Fig 1.
Schematic overview of two-sample MR and two-fold CFMR.
Panel (a) shows the two-sample MR setup in which the first sample is used to build the instrument and the second sample is used to estimate the causal effect. Panel (b) shows the two-fold CFMR setup. Step 1 in panel (b) describes the random splitting of the dataset into two sub-samples. In step 2, two separate GWASs are performed: the first using sub-sample 1 and the exposure and the second using sub-sample 2 and the exposure. The predictors of the exposure are subsequently built based on sub-sample 1 (IV1) and sub-sample 2 (IV2). Step 3 refers to the 2SLS in which IV1 is applied to sub-sample 2 and IV2 is applied to sub-sample 1 to obtain the estimates of these IVRs. Finally, in step 4, the two 2SLS from step 3 are simply averaged to obtain the final estimate.
Fig 2.
Power curves for CFMR versus two-sample MR (2SMR) using the simulation setup described in the Simulations section in the main text (with h2 = 20%).
The dashed lines represent power curves for CFMR, while the solid lines represent the theoretical power for 2SMR [24]. Note that the solid pink line covers the solid red line perfectly (top part of the graph). These lines fully overlap as a result of symmetry. Given that the solid lines are generated from the theoretical power formula of two-sample MR (see Deng et al. [24]), the red and pink curves correspond to the same effect size (in terms of magnitude) but have opposite signs. The same is the case for the solid blue and gold lines in the middle part of the graph.
Fig 3.
Summary of the results of the simulations to assess bias due to complete sample overlap and weak instruments across different MR methods.
For details, see Section 3.2 in the main text. Each panel displays the box plots of the estimated effect according to method used (1SMR, Barry et al. [26], CFMR, and MR RAPS) and sample size (1000, 5, 000, 10, 000, and 50, 000). The y-axis corresponds to the estimated effect. The solid horizontal black line corresponds to the true value of the effect to be estimated. The different types of box plots correspond to the variance X explained by the genetic marker used as instruments (10% and 20%). The red box plots correspond to the estimates based on one-sample MR, the green box plots the estimates based on the Barry et al. [26] method, the purple box plots the estimate using MR RAPS, and finally, the blue box plots the estimates using CFMR.
Table 1.
CFMR estimates of maternal pre-pregnancy BMI on newborn’s birth weight per 1 SD increase in maternal pre-pregnancy BMI.
Fig 4.
Schematic overview of the application of CFMR to a dataset comprising two ethniticies.
In step 1, the two ethnicities are first separated into two distinct datasets, where each dataset contains individuals of the same ethnicity. In step 2, the dataset is split at random for each ethnicity. In step 3, two separate GWASs are performed: the first using sub-sample 1 and the exposure and the second using sub-sample 2 and the exposure. The predictors of the exposure are subsequently built based on sub-sample 1 (IV1) and sub-sample 2 (IV2). Step 4 refers to the 2SLS using IV1 on sub-sample 2 and IV2 on sub-sample 1, and, for each dataset, the two 2SLS from step 3 are averaged. Finally, in step 5 the two estimates are meta-analyzed to obtain the final estimate.