

Where:

\( n \) — Sample size per group
\( Z \) — Z-score (based on desired power and significance level)
\( p_1 \) — Proportion in group 1
\( p_2 \) — Proportion in group 2
\( p_1 - p_2 \) — Expected difference between proportions

Explanation: This formula calculates the required sample size per group to detect a specified difference between two proportions with given statistical power and significance level.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation prevents underpowered studies (missing true effects) and overpowered studies (wasting resources). It ensures ethical research conduct and valid statistical conclusions.

4. Using the Calculator

Tips: Enter Z-score based on desired power (typically 1.96 for 95% confidence, 2.8 for 99.5% confidence), expected proportions for both groups. All values must be valid (proportions between 0-1, Z-score > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the typical Z-score for clinical trials?
A: For 80% power and 5% significance (two-sided), Z-score is approximately 1.96. For 90% power, it's approximately 2.8.

Q2: How do I estimate proportions for sample size calculation?
A: Use data from previous studies, pilot studies, or clinical expertise. Conservative estimates are often preferred.

Q3: What if my proportions are very close?
A: Smaller differences require larger sample sizes. Consider whether the clinical difference is meaningful.

Q4: Should I account for dropout rates?
A: Yes, increase the calculated sample size by expected dropout rate (e.g., multiply by 1/(1-dropout_rate)).

Q5: When is this formula appropriate?
A: For randomized controlled trials comparing binary outcomes between two independent groups with equal allocation.