Calculation of Sample Size in Clinical Trials

Power Analysis for Superiority Trials

Sample Size Formula:

\[ n = (Z_{1-\alpha/2} + Z_{1-\beta})^2 \times \frac{\sigma^2}{\delta^2} \]

Alpha (Significance Level):

(e.g., 0.05)

Power (1-β):

(e.g., 0.8)

Standard Deviation (σ):

units

Effect Size (δ):

units

Sample Size per Group (n):

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1. What is Power Analysis for Superiority Trials?

Power analysis for superiority trials determines the sample size needed to detect a statistically significant difference between treatment groups when one treatment is expected to be superior to another. It ensures the study has adequate power to detect the hypothesized effect size.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for continuous outcomes:

\[ n = (Z_{1-\alpha/2} + Z_{1-\beta})^2 \times \frac{\sigma^2}{\delta^2} \]

Where:

\( n \) — Sample size per group (unitless)
\( Z_{1-\alpha/2} \) — Z-score for significance level (two-tailed)
\( Z_{1-\beta} \) — Z-score for power
\( \sigma \) — Standard deviation (units)
\( \delta \) — Effect size (units)

Explanation: This formula calculates the number of participants needed in each group to detect a specified effect size with given statistical power and significance level.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for clinical trial design. It ensures the study has sufficient power to detect meaningful differences while controlling Type I and Type II errors, optimizing resource allocation and ethical considerations.

4. Using the Calculator

Tips: Enter alpha (typically 0.05), power (typically 0.8 or 0.9), standard deviation based on pilot data or literature, and the minimum clinically important difference you wish to detect.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between superiority and non-inferiority trials?
A: Superiority trials aim to show one treatment is better than another, while non-inferiority trials aim to show a new treatment is not worse than an existing one by a pre-specified margin.

Q2: How do I determine the appropriate effect size?
A: Effect size should be based on clinical relevance, previous studies, or pilot data. It represents the minimum difference considered important in clinical practice.

Q3: What are typical values for alpha and power?
A: Alpha is typically 0.05 (5% significance level), and power is typically 0.8 or 0.9 (80% or 90% chance of detecting a true effect).

Q4: Can this formula be used for binary outcomes?
A: No, this formula is for continuous outcomes. Binary outcomes require a different formula based on proportions.

Q5: Should I adjust for multiple comparisons?
A: Yes, if conducting multiple tests, consider adjusting alpha (e.g., Bonferroni correction) to maintain the overall Type I error rate.