Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary...

Area of Science:

• Epidemiology
• Genetic Epidemiology
• Statistical Genetics

Background:

• Sample size calculations are essential for planning epidemiological studies.
• Mendelian randomization investigations often necessitate large sample sizes.
• Accurate sample size determination is critical for study validity and power.

Purpose of the Study:

• To provide methodologies for sample size and power calculations in Mendelian randomization (MR) studies with binary outcomes.
• To offer practical resources, including formulas and computational tools, for researchers.
• To facilitate the planning of MR studies by clarifying sample size requirements.

Main Methods:

• Derivation of formulas for sample size and power calculations for MR with binary outcomes, building upon existing methods for continuous outcomes.
• Formulas are applicable to single instrumental variables, including individual genetic variants and allele scores.
• Development of graphical representations and R code for practical application.

Main Results:

• Formulas and tools are presented for calculating required sample sizes for a specified power (e.g., 80%) based on causal effect estimates and instrumental variable strength.
• The relationship between sample size, power, causal effect, and instrumental variable characteristics is illustrated.
• An online calculator and R code are provided for flexible sample size and power computations.

Conclusions:

• The sample size needed for Mendelian randomization studies is highly dependent on the proportion of variance in the risk factor explained by the instrumental variable(s).
• Utilizing allele scores with multiple variants can enhance statistical power by explaining more variance, but requires careful validation to avoid bias.
• These findings underscore the importance of selecting strong and valid instrumental variables for efficient MR study design.