Two sample Mendelian Randomisation using an outcome from a multilevel model of disease progression

Identifying factors that are causes of disease progression, especially in neurodegenerative diseases, is of considerable interest. Disease progression can be described as a trajectory of outcome over time-for example, a linear trajectory having both an intercept (severity at time zero) and a slope (rate of change). A technique for identifying causal relationships between one exposure and one outcome in observational data whilst avoiding bias due to confounding is two sample Mendelian Randomisation (2SMR). We consider a multivariate approach to 2SMR using a multilevel model for disease progression to estimate the causal effect an exposure has on the intercept and slope. We carry out a simulation study comparing a naïve univariate 2SMR approach to a multivariate 2SMR approach with one exposure that effects both the intercept and slope of an outcome that changes linearly with time since diagnosis. The simulation study results, across six different scenarios, for both approaches were similar with no evidence against a non-zero bias and appropriate coverage of the 95% confidence intervals (for intercept 93.4-96.2% and the slope 94.5-96.0%). The multivariate approach gives a better joint coverage of both the intercept and slope effects. We also apply our method to two Parkinson's cohorts to examine the effect body mass index has on disease progression. There was no strong evidence that BMI affects disease progression, however the confidence intervals for both intercept and slope were wide.

Using genetic association data to guide drug discovery and development: Review of methods and applications

Evidence on the validity of drug targets from randomized trials is reliable but typically expensive and slow to obtain. In contrast, evidence from conventional observational epidemiological studies is less reliable because of the potential for bias from confounding and reverse causation. Mendelian randomization is a quasi-experimental approach analogous to a randomized trial that exploits naturally occurring randomization in the transmission of genetic variants. In Mendelian randomization, genetic variants that can be regarded as proxies for an intervention on the proposed drug target are leveraged as instrumental variables to investigate potential effects on biomarkers and disease outcomes in large-scale observational datasets. This approach can be implemented rapidly for a range of drug targets to provide evidence on their effects and thus inform on their priority for further investigation. In this review, we present statistical methods and their applications to showcase the diverse opportunities for applying Mendelian randomization in guiding clinical development efforts, thus enabling interventions to target the right mechanism in the right population group at the right time. These methods can inform investigators on the mechanisms underlying drug effects, their related biomarkers, implications for the timing of interventions, and the population subgroups that stand to gain the most benefit. Most methods can be implemented with publicly available data on summarized genetic associations with traits and diseases, meaning that the only major limitations to their usage are the availability of appropriately powered studies for the exposure and outcome and the existence of a suitable genetic proxy for the proposed intervention.

Statistical methods for cis-Mendelian randomization with two-sample summary-level data

Mendelian randomization (MR) is the use of genetic variants to assess the existence of a causal relationship between a risk factor and an outcome of interest. Here, we focus on two-sample summary-data MR analyses with many correlated variants from a single gene region, particularly on cis-MR studies which use protein expression as a risk factor. Such studies must rely on a small, curated set of variants from the studied region; using all variants in the region requires inverting an ill-conditioned genetic correlation matrix and results in numerically unstable causal effect estimates. We review methods for variable selection and estimation in cis-MR with summary-level data, ranging from stepwise pruning and conditional analysis to principal components analysis, factor analysis, and Bayesian variable selection. In a simulation study, we show that the various methods have comparable performance in analyses with large sample sizes and strong genetic instruments. However, when weak instrument bias is suspected, factor analysis and Bayesian variable selection produce more reliable inferences than simple pruning approaches, which are often used in practice. We conclude by examining two case studies, assessing the effects of low-density lipoprotein-cholesterol and serum testosterone on coronary heart disease risk using variants in the HMGCR and SHBG gene regions, respectively.

Strategies to investigate and mitigate collider bias in genetic and Mendelian randomisation studies of disease progression

Genetic studies of disease progression can be used to identify factors that may influence survival or prognosis, which may differ from factors that influence on disease susceptibility. Studies of disease progression feed directly into therapeutics for disease, whereas studies of incidence inform prevention strategies. However, studies of disease progression are known to be affected by collider (also known as "index event") bias since the disease progression phenotype can only be observed for individuals who have the disease. This applies equally to observational and genetic studies, including genome-wide association studies and Mendelian randomisation (MR) analyses. In this paper, our aim is to review several statistical methods that can be used to detect and adjust for index event bias in studies of disease progression, and how they apply to genetic and MR studies using both individual- and summary-level data. Methods to detect the presence of index event bias include the use of negative controls, a comparison of associations between risk factors for incidence in individuals with and without the disease, and an inspection of Miami plots. Methods to adjust for the bias include inverse probability weighting (with individual-level data), or Slope-Hunter and Dudbridge et al.'s index event bias adjustment (when only summary-level data are available). We also outline two approaches for sensitivity analysis. We then illustrate how three methods to minimise bias can be used in practice with two applied examples. Our first example investigates the effects of blood lipid traits on mortality from coronary heart disease, while our second example investigates genetic associations with breast cancer mortality.

Lipid traits and type 2 diabetes risk in African ancestry individuals: A Mendelian Randomization study

BACKGROUND

Dyslipidaemia is highly prevalent in individuals with type 2 diabetes mellitus (T2DM). Numerous studies have sought to disentangle the causal relationship between dyslipidaemia and T2DM liability. However, conventional observational studies are vulnerable to confounding. Mendelian Randomization (MR) studies (which address this bias) on lipids and T2DM liability have focused on European ancestry individuals, with none to date having been performed in individuals of African ancestry. We therefore sought to use MR to investigate the causal effect of various lipid traits on T2DM liability in African ancestry individuals.

METHODS

Using univariable and multivariable two-sample MR, we leveraged summary-level data for lipid traits and T2DM liability from the African Partnership for Chronic Disease Research (APCDR) (N = 13,612, 36.9% men) and from African ancestry individuals in the Million Veteran Program (Ncases = 23,305 and Ncontrols = 30,140, 87.2% men), respectively. Genetic instruments were thus selected from the APCDR after which they were clumped to obtain independent instruments. We used a random-effects inverse variance weighted method in our primary analysis, complementing this with additional sensitivity analyses robust to the presence of pleiotropy.

FINDINGS

Increased genetically proxied low-density lipoprotein cholesterol (LDL-C) and total cholesterol (TC) levels were associated with increased T2DM liability in African ancestry individuals (odds ratio (OR) [95% confidence interval, P-value] per standard deviation (SD) increase in LDL-C = 1.052 [1.000 to 1.106, P = 0.046] and per SD increase in TC = 1.089 [1.014 to 1.170, P = 0.019]). Conversely, increased genetically proxied high-density lipoprotein cholesterol (HDL-C) was associated with reduced T2DM liability (OR per SD increase in HDL-C = 0.915 [0.843 to 0.993, P = 0.033]). The OR on T2DM per SD increase in genetically proxied triglyceride (TG) levels was 0.884 [0.773 to 1.011, P = 0.072] . With respect to lipid-lowering drug targets, we found that genetically proxied 3-hydroxy-3-methylglutaryl-CoA reductase (HMGCR) inhibition was associated with increased T2DM liability (OR per SD decrease in genetically proxied LDL-C = 1.68 [1.03-2.72, P = 0.04]) but we did not find evidence of a relationship between genetically proxied proprotein convertase subtilisin/kexin type 9 (PCSK9) inhibition and T2DM liability.

INTERPRETATION

Consistent with MR findings in Europeans, HDL-C exerts a protective effect on T2DM liability and HMGCR inhibition increases T2DM liability in African ancestry individuals. However, in contrast to European ancestry individuals, LDL-C may increase T2DM liability in African ancestry individuals. This raises the possibility of ethnic differences in the metabolic effects of dyslipidaemia in T2DM.

FUNDING

See the Acknowledgements section for more information.

Bayesian variable selection with a pleiotropic loss function in Mendelian randomization

Mendelian randomization is the use of genetic variants as instruments to assess the existence of a causal relationship between a risk factor and an outcome. A Mendelian randomization analysis requires a set of genetic variants that are strongly associated with the risk factor and only associated with the outcome through their effect on the risk factor. We describe a novel variable selection algorithm for Mendelian randomization that can identify sets of genetic variants which are suitable in both these respects. Our algorithm is applicable in the context of two-sample summary-data Mendelian randomization and employs a recently proposed theoretical extension of the traditional Bayesian statistics framework, including a loss function to penalize genetic variants that exhibit pleiotropic effects. The algorithm offers robust inference through the use of model averaging, as we illustrate by running it on a range of simulation scenarios and comparing it against established pleiotropy-robust Mendelian randomization methods. In a real-data application, we study the effect of systolic and diastolic blood pressure on the risk of suffering from coronary heart disease (CHD). Based on a recent large-scale GWAS for blood pressure, we use 395 genetic variants for systolic and 391 variants for diastolic blood pressure. Both traits are shown to have significant risk-increasing effects on CHD risk.

Mendelian randomization for studying the effects of perturbing drug targets

Drugs whose targets have genetic evidence to support efficacy and safety are more likely to be approved after clinical development. In this paper, we provide an overview of how natural sequence variation in the genes that encode drug targets can be used in Mendelian randomization analyses to offer insight into mechanism-based efficacy and adverse effects. Large databases of summary level genetic association data are increasingly available and can be leveraged to identify and validate variants that serve as proxies for drug target perturbation. As with all empirical research, Mendelian randomization has limitations including genetic confounding, its consideration of lifelong effects, and issues related to heterogeneity across different tissues and populations. When appropriately applied, Mendelian randomization provides a useful empirical framework for using population level data to improve the success rates of the drug development pipeline.

Mendelian randomization for studying the effects of perturbing drug targets

Drugs whose targets have genetic evidence to support efficacy and safety are more likely to be approved after clinical development. In this paper, we provide an overview of how natural sequence variation in the genes that encode drug targets can be used in Mendelian randomization analyses to offer insight into mechanism-based efficacy and adverse effects. Large databases of summary level genetic association data are increasingly available and can be leveraged to identify and validate variants that serve as proxies for drug target perturbation. As with all empirical research, Mendelian randomization has limitations including genetic confounding, its consideration of lifelong effects, and issues related to heterogeneity across different tissues and populations. When appropriately applied, Mendelian randomization provides a useful empirical framework for using population level data to improve the success rates of the drug development pipeline.

Shared mechanisms between coronary heart disease and depression: findings from a large UK general population-based cohort

While comorbidity between coronary heart disease (CHD) and depression is evident, it is unclear whether the two diseases have shared underlying mechanisms. We performed a range of analyses in 367,703 unrelated middle-aged participants of European ancestry from UK Biobank, a population-based cohort study, to assess whether comorbidity is primarily due to genetic or environmental factors, and to test whether cardiovascular risk factors and CHD are likely to be causally related to depression using Mendelian randomization. We showed family history of heart disease was associated with a 20% increase in depression risk (95% confidence interval [CI] 16-24%, p < 0.0001), but a genetic risk score that is strongly associated with CHD risk was not associated with depression. An increase of 1 standard deviation in the CHD genetic risk score was associated with 71% higher CHD risk, but 1% higher depression risk (95% CI 0-3%; p = 0.11). Mendelian randomization analyses suggested that triglycerides, interleukin-6 (IL-6), and C-reactive protein (CRP) are likely causal risk factors for depression. The odds ratio for depression per standard deviation increase in genetically-predicted triglycerides was 1.18 (95% CI 1.09-1.27; p = 2 × 10-5); per unit increase in genetically-predicted log-transformed IL-6 was 0.74 (95% CI 0.62-0.89; p = 0.0012); and per unit increase in genetically-predicted log-transformed CRP was 1.18 (95% CI 1.07-1.29; p = 0.0009). Our analyses suggest that comorbidity between depression and CHD arises largely from shared environmental factors. IL-6, CRP and triglycerides are likely to be causally linked with depression, so could be targets for treatment and prevention of depression.

Genetic Determinants of Lipids and Cardiovascular Disease Outcomes: A Wide-Angled Mendelian Randomization Investigation

BACKGROUND

Evidence from randomized trials has shown that therapies that lower LDL (low-density lipoprotein)-cholesterol and triglycerides reduce coronary artery disease (CAD) risk. However, there is still uncertainty about their effects on other cardiovascular outcomes. We therefore performed a systematic investigation of causal relationships between circulating lipids and cardiovascular outcomes using a Mendelian randomization approach.

METHODS

In the primary analysis, we performed 2-sample multivariable Mendelian randomization using data from participants of European ancestry. We also conducted univariable analyses using inverse-variance weighted and robust methods, and gene-specific analyses using variants that can be considered as proxies for specific lipid-lowering medications. We obtained associations with lipid fractions from the Global Lipids Genetics Consortium, a meta-analysis of 188 577 participants, and genetic associations with cardiovascular outcomes from 367 703 participants in UK Biobank.

RESULTS

For LDL-cholesterol, in addition to the expected positive associations with CAD risk (odds ratio [OR] per 1 SD increase, 1.45 [95% CI, 1.35-1.57]) and other atheromatous outcomes (ischemic cerebrovascular disease and peripheral vascular disease), we found independent associations of genetically predicted LDL-cholesterol with abdominal aortic aneurysm (OR, 1.75 [95% CI, 1.40-2.17]) and aortic valve stenosis (OR, 1.46 [95% CI, 1.25-1.70]). Genetically predicted triglyceride levels were positively associated with CAD (OR, 1.25 [95% CI, 1.12-1.40]), aortic valve stenosis (OR, 1.29 [95% CI, 1.04-1.61]), and hypertension (OR, 1.17 [95% CI, 1.07-1.27]), but inversely associated with venous thromboembolism (OR, 0.79 [95% CI, 0.67-0.93]) and hemorrhagic stroke (OR, 0.78 [95% CI, 0.62-0.98]). We also found positive associations of genetically predicted LDL-cholesterol and triglycerides with heart failure that appeared to be mediated by CAD.

CONCLUSIONS

Lowering LDL-cholesterol is likely to prevent abdominal aortic aneurysm and aortic stenosis, in addition to CAD and other atheromatous cardiovascular outcomes. Lowering triglycerides is likely to prevent CAD and aortic valve stenosis but may increase thromboembolic risk.

Contextualizing selection bias in Mendelian randomization: how bad is it likely to be?

BACKGROUND

Selection bias affects Mendelian randomization investigations when selection into the study sample depends on a collider between the genetic variant and confounders of the risk factor-outcome association. However, the relative importance of selection bias for Mendelian randomization compared with other potential biases is unclear.

METHODS

We performed an extensive simulation study to assess the impact of selection bias on a typical Mendelian randomization investigation. We considered inverse probability weighting as a potential method for reducing selection bias. Finally, we investigated whether selection bias may explain a recently reported finding that lipoprotein(a) is not a causal risk factor for cardiovascular mortality in individuals with previous coronary heart disease.

RESULTS

Selection bias had a severe impact on bias and Type 1 error rates in our simulation study, but only when selection effects were large. For moderate effects of the risk factor on selection, bias was generally small and Type 1 error rate inflation was not considerable. Inverse probability weighting ameliorated bias when the selection model was correctly specified, but increased bias when selection bias was moderate and the model was misspecified. In the example of lipoprotein(a), strong genetic associations and strong confounder effects on selection mean the reported null effect on cardiovascular mortality could plausibly be explained by selection bias.

CONCLUSIONS

Selection bias can adversely affect Mendelian randomization investigations, but its impact is likely to be less than other biases. Selection bias is substantial when the effects of the risk factor and confounders on selection are particularly large.

Modal-based estimation via heterogeneity-penalized weighting: model averaging for consistent and efficient estimation in Mendelian randomization when a plurality of candidate instruments are valid

Background

A robust method for Mendelian randomization does not require all genetic variants to be valid instruments to give consistent estimates of a causal parameter. Several such methods have been developed, including a mode-based estimation method giving consistent estimates if a plurality of genetic variants are valid instruments; i.e. there is no larger subset of invalid instruments estimating the same causal parameter than the subset of valid instruments.

Methods

We here develop a model-averaging method that gives consistent estimates under the same 'plurality of valid instruments' assumption. The method considers a mixture distribution of estimates derived from each subset of genetic variants. The estimates are weighted such that subsets with more genetic variants receive more weight, unless variants in the subset have heterogeneous causal estimates, in which case that subset is severely down-weighted. The mode of this mixture distribution is the causal estimate. This heterogeneity-penalized model-averaging method has several technical advantages over the previously proposed mode-based estimation method.

Results

The heterogeneity-penalized model-averaging method outperformed the mode-based estimation in terms of efficiency and outperformed other robust methods in terms of Type 1 error rate in an extensive simulation analysis. The proposed method suggests two distinct mechanisms by which inflammation affects coronary heart disease risk, with subsets of variants suggesting both positive and negative causal effects.

Conclusions

The heterogeneity-penalized model-averaging method is an additional robust method for Mendelian randomization with excellent theoretical and practical properties, and can reveal features in the data such as the presence of multiple causal mechanisms.