Fig 1.
Unidirectional Mendelian randomization model.
Fig 2.
Bidirectional Mendelian randomization model with a feedback loop.
Table 1.
Simulation scenario 1: The unidirectional Mendelian randomization model is used.
Parameter estimates are based on 1000 replicates.
Fig 3.
Median of absolute bias (MAB) of bidirectional causal effect estimations for simulation scenario 2: Simulation using the bidirectional Mendelian randomization model and strong instrumental variables (IVs).
Parameter estimations are based on 1000 simulation replicates. A: MAB of estimations using one strong IV. B: MAB of estimations using 20 strong IVs. The color bar shows the range of MAB. BiRatio = bidirectional ratio method; BiLIML = limited information maximum likelihood method; LIML = limited information maximum likelihood method.
Table 2.
Simulation scenario 2 with strong instrumental variables (IVs): The bidirectional Mendelian randomization model is used.
Parameter estimates are based on 1000 replicates.
Fig 4.
Median of absolute bias (MAB) of bidirectional causal effect estimations for simulation scenario 3: Simulation using the bidirectional Mendelian randomization model and weak instrumental variables (IVs).
Parameter estimations are based on 1000 simulation replicates. A: MAB of estimations using 20 weak IVs. B: MAB of estimations using 100 weak IVs. The color bar for each figure shows the range of the MAB. BiRatio = bidirectional ratio method; BiLIML = limited information maximum likelihood method.
Table 3.
Simulation scenario 3 with weak instrumental variables: The simulation model is the bidirectional Mendelian randomization model.
Parameter estimates are based on 1000 replicates.
Table 4.
The bidirectional causal effects estimation between body mass index and fasting glucose.