Severity of bias of a simple estimator of the causal odds ratio in Mendelian randomization studies

Causal relationship between asthma and ulcerative colitis and the mediating role of interleukin-18: a bidirectional Mendelian study and mediation analysis

Objective

Numerous observational investigations have documented a correlation between asthma and ulcerative colitis(UC). In this Mendelian Randomization (MR) study, we utilized extensive summary data from Genome-Wide Association Studies (GWAS) to further estimate the association between adult-onset asthma and the risk of UC, and to investigate the role of Interleukin-18 (IL-18) as a potential mediator.

Materials and methods

A two-step, two-sample MR study was conducted through mediation analysis. For this study, we employed a two-sample MR analysis using the inverse variance-weighted (IVW), weighted median, weighted mode, and MR-Egger regression techniques. We utilized publicly accessible summary statistics from a GWAS meta-analysis of adult-onset asthma in the UK Biobank (n=327,253; cases=26,582; controls=300,671) as the exposure factor. The outcomes were derived from GWAS data of individuals with European ancestry (n=26,405; cases=6,687; controls=19,718). GWAS data for IL-18 were obtained from individuals of European ancestry (n=9,785,222; cases=3,636; controls=9,781,586).

Results

The MR analysis indicates that adult-onset asthma is associated with an increased risk of UC, with an odds ratio (OR) of 1.019 (95% CI 1.001-1.045, P=0.006). However, there is no strong evidence to suggest that UC significantly impacts the risk of adult-onset asthma. IL-18 may act as a potential mediator in the causal relationship between adult-onset asthma and UC, with a mediation proportion of 3.9% (95% CI, 0.6%-6.9%).

Conclusion

In summary, our study established a causal relationship between asthma and UC, in which IL-18 contributes to a small extent. However, the primary factors underlying the influence of asthma on UC remain unclear. Future research should focus on identifying other potential mediators. In clinical practice, it is important to pay greater attention to intestinal lesions in patients with asthma.

MR-BOIL: Causal inference in one-sample Mendelian randomization for binary outcome with integrated likelihood method

Mendelian randomization is a statistical method for inferring the causal relationship between exposures and outcomes using an economics-derived instrumental variable approach. The research results are relatively complete when both exposures and outcomes are continuous variables. However, due to the noncollapsing nature of the logistic model, the existing methods inherited from the linear model for exploring binary outcome cannot take the effect of confounding factors into account, which leads to biased estimate of the causal effect. In this article, we propose an integrated likelihood method MR-BOIL to investigate causal relationships for binary outcomes by treating confounders as latent variables in one-sample Mendelian randomization. Under the assumption of a joint normal distribution of the confounders, we use expectation maximization algorithm to estimate the causal effect. Extensive simulations demonstrate that the estimator of MR-BOIL is asymptotically unbiased and that our method improves statistical power without inflating type I error rate. We then apply this method to analyze the data from Atherosclerosis Risk in Communications Study. The results show that MR-BOIL can better identify plausible causal relationships with high reliability, compared with the unreliable results of existing methods. MR-BOIL is implemented in R and the corresponding R code is provided for free download.

Unbiased metabolome screen leads to personalized medicine strategy for amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis is a rapidly progressive neurodegenerative disease that affects 1/350 individuals in the United Kingdom. The cause of amyotrophic lateral sclerosis is unknown in the majority of cases. Two-sample Mendelian randomization enables causal inference between an exposure, such as the serum concentration of a specific metabolite, and disease risk. We obtained genome-wide association study summary statistics for serum concentrations of 566 metabolites which were population matched with a genome-wide association study of amyotrophic lateral sclerosis. For each metabolite, we performed Mendelian randomization using an inverse variance weighted estimate for significance testing. After stringent Bonferroni multiple testing correction, our unbiased screen revealed three metabolites that were significantly linked to the risk of amyotrophic lateral sclerosis: Estrone-3-sulphate and bradykinin were protective, which is consistent with literature describing a male preponderance of amyotrophic lateral sclerosis and a preventive effect of angiotensin-converting enzyme inhibitors which inhibit the breakdown of bradykinin. Serum isoleucine was positively associated with amyotrophic lateral sclerosis risk. All three metabolites were supported by robust Mendelian randomization measures and sensitivity analyses; estrone-3-sulphate and isoleucine were confirmed in a validation amyotrophic lateral sclerosis genome-wide association study. Estrone-3-sulphate is metabolized to the more active estradiol by the enzyme 17β-hydroxysteroid dehydrogenase 1; further, Mendelian randomization demonstrated a protective effect of estradiol and rare variant analysis showed that missense variants within HSD17B1, the gene encoding 17β-hydroxysteroid dehydrogenase 1, modify risk for amyotrophic lateral sclerosis. Finally, in a zebrafish model of C9ORF72-amyotrophic lateral sclerosis, we present evidence that estradiol is neuroprotective. Isoleucine is metabolized via methylmalonyl-CoA mutase encoded by the gene MMUT in a reaction that consumes vitamin B12. Multivariable Mendelian randomization revealed that the toxic effect of isoleucine is dependent on the depletion of vitamin B12; consistent with this, rare variants which reduce the function of MMUT are protective against amyotrophic lateral sclerosis. We propose that amyotrophic lateral sclerosis patients and family members with high serum isoleucine levels should be offered supplementation with vitamin B12.

Genetic effects of iron levels on liver injury and risk of liver diseases: A two-sample Mendelian randomization analysis

Background and aims

Although iron homeostasis has been associated with liver function in many observational studies, the causality in this relationship remains unclear. By using Mendelian Randomization analyses, we aimed to evaluate the genetic effects of increased systemic iron levels on the risk of liver injury and various liver diseases. Moreover, in light of the sex-dependent iron regulation in human beings, we further estimated the sex-specific effect of iron levels in liver diseases.

Methods

Independent single nucleotide polymorphisms associated with systemic iron status (including four indicators) at the genome-wide significance level from the Genetics of Iron Status (GIS) Consortium were selected as instrumental variables. Summary data for six liver function biomarkers and five liver diseases were obtained from the UK Biobank, the Estonian Biobank, the eMERGE network, and FinnGen consortium. Mendelian Randomization assessment of the effect of iron on liver function and liver diseases was conducted.

Results

Genetically predicted iron levels were positively and significantly associated with an increased risk of different dimensions of liver injury. Furthermore, increased iron status posed hazardous effects on non-alcoholic fatty liver disease, alcoholic liver disease, and liver fibrosis/cirrhosis. Sex-stratified analyses indicated that the hepatoxic role of iron might exist in NAFLD and liver fibrosis/cirrhosis development among men. No significantly causal relationship was found between iron status and viral hepatitis.

Conclusion

Our study adds to current knowledge on the genetic role of iron in the risk of liver injury and related liver diseases, which provides clinical and public health implications for liver disease prevention as iron status can be modified.

Long-term cost-effectiveness of interventions for obesity: A mendelian randomisation study

BACKGROUND

The prevalence of obesity has increased in the United Kingdom, and reliably measuring the impact on quality of life and the total healthcare cost from obesity is key to informing the cost-effectiveness of interventions that target obesity, and determining healthcare funding. Current methods for estimating cost-effectiveness of interventions for obesity may be subject to confounding and reverse causation. The aim of this study is to apply a new approach using mendelian randomisation for estimating the cost-effectiveness of interventions that target body mass index (BMI), which may be less affected by confounding and reverse causation than previous approaches.

METHODS AND FINDINGS

We estimated health-related quality-adjusted life years (QALYs) and both primary and secondary healthcare costs for 310,913 men and women of white British ancestry aged between 39 and 72 years in UK Biobank between recruitment (2006 to 2010) and 31 March 2017. We then estimated the causal effect of differences in BMI on QALYs and total healthcare costs using mendelian randomisation. For this, we used instrumental variable regression with a polygenic risk score (PRS) for BMI, derived using a genome-wide association study (GWAS) of BMI, with age, sex, recruitment centre, and 40 genetic principal components as covariables to estimate the effect of a unit increase in BMI on QALYs and total healthcare costs. Finally, we used simulations to estimate the likely effect on BMI of policy relevant interventions for BMI, then used the mendelian randomisation estimates to estimate the cost-effectiveness of these interventions. A unit increase in BMI decreased QALYs by 0.65% of a QALY (95% confidence interval [CI]: 0.49% to 0.81%) per year and increased annual total healthcare costs by £42.23 (95% CI: £32.95 to £51.51) per person. When considering only health conditions usually considered in previous cost-effectiveness modelling studies (cancer, cardiovascular disease, cerebrovascular disease, and type 2 diabetes), we estimated that a unit increase in BMI decreased QALYs by only 0.16% of a QALY (95% CI: 0.10% to 0.22%) per year. We estimated that both laparoscopic bariatric surgery among individuals with BMI greater than 35 kg/m2, and restricting volume promotions for high fat, salt, and sugar products, would increase QALYs and decrease total healthcare costs, with net monetary benefits (at £20,000 per QALY) of £13,936 (95% CI: £8,112 to £20,658) per person over 20 years, and £546 million (95% CI: £435 million to £671 million) in total per year, respectively. The main limitations of this approach are that mendelian randomisation relies on assumptions that cannot be proven, including the absence of directional pleiotropy, and that genotypes are independent of confounders.

CONCLUSIONS

Mendelian randomisation can be used to estimate the impact of interventions on quality of life and healthcare costs. We observed that the effect of increasing BMI on health-related quality of life is much larger when accounting for 240 chronic health conditions, compared with only a limited selection. This means that previous cost-effectiveness studies have likely underestimated the effect of BMI on quality of life and, therefore, the potential cost-effectiveness of interventions to reduce BMI.

Impact of lung function on cardiovascular diseases and cardiovascular risk factors: a two sample bidirectional Mendelian randomisation study

INTRODUCTION

Observational studies suggested lung function is inversely associated with cardiovascular disease (CVD) although these studies could be confounded. We conducted a two sample Mendelian randomisation study using summary statistics from genome-wide association studies (GWAS) to clarify the role of lung function in CVD and its risk factors, and conversely the role of CVD in lung function.

METHODS

We obtained genetic instruments for forced expiratory volume in 1 s (FEV₁: 260) and forced vital capacity (FVC: 320) from publicly available UK Biobank summary statistics (n=421 986) and applied to GWAS summary statistics for coronary artery disease (CAD) (n=184 305), stroke (n=446 696), atrial fibrillation (n=1 030 836) and heart failure (n=977 320) and cardiovascular risk factors. Inverse variance weighting was used to assess the impact of lung function on these outcomes, with various sensitivity analyses. Bidirectional Mendelian randomisation was used to assess reverse causation.

RESULTS

FEV₁ and FVC were inversely associated with CAD (OR per SD increase, 0.72 (95% CI 0.63 to 0.82) and 0.70 (95%CI 0.62 to 0.78)), overall stroke (0.87 (95%CI 0.77 to 0.97), 0.90 (95% CI 0.82 to 1.00)) and some stroke subtypes. FEV₁ and FVC were inversely associated with type 2 diabetes and systolic blood pressure. Sensitivity analyses produced similar findings although the association with CAD was attenuated after adjusting for height (eg, OR for 1SD FEV₁0.95 (0.75 to 1.19), but not for stroke or type 2 diabetes. There was no strong evidence for reverse causation.

CONCLUSION

Higher lung function likely protect against CAD and stroke.

The causal effects of health conditions and risk factors on social and socioeconomic outcomes: Mendelian randomization in UK Biobank

BACKGROUND

We aimed to estimate the causal effect of health conditions and risk factors on social and socioeconomic outcomes in UK Biobank. Evidence on socioeconomic impacts is important to understand because it can help governments, policy makers and decision makers allocate resources efficiently and effectively.

METHODS

We used Mendelian randomization to estimate the causal effects of eight health conditions (asthma, breast cancer, coronary heart disease, depression, eczema, migraine, osteoarthritis, type 2 diabetes) and five health risk factors [alcohol intake, body mass index (BMI), cholesterol, systolic blood pressure, smoking] on 19 social and socioeconomic outcomes in 336 997 men and women of White British ancestry in UK Biobank, aged between 39 and 72 years. Outcomes included annual household income, employment, deprivation [measured by the Townsend deprivation index (TDI)], degree-level education, happiness, loneliness and 13 other social and socioeconomic outcomes.

RESULTS

Results suggested that BMI, smoking and alcohol intake affect many socioeconomic outcomes. For example, smoking was estimated to reduce household income [mean difference = -£22 838, 95% confidence interval (CI): -£31 354 to -£14 321] and the chance of owning accommodation [absolute percentage change (APC) = -20.8%, 95% CI: -28.2% to -13.4%], of being satisfied with health (APC = -35.4%, 95% CI: -51.2% to -19.5%) and of obtaining a university degree (APC = -65.9%, 95% CI: -81.4% to -50.4%), while also increasing deprivation (mean difference in TDI = 1.73, 95% CI: 1.02 to 2.44, approximately 216% of a decile of TDI). There was evidence that asthma decreased household income, the chance of obtaining a university degree and the chance of cohabiting, and migraine reduced the chance of having a weekly leisure or social activity, especially in men. For other associations, estimates were null.

CONCLUSIONS

Higher BMI, alcohol intake and smoking were all estimated to adversely affect multiple social and socioeconomic outcomes. Effects were not detected between health conditions and socioeconomic outcomes using Mendelian randomization, with the exceptions of depression, asthma and migraines. This may reflect true null associations, selection bias given the relative health and age of participants in UK Biobank, and/or lack of power to detect effects.

Thyroid Function Affects the Risk of Stroke via Atrial Fibrillation: A Mendelian Randomization Study

CONTEXT

Observational studies suggest that variations in normal range thyroid function are associated with cardiovascular diseases. However, it remains to be determined whether these associations are causal or not.

OBJECTIVE

To test whether genetically determined variation in normal range thyroid function is causally associated with the risk of stroke and coronary artery disease (CAD) and investigate via which pathways these relations may be mediated.

DESIGN, SETTING, AND PARTICIPANTS

Mendelian randomization analyses for stroke and CAD using genetic instruments associated with normal range thyrotropin (TSH) and free thyroxine levels or Hashimoto's thyroiditis and Graves' disease. The potential mediating role of known stroke and CAD risk factors was examined. Publicly available summary statistics data were used.

MAIN OUTCOME MEASURES

Stroke or CAD risk per genetically predicted increase in TSH or FT4 levels.

RESULTS

A 1 standard deviation increase in TSH was associated with a 5% decrease in the risk of stroke (odds ratio [OR], 0.95; 95% confidence interval [CI], 0.91-0.99; P = 0.008). Multivariable MR analyses indicated that this effect is mainly mediated via atrial fibrillation. MR analyses did not show a causal association between normal range thyroid function and CAD. Secondary analyses showed a causal relationship between Hashimoto's thyroiditis and a 7% increased risk of CAD (OR, 1.07; 95% CI, 1.01-1.13; P = 0.026), which was mainly mediated via body mass index.

CONCLUSION

These results provide important new insights into the causal relationships and mediating pathways between thyroid function, stroke, and CAD. We identify variation in normal range thyroid function and Hashimoto's thyroiditis as risk factors for stroke and CAD, respectively.

Epidemiology, genetic epidemiology and Mendelian randomisation: more need than ever to attend to detail

In the current era, with increasing availability of results from genetic association studies, finding genetic instruments for inferring causality in observational epidemiology has become apparently simple. Mendelian randomisation (MR) analyses are hence growing in popularity and, in particular, methods that can incorporate multiple instruments are being rapidly developed for these applications. Such analyses have enormous potential, but they all rely on strong, different, and inherently untestable assumptions. These have to be clearly stated and carefully justified for every application in order to avoid conclusions that cannot be replicated. In this article, we review the instrumental variable assumptions and discuss the popular linear additive structural model. We advocate the use of tests for the null hypothesis of ‘no causal effect’ and calculation of the bounds for a causal effect, whenever possible, as these do not rely on parametric modelling assumptions. We clarify the difference between a randomised trial and an MR study and we comment on the importance of validating instruments, especially when considering them for joint use in an analysis. We urge researchers to stand by their convictions, if satisfied that the relevant assumptions hold, and to interpret their results causally since that is the only reason for performing an MR analysis in the first place.

Mendelian randomisation analyses find pulmonary factors mediate the effect of height on coronary artery disease

There is evidence that lower height is associated with a higher risk of coronary artery disease (CAD) and increased risk of type 2 diabetes (T2D). It is not clear though whether these associations are causal, direct or mediated by other factors. Here we show that one standard deviation higher genetically determined height (~6.5 cm) is causally associated with a 16% decrease in CAD risk (OR = 0.84, 95% CI 0.80-0.87). This causal association remains after performing sensitivity analyses relaxing pleiotropy assumptions. The causal effect of height on CAD risk is reduced by 1-3% after adjustment for potential mediators (lipids, blood pressure, glycaemic traits, body mass index, socio-economic status). In contrast, our data suggest that lung function (measured by forced expiratory volume [FEV1] and forced vital capacity [FVC]) is a mediator of the effect of height on CAD. We observe no direct causal effect of height on the risk of T2D.

Genetically high plasma vitamin C and urate: a Mendelian randomization study in 106 147 individuals from the general population

Objective

Gout is the most common form of inflammatory arthritis and is caused by hyperuricaemia. Some studies have found a reduction in plasma urate with vitamin C supplementation. We tested the hypothesis that high plasma vitamin C is causally associated with low plasma urate and low risk of hyperuricaemia, using a Mendelian randomization approach.

Methods

We measured plasma urate and genotyped for the SLC23A1 rs33972313 vitamin C variant in 106 147 individuals from the Copenhagen General Population Study, of which 24 099 had hyperuricaemia. We measured plasma vitamin C in 9234 individuals and genotyped for the SLC2A9 rs7442295 urate variant in 102 345 individuals.

Results

Each 10 µmol/l higher plasma vitamin C was associated with a -2.3(95%CI: -0.69 to -3.9) µmol/l lower plasma urate after multivariable adjustments. The SLC23A1 rs33972313 GG genotype was associated with a 9% (5.6%, 11.9%) higher plasma vitamin C compared with AA and AG combined but was not associated with plasma urate (P = 0.31). Likewise, for each 10 µmol/l higher plasma vitamin C the odds ratios for hyperuricaemia were 0.92 (0.86, 0.98) observationally after multivariable adjustments, but 1.01 (0.84, 1.23) genetically.

Conclusion

High plasma vitamin C was associated with low plasma urate and with low risk of hyperuricaemia. However, the SLC23A1 genetic variant causing lifelong high plasma vitamin C was not associated with plasma urate levels or with risk of hyperuricaemia. Thus, our data do not support a causal relationship between high plasma vitamin C and low plasma urate.

Plasma urate and risk of Parkinson's disease: A mendelian randomization study

OBJECTIVE

Urate is a potent antioxidant, and high plasma urate has been associated with lower incidence of Parkinson's disease (PD) in epidemiological studies. We tested the hypothesis that high concentrations of plasma urate are associated with low incidence of PD.

METHODS

We performed observational and genetic analyses using plasma urate and the urate SLC2A9 rs7442295 and ABCG2 rs2231142 genotype in >102,000 individuals from the CGPS (Copenhagen General Population Study). Information on PD and mortality was from national patient and death registries. Incidences of PD were calculated using Cox regression, Fine and Gray competing-risks regression, and instrumental variable analyses.

RESULTS

In total, 398 individuals were diagnosed with PD, of which 285 were incident cases. The multivariable adjusted hazard ratio for PD was 0.56 (95% confidence interval [CI], 0.41-0.77) for the highest versus the lowest tertile of plasma urate (p for trend across 3 groups, 8 × 10^-5 ). Each one-allele increase in the combined allele score was associated with 19μmol/l (95% CI, 18.5-19.9) higher plasma urate. In observational analyses, a 50μmol/l higher plasma urate was associated with a hazard ratio of 0.85 (0.77-0.92) for PD; in instrumental variable analyses, 50μmol/l higher plasma urate was associated with an odds ratio of 1.20 (0.85-1.71) for PD.

INTERPRETATION

High plasma urate was associated with lower risk of PD in observational analyses; however, in instrumental variable analysis, high plasma urate was not associated with low risk of PD. Thus, our data do not support a causal relationship between high plasma urate and low risk of PD. Ann Neurol 2018;84:178-190.

Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption

Background

Mendelian randomization (MR) is being increasingly used to strengthen causal inference in observational studies. Availability of summary data of genetic associations for a variety of phenotypes from large genome-wide association studies (GWAS) allows straightforward application of MR using summary data methods, typically in a two-sample design. In addition to the conventional inverse variance weighting (IVW) method, recently developed summary data MR methods, such as the MR-Egger and weighted median approaches, allow a relaxation of the instrumental variable assumptions.

Methods

Here, a new method - the mode-based estimate (MBE) - is proposed to obtain a single causal effect estimate from multiple genetic instruments. The MBE is consistent when the largest number of similar (identical in infinite samples) individual-instrument causal effect estimates comes from valid instruments, even if the majority of instruments are invalid. We evaluate the performance of the method in simulations designed to mimic the two-sample summary data setting, and demonstrate its use by investigating the causal effect of plasma lipid fractions and urate levels on coronary heart disease risk.

Results

The MBE presented less bias and lower type-I error rates than other methods under the null in many situations. Its power to detect a causal effect was smaller compared with the IVW and weighted median methods, but was larger than that of MR-Egger regression, with sample size requirements typically smaller than those available from GWAS consortia.

Conclusions

The MBE relaxes the instrumental variable assumptions, and should be used in combination with other approaches in sensitivity analyses.

Mendelian Randomization using Public Data from Genetic Consortia

Mendelian randomization (MR) is a technique that seeks to establish causation between an exposure and an outcome using observational data. It is an instrumental variable analysis in which genetic variants are used as the instruments. Many consortia have meta-analysed genome-wide associations between variants and specific traits and made their results publicly available. Using such data, it is possible to derive genetic risk scores for one trait and to deduce the association of that same risk score with a second trait. The properties of this approach are investigated by simulation and by evaluating the potentially causal effect of birth weight on adult glucose level. In such analyses, it is important to decide whether one is interested in the risk score based on a set of estimated regression coefficients or the score based on the true underlying coefficients. MR is primarily concerned with the latter. Methods designed for the former question will under-estimate the variance if used for MR. This variance can be corrected but it needs to be done with care to avoid introducing bias. MR based on public data sources is useful and easy to perform, but care must be taken to avoid false precision or bias.

Arsenic trioxide combined with transarterial chemoembolization for unresectable primary hepatic carcinoma: A systematic review and meta-analysis

BACKGROUND

Primary hepatic carcinoma (PHC) is the third commonest leading to cancer death around the world, and transarterial chemoembolization (TACE) has been proposed as the first-line therapeutic treatment for patients with unresectable PHC. This study aims to determine whether the combination of As2O3 and TACE is superior to alone TACE for achieving more clinical therapeutic efficacy, survival time, life quality and safety in patients with unresectable PHC.

METHODS

A comprehensive literature search was conducted on the clinical controlled trials comparing therapeutic effects of As2O3 & TACE versus alone TACE for unresectable PHC through English databases (including PubMed, Embase, and the Cochrane Library) and Chinese databases (including China Knowledge Resource Integrated Database, Wanfang Database, Weipu Database, and Chinese Biomedical Database). The last search was in 30 August 2017. A recursive search was performed with bibliographies of relevant studies. There were no language restrictions. Primary outcomes, defined a priori, were therapeutic responses (clinical effective rate and clinical benefit rate), survival time, life quality, and adverse events of As2O3 & TACE compared with alone TACE expressed as relative risk (RR) with 95% confidence intervals (CI).

RESULTS

25 clinical controlled trials involving 1886 participants were included. We found that there were significant superiority associated with As2O3 & TACE compared with alone TACE in clinical benefit rate (RR: 1.24, 95% CI: 1.12-1.37), clinical effective rate (RR: 1.35, 95% CI: 1.17-1.55), 2-year survival rate (RR: 1.45, 95% CI: 1.20-1.75), and improving of KPS (RR: 1.31, 95% CI: 1.14-1.50). These associations were also observed in subgroups by intervened methods of As2O3 and pulmonary metastasis. Notably, the pooled relative risk of retention of sodium and water was obviously raised in patients with As2O3 & TACE therapy (RR: 16.616, 95% CI: 8.01 - 34.486).

CONCLUSION

The superiority of adjuvant As2O3 therapy combined with TACE in PHC individuals will outweigh alone TACE therapy, especially in PHC populations with pulmonary metastasis.

Correcting the Standard Errors of 2-Stage Residual Inclusion Estimators for Mendelian Randomization Studies

Mendelian randomization studies use genotypes as instrumental variables to test for and estimate the causal effects of modifiable risk factors on outcomes. Two-stage residual inclusion (TSRI) estimators have been used when researchers are willing to make parametric assumptions. However, researchers are currently reporting uncorrected or heteroscedasticity-robust standard errors for these estimates. We compared several different forms of the standard error for linear and logistic TSRI estimates in simulations and in real-data examples. Among others, we consider standard errors modified from the approach of Newey (1987), Terza (2016), and bootstrapping. In our simulations Newey, Terza, bootstrap, and corrected 2-stage least squares (in the linear case) standard errors gave the best results in terms of coverage and type I error. In the real-data examples, the Newey standard errors were 0.5% and 2% larger than the unadjusted standard errors for the linear and logistic TSRI estimators, respectively. We show that TSRI estimators with modified standard errors have correct type I error under the null. Researchers should report TSRI estimates with modified standard errors instead of reporting unadjusted or heteroscedasticity-robust standard errors.

Mendelian Randomization as an Approach to Assess Causality Using Observational Data

Mendelian randomization refers to an analytic approach to assess the causality of an observed association between a modifiable exposure or risk factor and a clinically relevant outcome. It presents a valuable tool, especially when randomized controlled trials to examine causality are not feasible and observational studies provide biased associations because of confounding or reverse causality. These issues are addressed by using genetic variants as instrumental variables for the tested exposure: the alleles of this exposure-associated genetic variant are randomly allocated and not subject to reverse causation. This, together with the wide availability of published genetic associations to screen for suitable genetic instrumental variables make Mendelian randomization a time- and cost-efficient approach and contribute to its increasing popularity for assessing and screening for potentially causal associations. An observed association between the genetic instrumental variable and the outcome supports the hypothesis that the exposure in question is causally related to the outcome. This review provides an overview of the Mendelian randomization method, addresses assumptions and implications, and includes illustrative examples. We also discuss special issues in nephrology, such as inverse risk factor associations in advanced disease, and outline opportunities to design Mendelian randomization studies around kidney function and disease.

Best (but oft-forgotten) practices: the design, analysis, and interpretation of Mendelian randomization studies

Mendelian randomization (MR) is an increasingly important tool for appraising causality in observational epidemiology. The technique exploits the principle that genotypes are not generally susceptible to reverse causation bias and confounding, reflecting their fixed nature and Mendel’s first and second laws of inheritance. The approach is, however, subject to important limitations and assumptions that, if unaddressed or compounded by poor study design, can lead to erroneous conclusions. Nevertheless, the advent of 2-sample approaches (in which exposure and outcome are measured in separate samples) and the increasing availability of open-access data from large consortia of genome-wide association studies and population biobanks mean that the approach is likely to become routine practice in evidence synthesis and causal inference research. In this article we provide an overview of the design, analysis, and interpretation of MR studies, with a special emphasis on assumptions and limitations. We also consider different analytic strategies for strengthening causal inference. Although impossible to prove causality with any single approach, MR is a highly cost-effective strategy for prioritizing intervention targets for disease prevention and for strengthening the evidence base for public health policy.

MR_predictor: a simulation engine for Mendelian Randomization studies

I present MR_predictor, a simulation engine designed to guide the development and interpretation of statistical tests of causality between phenotypes using genetic instruments. MR_predictor provides a framework to model either individual traits or complex scenarios where multiple phenotypes are correlated or dependent on each other. Crucially, MR_predictor can incorporate the effects of multiple biallelic loci (linked or unlinked) contributing genotypic variability to one or more simulated phenotypes. The software has a range of options for sample generation, and output files generated by MR_predictor port into commonly used analysis tools (e.g. PLINK, R), facilitating analyses germane for Mendelian Randomization studies. Benchmarks for speed and power calculations for summary statistic-based Mendelian Randomization analyses are presented and compared with analytical expectation.

AVAILABILITY AND IMPLEMENTATION

The simulation engine is implemented in PERL, and the associated scripts can be downloaded from github.com, and online documentation, tutorial and example datasets are available at http://coruscant.itmat.upenn.edu/mr_predictor.

Methodological challenges in mendelian randomization

We give critical attention to the assumptions underlying Mendelian randomization analysis and their biological plausibility. Several scenarios violating the Mendelian randomization assumptions are described, including settings with inadequate phenotype definition, the setting of time-varying exposures, the presence of gene-environment interaction, the existence of measurement error, the possibility of reverse causation, and the presence of linkage disequilibrium. Data analysis examples are given, illustrating that the inappropriate use of instrumental variable techniques when the Mendelian randomization assumptions are violated can lead to biases of enormous magnitude. To help address some of the strong assumptions being made, three possible approaches are suggested. First, the original proposal of Katan (Lancet. 1986;1:507-508) for Mendelian randomization was not to use instrumental variable techniques to obtain estimates but merely to examine genotype-outcome associations to test for the presence of an effect of the exposure on the outcome. We show that this more modest goal and approach can circumvent many, though not all, the potential biases described. Second, we discuss the use of sensitivity analysis in evaluating the consequences of violations in the assumptions and in attempting to correct for those violations. Third, we suggest that a focus on negative, rather than positive, Mendelian randomization results may turn out to be more reliable.

Sample size and power calculations in Mendelian randomization with a single instrumental variable and a binary outcome

Background: Sample size calculations are an important tool for planning epidemiological studies. Large sample sizes are often required in Mendelian randomization investigations.

Methods and results: Resources are provided for investigators to perform sample size and power calculations for Mendelian randomization with a binary outcome. We initially provide formulae for the continuous outcome case, and then analogous formulae for the binary outcome case. The formulae are valid for a single instrumental variable, which may be a single genetic variant or an allele score comprising multiple variants. Graphs are provided to give the required sample size for 80% power for given values of the causal effect of the risk factor on the outcome and of the squared correlation between the risk factor and instrumental variable. R code and an online calculator tool are made available for calculating the sample size needed for a chosen power level given these parameters, as well as the power given the chosen sample size and these parameters.

Conclusions: The sample size required for a given power of Mendelian randomization investigation depends greatly on the proportion of variance in the risk factor explained by the instrumental variable. The inclusion of multiple variants into an allele score to explain more of the variance in the risk factor will improve power, however care must be taken not to introduce bias by the inclusion of invalid variants.

Identifying the odds ratio estimated by a two-stage instrumental variable analysis with a logistic regression model

An adjustment for an uncorrelated covariate in a logistic regression changes the true value of an odds ratio for a unit increase in a risk factor. Even when there is no variation due to covariates, the odds ratio for a unit increase in a risk factor also depends on the distribution of the risk factor. We can use an instrumental variable to consistently estimate a causal effect in the presence of arbitrary confounding. With a logistic outcome model, we show that the simple ratio or two-stage instrumental variable estimate is consistent for the odds ratio of an increase in the population distribution of the risk factor equal to the change due to a unit increase in the instrument divided by the average change in the risk factor due to the increase in the instrument. This odds ratio is conditional within the strata of the instrumental variable, but marginal across all other covariates, and is averaged across the population distribution of the risk factor. Where the proportion of variance in the risk factor explained by the instrument is small, this is similar to the odds ratio from a RCT without adjustment for any covariates, where the intervention corresponds to the effect of a change in the population distribution of the risk factor. This implies that the ratio or two-stage instrumental variable method is not biased, as has been suggested, but estimates a different quantity to the conditional odds ratio from an adjusted multiple regression, a quantity that has arguably more relevance to an epidemiologist or a policy maker, especially in the context of Mendelian randomization.

Mendelian randomization analysis with multiple genetic variants using summarized data

Genome-wide association studies, which typically report regression coefficients summarizing the associations of many genetic variants with various traits, are potentially a powerful source of data for Mendelian randomization investigations. We demonstrate how such coefficients from multiple variants can be combined in a Mendelian randomization analysis to estimate the causal effect of a risk factor on an outcome. The bias and efficiency of estimates based on summarized data are compared to those based on individual-level data in simulation studies. We investigate the impact of gene–gene interactions, linkage disequilibrium, and ‘weak instruments’ on these estimates. Both an inverse-variance weighted average of variant-specific associations and a likelihood-based approach for summarized data give similar estimates and precision to the two-stage least squares method for individual-level data, even when there are gene–gene interactions. However, these summarized data methods overstate precision when variants are in linkage disequilibrium. If the P-value in a linear regression of the risk factor for each variant is less than , then weak instrument bias will be small. We use these methods to estimate the causal association of low-density lipoprotein cholesterol (LDL-C) on coronary artery disease using published data on five genetic variants. A 30% reduction in LDL-C is estimated to reduce coronary artery disease risk by 67% (95% CI: 54% to 76%). We conclude that Mendelian randomization investigations using summarized data from uncorrelated variants are similarly efficient to those using individual-level data, although the necessary assumptions cannot be so fully assessed.

F, Gögele M, Lill CM, Bertram L, Do CB, Eriksson N, Foroud T, Myers RH, Nalls M, Keller MF, Benyamin B, Whitfield JB, Pramstaller PP, Hicks AA, Thompson JR, Minelli C. Serum iron levels and the risk of Parkinson disease: a Mendelian randomization study

BACKGROUND

Although levels of iron are known to be increased in the brains of patients with Parkinson disease (PD), epidemiological evidence on a possible effect of iron blood levels on PD risk is inconclusive, with effects reported in opposite directions. Epidemiological studies suffer from problems of confounding and reverse causation, and mendelian randomization (MR) represents an alternative approach to provide unconfounded estimates of the effects of biomarkers on disease. We performed a MR study where genes known to modify iron levels were used as instruments to estimate the effect of iron on PD risk, based on estimates of the genetic effects on both iron and PD obtained from the largest sample meta-analyzed to date.

METHODS AND FINDINGS

We used as instrumental variables three genetic variants influencing iron levels, HFE rs1800562, HFE rs1799945, and TMPRSS6 rs855791. Estimates of their effect on serum iron were based on a recent genome-wide meta-analysis of 21,567 individuals, while estimates of their effect on PD risk were obtained through meta-analysis of genome-wide and candidate gene studies with 20,809 PD cases and 88,892 controls. Separate MR estimates of the effect of iron on PD were obtained for each variant and pooled by meta-analysis. We investigated heterogeneity across the three estimates as an indication of possible pleiotropy and found no evidence of it. The combined MR estimate showed a statistically significant protective effect of iron, with a relative risk reduction for PD of 3% (95% CI 1%-6%; p = 0.001) per 10 µg/dl increase in serum iron.

CONCLUSIONS

Our study suggests that increased iron levels are causally associated with a decreased risk of developing PD. Further studies are needed to understand the pathophysiological mechanism of action of serum iron on PD risk before recommendations can be made.