Background Mendelian randomization is used to test and estimate the magnitude of a causal effect of a phenotype on an outcome by using genetic variants as instrumental variables (IVs). Estimates of association from IV analysis are biased in the direction of the confounded, observational association between phenotype and outcome. The magnitude of the bias depends on the F-statistic for the strength of relationship between IVs and phenotype. We seek to develop guidelines for the design and analysis of Mendelian randomization studies to minimize bias. Methods IV analysis was performed on simulated and real data to investigate the effect on bias of size of study, number and choice of instruments and method of analysis. Results Bias is shown to increase as the expected F-statistic decreases, and can be reduced by using parsimonious models of genetic association (i.e. not over-parameterized) and by adjusting for measured covariates. Using data from a single study, the causal estimate of a unit increase in log-transformed C-reactive protein on fibrinogen (μmol/l) is shown to increase from -0.005 (P = 0.99) to 0.792 (P = 0.00003) due to injudicious choice of instrument. Moreover, when the observed F-statistic is larger than expected in a particular study, the causal estimate is more biased towards the observational association and its standard error is smaller. This correlation between causal estimate and standard error introduces a second source of bias into meta-analysis of Mendelian randomization studies. Bias can be alleviated in meta-analyses by using individual level data and by pooling genetic effects across studies. Conclusions Weak instrument bias is of practical importance for the design and analysis of Mendelian randomization studies. Post hoc choice of instruments, genetic models or data based on measured F-statistics can exacerbate bias. In particular, the commonly cited rule of thumb that F > 10 avoids bias in IV analysis is misleading.

http://www.phpc.cam.ac.uk/ceu/files/2012/11/paper3four131110.pdf

Avoiding bias from weak instruments in Mendelian randomization studies

Mendelian randomization (MR) uses genetic variants as instrumental variables to infer whether a risk factor causally affects a health outcome. Meta-analysis has been used historically in MR to combine results from separate epidemiological studies, with each study using a small but select group of genetic variants. In recent years, it has been used to combine genome-wide association study (GWAS) summary data for large numbers of genetic variants. Heterogeneity among the causal estimates obtained from multiple genetic variants points to a possible violation of the necessary instrumental variable assumptions. In this article, we provide a basic introduction to MR and the instrumental variable theory that it relies upon. We then describe how random effects models, meta-regression, and robust regression are being used to test and adjust for heterogeneity in order to improve the rigor of the MR approach.

/pdf/meta-analysis-and-mendelian-randomization-a-review-3fim5tx5ty.pdf

Meta-analysis and Mendelian randomization: A review.

BACKGROUND: Obesity is associated with vitamin D deficiency, and both are areas of active public health concern. We explored the causality and direction of the relationship between body mass index (BMI) and 25-hydroxyvitamin D [25(OH)D] using genetic markers as instrumental variables (IVs) in bi-directional Mendelian randomization (MR) analysis. METHODS AND FINDINGS: We used information from 21 adult cohorts (up to 42,024 participants) with 12 BMI-related SNPs (combined in an allelic score) to produce an instrument for BMI and four SNPs associated with 25(OH)D (combined in two allelic scores, separately for genes encoding its synthesis or metabolism) as an instrument for vitamin D. Regression estimates for the IVs (allele scores) were generated within-study and pooled by meta-analysis to generate summary effects. Associations between vitamin D scores and BMI were confirmed in the Genetic Investigation of Anthropometric Traits (GIANT) consortium (n = 123,864). Each 1 kg/m(2) higher BMI was associated with 1.15% lower 25(OH)D (p = 6.52×10⁻²⁷). The BMI allele score was associated both with BMI (p = 6.30×10⁻⁶²) and 25(OH)D (-0.06% [95% CI -0.10 to -0.02], p = 0.004) in the cohorts that underwent meta-analysis. The two vitamin D allele scores were strongly associated with 25(OH)D (p≤8.07×10⁻⁵⁷ for both scores) but not with BMI (synthesis score, p = 0.88; metabolism score, p = 0.08) in the meta-analysis. A 10% higher genetically instrumented BMI was associated with 4.2% lower 25(OH)D concentrations (IV ratio: -4.2 [95% CI -7.1 to -1.3], p = 0.005). No association was seen for genetically instrumented 25(OH)D with BMI, a finding that was confirmed using data from the GIANT consortium (p≥0.57 for both vitamin D scores). CONCLUSIONS: On the basis of a bi-directional genetic approach that limits confounding, our study suggests that a higher BMI leads to lower 25(OH)D, while any effects of lower 25(OH)D increasing BMI are likely to be small. Population level interventions to reduce BMI are expected to decrease the prevalence of vitamin D deficiency.

/pdf/causal-relationship-between-obesity-and-vitamin-d-status-bi-abk51r02qz.pdf

Causal relationship between obesity and vitamin D status: bi-directional Mendelian randomization analysis of multiple cohorts.

Causal Relationship between Obesity and Vitamin D Status: Bi-Directional Mendelian Randomization Analysis of Multiple Cohorts

Objective To use genetic variants as unconfounded proxies of C reactive protein concentration to study its causal role in coronary heart disease. Design Mendelian randomisation meta-analysis of ind ...

/pdf/association-between-c-reactive-protein-and-coronary-heart-47v7hnmc9y.pdf

Association between C reactive protein and coronary heart disease: mendelian randomisation analysis based on individual participant data

Genetic markers can be used as instrumental variables, in an analogous way to randomization in a clinical trial, to estimate the causal relationship between a phenotype and an outcome variable. Our purpose is to extend the existing methods for such Mendelian randomization studies to the context of multiple genetic markers measured in multiple studies, based on the analysis of individual participant data. First, for a single genetic marker in one study, we show that the usual ratio of coefficients approach can be reformulated as a regression with heterogeneous error in the explanatory variable. This can be implemented using a Bayesian approach, which is next extended to include multiple genetic markers. We then propose a hierarchical model for undertaking a meta-analysis of multiple studies, in which it is not necessary that the same genetic markers are measured in each study. This provides an overall estimate of the causal relationship between the phenotype and the outcome, and an assessment of its heterogeneity across studies. As an example, we estimate the causal relationship of blood concentrations of C-reactive protein on fibrinogen levels using data from 11 studies. These methods provide a flexible framework for efficient estimation of causal relationships derived from multiple studies. Issues discussed include weak instrument bias, analysis of binary outcome data such as disease risk, missing genetic data, and the use of haplotypes.

/pdf/bayesian-methods-for-meta-analysis-of-causal-relationships-1k0w7vurqu.pdf

Bayesian methods for meta-analysis of causal relationships estimated using genetic instrumental variables

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Bayesian methods for meta-analysis of causal relationships estimated using genetic instrumental variables