Sample Size Calculation For Clinical Trials

Sample Size Formula for Two-Arm Superiority Trial:

\[ n = 2 (Z_{\alpha/2} + Z_{\beta})^2 \frac{\sigma^2}{\delta^2} \]

Z_α/2 (Standard Normal Value):

unitless

Z_β (Standard Normal Value):

unitless

Standard Deviation (σ):

units

Difference (δ):

units

Required Sample Size (n):

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1. What is Sample Size Calculation?

Sample size calculation is a critical step in clinical trial design that determines the number of participants needed to detect a statistically significant difference between treatment groups. This calculator uses the formula for two-arm superiority trials.

2. How Does the Calculator Work?

The calculator uses the sample size formula for two-arm superiority trials:

\[ n = 2 (Z_{\alpha/2} + Z_{\beta})^2 \frac{\sigma^2}{\delta^2} \]

Where:

\( n \) — Sample size per group (unitless)
\( Z_{\alpha/2} \) — Standard normal value for type I error (typically 1.96 for α=0.05)
\( Z_{\beta} \) — Standard normal value for type II error (typically 0.84 for 80% power)
\( \sigma \) — Standard deviation of the outcome (units)
\( \delta \) — Clinically important difference to detect (units)

Explanation: This formula calculates the required sample size per group to achieve specified statistical power while controlling type I error rate.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures clinical trials have adequate power to detect meaningful treatment effects, prevents underpowered studies, and optimizes resource allocation in research.

4. Using the Calculator

Tips: Enter standard normal values for type I and type II errors, the expected standard deviation of your outcome measure, and the clinically important difference you want to detect. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_α/2 and Z_β?
A: For α=0.05 (two-sided), Z_α/2=1.96; for 80% power, Z_β=0.84; for 90% power, Z_β=1.28.

Q2: How do I estimate standard deviation (σ)?
A: Use data from pilot studies, previous similar trials, or published literature. Conservative estimates are recommended.

Q3: What is a clinically important difference (δ)?
A: The smallest treatment effect that would be considered meaningful in clinical practice, determined by clinical expertise and patient input.

Q4: Does this account for dropout rates?
A: No, you should inflate the calculated sample size to account for expected dropout rates (e.g., divide by (1-dropout rate)).

Q5: When is this formula appropriate?
A: For continuous outcomes in two-arm superiority trials with equal allocation and normally distributed data.