Power and sample size calculations for Mendelian randomization studies using one genetic instrument

Mendelian randomization, which is instrumental variable analysis using genetic variants as instruments, is an increasingly popular method of making causal inferences from observational studies. In order to design efficient Mendelian randomization studies, it is essential to calculate the sample sizes required. We present formulas for calculating the power of a Mendelian randomization study using one genetic instrument to detect an effect of a given size, and the minimum sample size required to detect effects for given levels of significance and power, using asymptotic statistical theory. We apply the formulas to some example data and compare the results with those from simulation methods. Power and sample size calculations using these formulas should be more straightforward to carry out than simulation approaches. These formulas make explicit that the sample size needed for Mendelian randomization study is inversely proportional to the square of the correlation between the genetic instrument and the exposure and proportional to the residual variance of the outcome after removing the effect of the exposure, as well as inversely proportional to the square of the effect size.