Power Calculation for Mendelian Randomization

Power Calculation Formula:

\[ Power = f(\alpha, n, \beta_G, \beta_X, SE) \]

Significance Level (α):

(0.05)

Sample Size (n):

participants

Genetic Effect (β_G):

effect size

Exposure Effect (β_X):

effect size

Standard Error (SE):

standard error

Statistical Power:

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1. What is Mendelian Randomization Power Calculation?

Power calculation for Mendelian Randomization studies estimates the probability of detecting a causal effect when one truly exists. It helps researchers determine adequate sample sizes and assess study feasibility for genetic IVW (Inverse Variance Weighted) analyses.

2. How Does the Calculator Work?

The calculator uses the power calculation formula:

\[ Power = f(\alpha, n, \beta_G, \beta_X, SE) \]

Where:

\( \alpha \) — Significance level (typically 0.05)
\( n \) — Sample size
\( \beta_G \) — Genetic effect size
\( \beta_X \) — Exposure effect size
\( SE \) — Standard error of the estimate

Explanation: The calculation considers the non-centrality parameter derived from genetic and exposure effects, sample size, and measurement precision to estimate statistical power.

3. Importance of Power Calculation

Details: Adequate statistical power is crucial for Mendelian Randomization studies to avoid false negatives and ensure reliable causal inference. Power ≥80% is generally recommended for well-powered studies.

4. Using the Calculator

Tips: Enter significance level (typically 0.05), sample size, genetic effect, exposure effect, and standard error. All values must be valid positive numbers with appropriate ranges.

5. Frequently Asked Questions (FAQ)

Q1: What is considered adequate power for MR studies?
A: Typically 80% or higher is recommended, though this depends on the research context and consequences of false negatives.

Q2: How does sample size affect power?
A: Power increases with larger sample sizes, following a square root relationship with the non-centrality parameter.

Q3: What if my genetic instruments are weak?
A: Weak instruments (small β_G) require larger sample sizes to achieve adequate power and may be prone to bias.

Q4: Can I use this for binary outcomes?
A: This calculator is designed for continuous outcomes. Binary outcomes require different power calculation methods.

Q5: How accurate are these power estimates?
A: Estimates are approximate and assume ideal conditions. Actual power may vary due to genetic architecture and other factors.