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For a given pair of nodes X and Y and a given CPDAG, IDA calculates multiple causal effects of X on Y, if the CPDAG connects X to other nodes via undirected edges.
For example, if the instrumented risk factor (here: height) has multiple causal effects, or if the outcome of interest has a causal effect of its own on the covariates, adjusting for such post-treatment variables may lead to biased estimates of the causal effect of interest.
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Since Mendelian randomization is analogous to a randomized trial (12), the use of genetic variants to assess the causal effects of multiple risk factors in a single study is analogous to a factorial randomized trial (see Web Figure 1, available at http://aje.oxfordjournals.org/), where multiple randomized interventions are simultaneously assessed (13).
Both approaches do not consider the joint effects among multiple causal SNPs.
If effects of multiple causal SNPs are allowed, the number of both the RR and the δ parameters increases substantially.
Allelic heterogeneity refers to a situation where multiple causal variants of differing frequency and effect size exist within a gene.
Weak instrument scenarios will be common in multivariable Mendelian randomization, as it is necessary to use multiple instrumental variables to estimate the different causal effects.
Sample code for estimating causal effects from summarized data for multiple variants associated with a risk factor in a single study and in multiple studies for R and WinBUGS is provided in the Supporting Information.
The models differ in the structural coefficients considered: M0 is the standard multiple trait model; in M1 are considered the causal effects of both SCS and CAS on RCT and a30; in M2 is considered the causal effects of RCT on a30; in M3 the causal effects of SCS, CAS and RCT on a30 are considered.
All of these genes contained multiple causal rare variants with a moderate or high effect size.
Moreover, those present are multiallelic, a situation which reflects the complexity observed in the predicted founders' haplotype effects, and suggesting the presence of multiple causal variants (Fig. 6).
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