1. Figure 2. Number of cases required in a Mendelian randomization analysis with a binary outcome and a single instrumental variable for 80% power with a 5% significance level and 1:1 ratio of cases:controls varying the size of causal effect [odds ratio per standard deviation (SD) increase in risk factor, exp(β₁)] for different values of IV strength. Left panel: = 1%–8%. Right panel: = 0.5%–3.0%
From: Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome
Int J Epidemiol. 2014;43(3): doi: /ije/dyu005
Int J Epidemiol | © The Author Published by Oxford University Press on behalf of the International Epidemiological AssociationThis is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

2. Figure 1. Power curves varying the sample size with continuous outcome and a single instrumental variable. Left panel: for a fixed value of the IV strength and different values of the size of the causal effect (β₁ = 0.05, 0.1, … , 0.3). Right panel: for a fixed value of the causal effect (β₁ = 0.2) and varying the size of the IV strength
From: Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome
Int J Epidemiol. 2014;43(3): doi: /ije/dyu005
Int J Epidemiol | © The Author Published by Oxford University Press on behalf of the International Epidemiological AssociationThis is an Open Access article distributed under the terms of the Creative Commons Attribution License ( which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.