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Mendelian randomization in the multivariate general linear model framework
Phillip H Allman1, Inmaculada Aban1, Dustin M Long1
1Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama, USA.
Abstract:
Mendelian randomization (MR) is an application of instrumental variable (IV) methods to observational data in which the IV is a genetic variant. MR methods applicable to the general exponential family of distributions are currently not well characterized. We adapt a general linear model framework to the IV setting and propose a general MR method applicable to any full-rank distribution from the exponential family. Empirical bias and coverage are estimated via simulations. The proposed method is compared to several existing MR methods. Real data analyses are performed using data from the REGARDS study to estimate the potential causal effect of smoking frequency on stroke risk in African Americans. In simulations with binary variates and very weak instruments the proposed method had the lowest median [Q1 , Q3 ] bias (0.10 [-3.68 to 3.62]); compared with 2SPS (0.27 [-3.74 to 4.26]) and the Wald method (-0.69 [-1.72 to 0.35]). Low bias was observed throughout other simulation scenarios; as well as more than 90% coverage for the proposed method. In simulations with count variates, the proposed method performed comparably to 2SPS; the Wald method maintained the most consistent low bias; and 2SRI was biased towards the null. Real data analyses find no evidence for a causal effect of smoking frequency on stroke risk. The proposed MR method has low bias and acceptable coverage across a wide range of distributional scenarios and instrument strengths; and provides a more parsimonious framework for asymptotic hypothesis testing compared to existing two-stage procedures.
Insights
This study introduces a new Mendelian randomization (MR) method for analyzing observational data, showing low bias and good coverage. The new method found no causal link between smoking frequency and stroke risk in African Americans.
Area of Science:
- Epidemiology
- Biostatistics
- Genetic Epidemiology
Background:
- Mendelian randomization (MR) applies instrumental variable (IV) methods to observational data using genetic variants as IVs.
- Existing MR methods for the general exponential family of distributions are not well-defined.
- There is a need for robust MR methods applicable to diverse data distributions.
Purpose of the Study:
- To propose a general Mendelian randomization (MR) method applicable to any full-rank distribution from the exponential family.
- To evaluate the empirical bias and coverage of the proposed method through simulations.
- To compare the proposed method against existing MR techniques and apply it to real-world data.
Main Methods:
- Adaptation of a general linear model framework to the instrumental variable (IV) setting.
- Development of a generalized MR method for exponential family distributions.
- Simulations using binary and count variates with varying instrument strengths.
- Comparison with existing methods like 2SPS, Wald, and 2SRI.
- Application to the REGARDS study dataset to assess the effect of smoking frequency on stroke risk in African Americans.
Main Results:
- The proposed MR method demonstrated the lowest median bias in simulations with binary variates and weak instruments.
- The method achieved over 90% coverage across various simulation scenarios, indicating reliable estimation.
- In count variate simulations, the proposed method performed comparably to 2SPS, while the Wald method showed consistent low bias.
- Real data analysis from the REGARDS study revealed no statistically significant causal effect of smoking frequency on stroke risk.
Conclusions:
- The proposed generalized Mendelian randomization (MR) method offers low bias and acceptable coverage across diverse distributional assumptions and instrument strengths.
- It provides a more unified and parsimonious framework for hypothesis testing in MR compared to traditional two-stage methods.
- The study found no evidence of a causal relationship between smoking frequency and stroke risk in the studied African American population.
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