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- W2512043630 abstract "We propose a Bayesian approach to Mendelian Randomization studies based on a set of instruments, $Z$. The approach allows some instruments to violate the (untestable) no-pleiotropy condition, that $Z$ be independent of the (continuous) response $Y$, conditional on the (continuous) exposure $X$ and on the confounders of the relationship between $X$ and $Y$. However, it assumes that no instrument be associated with the confounders. Our approach introduces a vector $beta$ representing the unknown pleiotropic associations between $Z$ and $Y$. This makes the model unidentifiable from the likelihood. We make the posterior distribution proper by imposing on $beta$ a biologically justified prior that assumes some pleiotropic associations to be zero. This we do by imposing on $beta$ Carvalho's horseshoe shrinkage prior, which will shrink the components of this vector towards zero, but to different degrees, adaptively, without requiring the user to specify numerical values for the hyperparameters. Conditional on a particular value of the causal effect of interest, $theta$, this prior will allow instruments irreconcilable with the no-pleiotropy hypothesis to have their corresponding components of $beta$ unshrunk, so as to prevent the estimate of $theta$ from being corrupted by their presence. The components of $beta$ for the remaining instruments will be heavily shrunk towards zero, so that the information they provide will be used to estimate $theta$. Computational aspects of the method are discussed. We perform a simulation study to assess the type-I error probability and the power of our method to detect the causal effect of interest, relative to those of the weighted median estimator. Next we generalize the model by allowing instrument-exposure interactions, and assess performance in this case, too." @default.
- W2512043630 created "2016-09-16" @default.
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- W2512043630 date "2016-08-09" @default.
- W2512043630 modified "2023-09-27" @default.
- W2512043630 title "Mendelian Randomization with Poor Instruments: a Bayesian Approach" @default.
- W2512043630 hasPublicationYear "2016" @default.
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