Hyperopia Is Not Causally Associated With a Major Deficit in Educational Attainment

Purpose

Hyperopia (farsightedness) has been associated with a deficit in children's educational attainment in some studies. We aimed to investigate the causality of the relationship between refractive error and educational attainment.

Methods

Mendelian randomization (MR) analysis in 74,463 UK Biobank participants was used to estimate the causal effect of refractive error on years spent in full-time education, which was taken as a measure of educational attainment. A polygenic score for refractive error derived from 129 genetic variants was used as the instrumental variable. Both linear and nonlinear (allowing for a nonlinear relationship between refractive error and educational attainment) MR analyses were performed.

Results

Assuming a linear relationship between refractive error and educational attainment, the causal effect of refractive error on years spent in full-time education was estimated as -0.01 yr/D (95% confidence interval, -0.04 to +0.02; P = 0.52), suggesting minimal evidence for a non-zero causal effect. Nonlinear MR supported the hypothesis of the nonlinearity of the relationship (I2 = 80.3%; Cochran's Q = 28.2; P = 8.8e-05) but did not suggest that hyperopia was associated with a major deficit in years spent in education.

Conclusions

This work suggested that the causal relationship between refractive error and educational attainment was nonlinear but found no evidence that moderate hyperopia caused a major deficit in educational attainment. Importantly, however, because statistical power was limited and some participants with moderate hyperopia would have worn spectacles as children, modest adverse effects may have gone undetected.

Translational Relevance

These findings suggest that moderate hyperopia does not cause a major deficit in educational attainment.

The use of two-sample methods for Mendelian randomization analyses on single large datasets

BACKGROUND

With genome-wide association data for many exposures and outcomes now available from large biobanks, one-sample Mendelian randomization (MR) is increasingly used to investigate causal relationships. Many robust MR methods are available to address pleiotropy, but these assume independence between the gene-exposure and gene-outcome association estimates. Unlike in two-sample MR, in one-sample MR the two estimates are obtained from the same individuals, and the assumption of independence does not hold in the presence of confounding.

METHODS

With simulations mimicking a typical study in UK Biobank, we assessed the performance, in terms of bias and precision of the MR estimate, of the fixed-effect and (multiplicative) random-effects meta-analysis method, weighted median estimator, weighted mode estimator and MR-Egger regression, used in both one-sample and two-sample data. We considered scenarios differing by the: presence/absence of a true causal effect; amount of confounding; and presence and type of pleiotropy (none, balanced or directional).

RESULTS

Even in the presence of substantial correlation due to confounding, all two-sample methods used in one-sample MR performed similarly to when used in two-sample MR, except for MR-Egger which resulted in bias reflecting direction and magnitude of the confounding. Such bias was much reduced in the presence of very high variability in instrument strength across variants (IGX2 of 97%).

CONCLUSIONS

Two-sample MR methods can be safely used for one-sample MR performed within large biobanks, expect for MR-Egger. MR-Egger is not recommended for one-sample MR unless the correlation between the gene-exposure and gene-outcome estimates due to confounding can be kept low, or the variability in instrument strength is very high.

Assessing causal treatment effect estimation when using large observational datasets

Background

Recently, there has been a heightened interest in developing and evaluating different methods for analysing observational data. This has been driven by the increased availability of large data resources such as Electronic Health Record (EHR) data alongside known limitations and changing characteristics of randomised controlled trials (RCTs). A wide range of methods are available for analysing observational data. However, various, sometimes strict, and often unverifiable assumptions must be made in order for the resulting effect estimates to have a causal interpretation. In this paper we will compare some common approaches to estimating treatment effects from observational data in order to highlight the importance of considering, and justifying, the relevant assumptions prior to conducting an observational analysis.

Methods

A simulation study was conducted based upon a small cohort of patients with chronic obstructive pulmonary disease. Two-stage least squares instrumental variables, propensity score, and linear regression models were compared under a range of different scenarios including different strengths of instrumental variable and unmeasured confounding. The effects of violating the assumptions of the instrumental variables analysis were also assessed. Sample sizes of up to 200,000 patients were considered.

Results

Two-stage least squares instrumental variable methods can yield unbiased treatment effect estimates in the presence of unmeasured confounding provided the sample size is sufficiently large. Adjusting for measured covariates in the analysis reduces the variability in the two-stage least squares estimates. In the simulation study, propensity score methods produced very similar results to linear regression for all scenarios. A weak instrument or strong unmeasured confounding led to an increase in uncertainty in the two-stage least squares instrumental variable effect estimates. A violation of the instrumental variable assumptions led to bias in the two-stage least squares effect estimates. Indeed, these were sometimes even more biased than those from a naïve linear regression model.

Conclusions

Instrumental variable methods can perform better than naïve regression and propensity scores. However, the assumptions need to be carefully considered and justified prior to conducting an analysis or performance may be worse than if the problem of unmeasured confounding had been ignored altogether.

Improving the accuracy of two-sample summary-data Mendelian randomization: moving beyond the NOME assumption

BACKGROUND

Two-sample summary-data Mendelian randomization (MR) incorporating multiple genetic variants within a meta-analysis framework is a popular technique for assessing causality in epidemiology. If all genetic variants satisfy the instrumental variable (IV) and necessary modelling assumptions, then their individual ratio estimates of causal effect should be homogeneous. Observed heterogeneity signals that one or more of these assumptions could have been violated.

METHODS

Causal estimation and heterogeneity assessment in MR require an approximation for the variance, or equivalently the inverse-variance weight, of each ratio estimate. We show that the most popular 'first-order' weights can lead to an inflation in the chances of detecting heterogeneity when in fact it is not present. Conversely, ostensibly more accurate 'second-order' weights can dramatically increase the chances of failing to detect heterogeneity when it is truly present. We derive modified weights to mitigate both of these adverse effects.

RESULTS

Using Monte Carlo simulations, we show that the modified weights outperform first- and second-order weights in terms of heterogeneity quantification. Modified weights are also shown to remove the phenomenon of regression dilution bias in MR estimates obtained from weak instruments, unlike those obtained using first- and second-order weights. However, with small numbers of weak instruments, this comes at the cost of a reduction in estimate precision and power to detect a causal effect compared with first-order weighting. Moreover, first-order weights always furnish unbiased estimates and preserve the type I error rate under the causal null. We illustrate the utility of the new method using data from a recent two-sample summary-data MR analysis to assess the causal role of systolic blood pressure on coronary heart disease risk.

CONCLUSIONS

We propose the use of modified weights within two-sample summary-data MR studies for accurately quantifying heterogeneity and detecting outliers in the presence of weak instruments. Modified weights also have an important role to play in terms of causal estimation (in tandem with first-order weights) but further research is required to understand their strengths and weaknesses in specific settings.

A Bayesian approach to Mendelian randomisation with dependent instruments

Mendelian randomisation (MR) is a method for establishing causality between a risk factor and an outcome by using genetic variants as instrumental variables. In practice, the association between individual genetic variants and the risk factor is often weak, which may lead to a lack of precision in the MR and even biased MR estimates. Usually, the most significant variant within a genetic region is selected to represent the association with the risk factor, but there is no guarantee that this variant will be causal or that it will capture all of the genetic association within the region. It may be advantageous to use extra variants selected from the same region in the MR. The problem is to decide which variants to select. Rather than selecting a specific set of variants, we investigate the use of Bayesian model averaging (BMA) to average the MR over all possible combinations of genetic variants. Our simulations demonstrate that the BMA version of MR outperforms classical estimation with many dependent variants and performs much better than an MR based on variants selected by penalised regression. In further simulations, we investigate robustness to violations in the model assumptions and demonstrate sensitivity to the inclusion of invalid instruments. The method is illustrated by applying it to an MR of the effect of body mass index on blood pressure using SNPs in the FTO gene.

Age at puberty and risk of asthma: A Mendelian randomisation study

BACKGROUND

Observational studies on pubertal timing and asthma, mainly performed in females, have provided conflicting results about a possible association of early puberty with higher risk of adult asthma, possibly due to residual confounding. To overcome issues of confounding, we used Mendelian randomisation (MR), i.e., genetic variants were used as instrumental variables to estimate causal effects of early puberty on post-pubertal asthma in both females and males.

METHODS AND FINDINGS

MR analyses were performed in UK Biobank on 243,316 women using 254 genetic variants for age at menarche, and on 192,067 men using 46 variants for age at voice breaking. Age at menarche, recorded in years, was categorised as early (<12), normal (12-14), or late (>14); age at voice breaking was recorded and analysed as early (younger than average), normal (about average age), or late (older than average). In females, we found evidence for a causal effect of pubertal timing on asthma, with an 8% increase in asthma risk for early menarche (odds ratio [OR] 1.08; 95% CI 1.04 to 1.12; p = 8.7 × 10(-5)) and an 8% decrease for late menarche (OR 0.92; 95% CI 0.89 to 0.97; p = 3.4 × 10(-4)), suggesting a continuous protective effect of increasing age at puberty. In males, we found very similar estimates of causal effects, although with wider confidence intervals (early voice breaking: OR 1.07; 95% CI 1.00 to 1.16; p = 0.06; late voice breaking: OR 0.93; 95% CI 0.87 to 0.99; p = 0.03). We detected only modest pleiotropy, and our findings showed robustness when different methods to account for pleiotropy were applied. BMI may either introduce pleiotropy or lie on the causal pathway; secondary analyses excluding variants associated with BMI yielded similar results to those of the main analyses. Our study relies on self-reported exposures and outcomes, which may have particularly affected the power of the analyses on age at voice breaking.

CONCLUSIONS

This large MR study provides evidence for a causal detrimental effect of early puberty on asthma, and does not support previous observational findings of a U-shaped relationship between pubertal timing and asthma. Common biological or psychological mechanisms associated with early puberty might explain the similarity of our results in females and males, but further research is needed to investigate this. Taken together with evidence for other detrimental effects of early puberty on health, our study emphasises the need to further investigate and address the causes of the secular shift towards earlier puberty observed worldwide.

Age at menarche and adult body mass index: a Mendelian randomization study

BACKGROUND

Pubertal timing has psychological and physical sequelae. While observational studies have demonstrated an association between age at menarche and adult body mass index (BMI), confounding makes it difficult to infer causality.

METHODS

The Mendelian randomization (MR) technique is not limited by traditional confounding and was used to investigate the presence of a causal effect of age at menarche on adult BMI. MR uses genetic variants as instruments under the assumption that they act on BMI only through age at menarche (no pleiotropy). Using a two-sample MR approach, heterogeneity between the MR estimates from individual instruments was used as a proxy for pleiotropy, with sensitivity analyses performed if detected. Genetic instruments and estimates of their association with age at menarche were obtained from a genome-wide association meta-analysis on 182,416 women. The genetic effects on adult BMI were estimated using data on 80,465 women from the UK Biobank. The presence of a causal effect of age at menarche on adult BMI was further investigated using data on 70,692 women from the GIANT Consortium.

RESULTS

There was evidence of pleiotropy among instruments. Using the UK Biobank data, after removing instruments associated with childhood BMI that were likely exerting pleiotropy, fixed-effect meta-analysis across instruments demonstrated that a 1 year increase in age at menarche reduces adult BMI by 0.38 kg/m² (95% CI 0.25-0.51 kg/m²). However, evidence of pleiotropy remained. MR-Egger regression did not suggest directional bias, and similar estimates to the fixed-effect meta-analysis were obtained in sensitivity analyses when using a random-effect model, multivariable MR, MR-Egger regression, a weighted median estimator and a weighted mode-based estimator. The direction and significance of the causal effect were replicated using GIANT Consortium data.

CONCLUSION

MR provides evidence to support the hypothesis that earlier age at menarche causes higher adult BMI. Complex hormonal and psychological factors may be responsible.

Assessing the suitability of summary data for two-sample Mendelian randomization analyses using MR-Egger regression: the role of the I2 statistic

Background

: MR-Egger regression has recently been proposed as a method for Mendelian randomization (MR) analyses incorporating summary data estimates of causal effect from multiple individual variants, which is robust to invalid instruments. It can be used to test for directional pleiotropy and provides an estimate of the causal effect adjusted for its presence. MR-Egger regression provides a useful additional sensitivity analysis to the standard inverse variance weighted (IVW) approach that assumes all variants are valid instruments. Both methods use weights that consider the single nucleotide polymorphism (SNP)-exposure associations to be known, rather than estimated. We call this the `NO Measurement Error' (NOME) assumption. Causal effect estimates from the IVW approach exhibit weak instrument bias whenever the genetic variants utilized violate the NOME assumption, which can be reliably measured using the F-statistic. The effect of NOME violation on MR-Egger regression has yet to be studied.

Methods

An adaptation of the I2 statistic from the field of meta-analysis is proposed to quantify the strength of NOME violation for MR-Egger. It lies between 0 and 1, and indicates the expected relative bias (or dilution) of the MR-Egger causal estimate in the two-sample MR context. We call it IGX2 . The method of simulation extrapolation is also explored to counteract the dilution. Their joint utility is evaluated using simulated data and applied to a real MR example.

Results

In simulated two-sample MR analyses we show that, when a causal effect exists, the MR-Egger estimate of causal effect is biased towards the null when NOME is violated, and the stronger the violation (as indicated by lower values of IGX2 ), the stronger the dilution. When additionally all genetic variants are valid instruments, the type I error rate of the MR-Egger test for pleiotropy is inflated and the causal effect underestimated. Simulation extrapolation is shown to substantially mitigate these adverse effects. We demonstrate our proposed approach for a two-sample summary data MR analysis to estimate the causal effect of low-density lipoprotein on heart disease risk. A high value of IGX2 close to 1 indicates that dilution does not materially affect the standard MR-Egger analyses for these data.

Conclusions

: Care must be taken to assess the NOME assumption via the IGX2 statistic before implementing standard MR-Egger regression in the two-sample summary data context. If IGX2 is sufficiently low (less than 90%), inferences from the method should be interpreted with caution and adjustment methods considered.

A Mendelian Randomization Study of Metabolite Profiles, Fasting Glucose, and Type 2 Diabetes

Mendelian randomization (MR) provides us the opportunity to investigate the causal paths of metabolites in type 2 diabetes and glucose homeostasis. We developed and tested an MR approach based on genetic risk scoring for plasma metabolite levels, utilizing a pathway-based sensitivity analysis to control for nonspecific effects. We focused on 124 circulating metabolites that correlate with fasting glucose in the Erasmus Rucphen Family (ERF) study (n = 2,564) and tested the possible causal effect of each metabolite with glucose and type 2 diabetes and vice versa. We detected 14 paths with potential causal effects by MR, following pathway-based sensitivity analysis. Our results suggest that elevated plasma triglycerides might be partially responsible for increased glucose levels and type 2 diabetes risk, which is consistent with previous reports. Additionally, elevated HDL components, i.e., small HDL triglycerides, might have a causal role of elevating glucose levels. In contrast, large (L) and extra large (XL) HDL lipid components, i.e., XL-HDL cholesterol, XL-HDL-free cholesterol, XL-HDL phospholipids, L-HDL cholesterol, and L-HDL-free cholesterol, as well as HDL cholesterol seem to be protective against increasing fasting glucose but not against type 2 diabetes. Finally, we demonstrate that genetic predisposition to type 2 diabetes associates with increased levels of alanine and decreased levels of phosphatidylcholine alkyl-acyl C42:5 and phosphatidylcholine alkyl-acyl C44:4. Our MR results provide novel insight into promising causal paths to and from glucose and type 2 diabetes and underline the value of additional information from high-resolution metabolomics over classic biochemistry.

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 incorporating uncertainty about pleiotropy

Mendelian randomization (MR) requires strong assumptions about the genetic instruments, of which the most difficult to justify relate to pleiotropy. In a two-sample MR, different methods of analysis are available if we are able to assume, M₁ : no pleiotropy (fixed effects meta-analysis), M₂ : that there may be pleiotropy but that the average pleiotropic effect is zero (random effects meta-analysis), and M₃ : that the average pleiotropic effect is nonzero (MR-Egger). In the latter 2 cases, we also require that the size of the pleiotropy is independent of the size of the effect on the exposure. Selecting one of these models without good reason would run the risk of misrepresenting the evidence for causality. The most conservative strategy would be to use M₃ in all analyses as this makes the weakest assumptions, but such an analysis gives much less precise estimates and so should be avoided whenever stronger assumptions are credible. We consider the situation of a two-sample design when we are unsure which of these 3 pleiotropy models is appropriate. The analysis is placed within a Bayesian framework and Bayesian model averaging is used. We demonstrate that even large samples of the scale used in genome-wide meta-analysis may be insufficient to distinguish the pleiotropy models based on the data alone. Our simulations show that Bayesian model averaging provides a reasonable trade-off between bias and precision. Bayesian model averaging is recommended whenever there is uncertainty about the nature of the pleiotropy.

Age at Menarche and Time Spent in Education: A Mendelian Randomization Study

Menarche signifies the primary event in female puberty and is associated with changes in self-identity. It is not clear whether earlier puberty causes girls to spend less time in education. Observational studies on this topic are likely to be affected by confounding environmental factors. The Mendelian randomization (MR) approach addresses these issues by using genetic variants (such as single nucleotide polymorphisms, SNPs) as proxies for the risk factor of interest. We use this technique to explore whether there is a causal effect of age at menarche on time spent in education. Instruments and SNP-age at menarche estimates are identified from a Genome Wide Association Study (GWAS) meta-analysis of 182,416 women of European descent. The effects of instruments on time spent in education are estimated using a GWAS meta-analysis of 118,443 women performed by the Social Science Genetic Association Consortium (SSGAC). In our main analysis, we demonstrate a small but statistically significant causal effect of age at menarche on time spent in education: a 1 year increase in age at menarche is associated with 0.14 years (53 days) increase in time spent in education (95% CI 0.10–0.21 years, p = 3.5 × 10⁻⁸). The causal effect is confirmed in sensitivity analyses. In identifying this positive causal effect of age at menarche on time spent in education, we offer further insight into the social effects of puberty in girls.

Age at menarche and lung function: a Mendelian randomization study

A trend towards earlier menarche in women has been associated with childhood factors (e.g. obesity) and hypothesised environmental exposures (e.g. endocrine disruptors present in household products). Observational evidence has shown detrimental effects of early menarche on various health outcomes including adult lung function, but these might represent spurious associations due to confounding. To address this we used Mendelian randomization where genetic variants are used as proxies for age at menarche, since genetic associations are not affected by classical confounding. We estimated the effects of age at menarche on forced vital capacity (FVC), a proxy for restrictive lung impairment, and ratio of forced expiratory volume in one second to FVC (FEV1/FVC), a measure of airway obstruction, in both adulthood and adolescence. We derived SNP-age at menarche association estimates for 122 variants from a published genome-wide meta-analysis (N = 182,416), with SNP-lung function estimates obtained by meta-analysing three studies of adult women (N = 46,944) and two of adolescent girls (N = 3025). We investigated the impact of departures from the assumption of no pleiotropy through sensitivity analyses. In adult women, in line with previous evidence, we found an effect on restrictive lung impairment with a 24.8 mL increase in FVC per year increase in age at menarche (95% CI 1.8-47.9; p = 0.035); evidence was stronger after excluding potential pleiotropic variants (43.6 mL; 17.2-69.9; p = 0.001). In adolescent girls we found an opposite effect (-56.5 mL; -108.3 to -4.7; p = 0.033), suggesting that the detrimental effect in adulthood may be preceded by a short-term post-pubertal benefit. Our secondary analyses showing results in the same direction in men and boys, in whom age at menarche SNPs have also shown association with sexual development, suggest a role for pubertal timing in general rather than menarche specifically. We found no effect on airway obstruction (FEV1/FVC).

Family tree and ancestry inference: is there a need for a 'generational' consent?

Background

Genealogical research and ancestry testing are popular recreational activities but little is known about the impact of the use of these services on clients’ biological and social families. Ancestry databases are being enriched with self-reported data and data from deoxyribonucleic acid (DNA) analyses, but also are being linked to other direct-to-consumer genetic testing and research databases. As both family history data and DNA can provide information on more than just the individual, we asked whether companies, as a part of the consent process, were informing clients, and through them clients’ relatives, of the potential implications of the use and linkage of their personal data.

Methods

We used content analysis to analyse publically-available consent and informational materials provided to potential clients of ancestry and direct-to-consumer genetic testing companies to determine what consent is required, what risks associated with participation were highlighted, and whether the consent or notification of third parties was suggested or required.

Results

We identified four categories of companies providing: 1) services based only on self-reported data, such as personal or family history; 2) services based only on DNA provided by the client; 3) services using both; and 4) services using both that also have a research component. The amount of information provided on the potential issues varied significantly across the categories of companies. ‘Traditional’ ancestry companies showed the greatest awareness of the implications for family members, while companies only asking for DNA focused solely on the client. While in some cases companies included text recommending clients inform their relatives, showing they recognised the issues, often it was located within lengthy terms and conditions or privacy statements that may not be read by potential clients.

Conclusions

We recommend that companies should make it clearer that clients should inform third parties about their plans to participate, that third parties’ data will be provided to companies, and that that data will be linked to other databases, thus raising privacy and issues on use of data. We also suggest investigating whether a ‘generational consent’ should be created that would include more than just the individual in decisions about participating in genetic investigations.

On the use of dense SNP marker data for the identification of distant relative pairs

There has been recent interest in the exploitation of readily available dense genome scan marker data for the identification of relatives. However, there are conflicting findings on how informative these data are in practical situations and, in particular, sets of thinned markers are often used with no concrete justification for the chosen spacing. We explore the potential usefulness of dense single nucleotide polymorphism (SNP) arrays for this application with a focus on inferring distant relative pairs. We distinguish between relationship estimation, as defined by a pedigree connecting the two individuals of interest, and estimation of general relatedness as would be provided by a kinship coefficient or a coefficient of relatedness. Since our primary interest is in the former case, we adopt a pedigree likelihood approach. We consider the effect of additional SNPs and data on an additional typed relative, together with choice of that relative, on relationship inference. We also consider the effect of linkage disequilibrium. When overall relatedness, rather than the specific relationship, would suffice, we propose an approximate approach that is easy to implement and appears to compete well with a popular moment-based estimator and a recent maximum likelihood approach based on chromosomal sharing. We conclude that denser marker data are more informative for distant relatives. However, linkage disequilibrium cannot be ignored and will be the main limiting factor for applications to real data.

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

Mendelian randomization studies estimate causal effects using genetic variants as instruments. Instrumental variable methods are straightforward for linear models, but epidemiologists often use odds ratios to quantify effects. Also, odds ratios are often the quantities reported in meta-analyses. Many applications of Mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype-disease log odds ratio by the difference in mean exposure between genotypes. This 'Wald-type' estimator is biased even in large samples, but whether the magnitude of bias is of practical importance is unclear. We study the large-sample bias of this estimator in a simple model with a continuous normally distributed exposure, a single unobserved confounder that is not an effect modifier, and interpretable parameters. We focus on parameter values that reflect scenarios in which we apply Mendelian randomization, including realistic values for the degree of confounding and strength of the causal effect. We evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight. A small simulation study examines finite sample bias and mild violations of the normality assumption. For our simple data-generating model, we find that the Wald estimator is asymptotically biased with a bias of around 10% in fairly typical Mendelian randomization scenarios but which can be larger in more extreme situations. Recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individual-level data they require are available. The Wald-type estimator may retain a role as an approximate method for meta-analysis based on summary data.

Using multiple genetic variants as instrumental variables for modifiable risk factors

Mendelian randomisation analyses use genetic variants as instrumental variables (IVs) to estimate causal effects of modifiable risk factors on disease outcomes. Genetic variants typically explain a small proportion of the variability in risk factors; hence Mendelian randomisation analyses can require large sample sizes. However, an increasing number of genetic variants have been found to be robustly associated with disease-related outcomes in genome-wide association studies. Use of multiple instruments can improve the precision of IV estimates, and also permit examination of underlying IV assumptions. We discuss the use of multiple genetic variants in Mendelian randomisation analyses with continuous outcome variables where all relationships are assumed to be linear. We describe possible violations of IV assumptions, and how multiple instrument analyses can be used to identify them. We present an example using four adiposity-associated genetic variants as IVs for the causal effect of fat mass on bone density, using data on 5509 children enrolled in the ALSPAC birth cohort study. We also use simulation studies to examine the effect of different sets of IVs on precision and bias. When each instrument independently explains variability in the risk factor, use of multiple instruments increases the precision of IV estimates. However, inclusion of weak instruments could increase finite sample bias. Missing data on multiple genetic variants can diminish the available sample size, compared with single instrument analyses. In simulations with additive genotype-risk factor effects, IV estimates using a weighted allele score had similar properties to estimates using multiple instruments. Under the correct conditions, multiple instrument analyses are a promising approach for Mendelian randomisation studies. Further research is required into multiple imputation methods to address missing data issues in IV estimation.

Participant identification in genetic association studies: improved methods and practical implications

BACKGROUND

In a recent paper by Homer et al. (Resolving individuals contributing trace amounts of DNA to highly complex mixtures using high-density SNP genotyping microarrays. PLoS Genet 2008;4:e1000167), a method for detecting whether a given individual is a contributor to a particular genomic mixture was proposed. This prompted grave concern about the public dissemination of aggregate statistics from genome-wide association studies. It is of clear scientific importance that such data be shared widely, but the confidentiality of study participants must not be compromised. The issue of what summary genomic data can safely be posted on the web is only addressed satisfactorily when the theoretical underpinnings of the proposed method are clarified and its performance evaluated in terms of dependence on underlying assumptions.

METHODS

The original method raised a number of concerns and several alternatives have since been proposed, including a simple linear regression approach. In our proposed generalized estimating equation approach, we maintain the simplicity of the linear regression model but obtain inferences that are more robust to approximation of the variance/covariance structure and can accommodate linkage disequilibrium.

RESULTS

We affirm that, in principle, it is possible to determine that a 'candidate' individual has participated in a study, given a subset of aggregate statistics from that study. However, the methods depend critically on a number of key factors including: the ancestry of participants in the study; the absolute and relative numbers of cases and controls; and the number of single nucleotide polymorphisms.

CONCLUSIONS

Simple guidelines for publication that are based on a single criterion are therefore unlikely to suffice. In particular, 'directed' summary statistics should not be posted openly on the web but could be protected by an internet-based access check as proposed by the P3G_Consortium et al. (Public access to genome-wide data: five views on balancing research with privacy and protection. PLoS Genet 2009;5:e1000665).

On the choice of parameterisation and priors for the Bayesian analyses of Mendelian randomisation studies

Mendelian randomisation is a form of instrumental variable analysis that estimates the causal effect of an intermediate phenotype or exposure on an outcome or disease in the presence of unobserved confounding, using a genetic variant as the instrument. A Bayesian approach allows current knowledge to be incorporated into the analysis in the form of informative prior distributions, and the unobserved confounder can be modelled explicitly. We consider Bayesian methods for Mendelian randomisation in the case where all relationships are linear and there are no interactions. A 'full' model in which the unobserved confounder is included explicitly is not completely identifiable, although the causal parameter can be estimated. We compare inferences from this general but non-identified model with a reduced parameter model that is identifiable. We show that, theoretically, additional information about the causal parameter can be obtained by using the non-identifiable full model, rather than the identifiable reduced model, but that this is advantageous only when realistically informative priors are used and when the instrument is weak or the sample size is small. Furthermore, we consider the impact of using 'vague' versus 'informative' priors.

Instrumental variable estimation of causal risk ratios and causal odds ratios in Mendelian randomization analyses

In this paper, the authors describe different instrumental variable (IV) estimators of causal risk ratios and odds ratios with particular attention to methods that can handle continuously measured exposures. The authors present this discussion in the context of a Mendelian randomization analysis of the effect of body mass index (BMI; weight (kg)/height (m)(2)) on the risk of asthma at age 7 years (Avon Longitudinal Study of Parents and Children, 1991-1992). The authors show that the multiplicative structural mean model (MSMM) and the multiplicative generalized method of moments (MGMM) estimator produce identical estimates of the causal risk ratio. In the example, MSMM and MGMM estimates suggested an inverse relation between BMI and asthma but other IV estimates suggested a positive relation, although all estimates had wide confidence intervals. An interaction between the associations of BMI and fat mass and obesity-associated (FTO) genotype with asthma explained the different directions of the different estimates, and a simulation study supported the observation that MSMM/MGMM estimators are negatively correlated with the other estimators when such an interaction is present. The authors conclude that point estimates from various IV methods can differ in practical applications. Based on the theoretical properties of the estimators, structural mean models make weaker assumptions than other IV estimators and can therefore be expected to be consistent in a wider range of situations.

Pharmacogenetic interactions and their potential effects on genetic analyses of blood pressure

BACKGROUND

In observational studies, analyses of blood pressure (BP) typically require some correction for the use of antihypertensive medications by study participants. Different approaches to correcting for treatment have been compared, but the impact of pharmacogenetic interactions that influence the efficacy of antihypertensive treatments on estimates of genetic main effects has not been considered. This work demonstrates the potential influence of pharmacogenetic interactions in genetic analyses of BP.

METHODS

A simulation study is conducted to test the influence of pharmacogenetic interactions on approaches to the analysis of BP. Results from three plausible scenarios are presented.

RESULTS

Informative BP approaches (Fixed Treatment Effect, Non-parametric adjustment, Censored Normal Regression) perform well when there is no pharmacogenetic interaction, but yield biased estimates of the main effects of particular genetic variants when pharmacogenetic interactions exist. Substitution approaches (Binary Trait, Fixed Substitution, Random Substitution, Median Method) are unaffected by pharmacogenetic interactions, but consistently perform sub-optimally.

CONCLUSIONS

We recommend that the Informative BP approaches remain the most appropriate methods to use in practice, but stress that caution is required in the interpretation of their results-especially when an interaction between treatment and a genetic variant of interest is suspected. We make some suggestions as to how to check for possible interactions and confirm the results from genetic analyses of BP, but warn that these should be reviewed when data on real pharmacogenetic interactions become available.

DataSHIELD: resolving a conflict in contemporary bioscience--performing a pooled analysis of individual-level data without sharing the data

BACKGROUND

Contemporary bioscience sometimes demands vast sample sizes and there is often then no choice but to synthesize data across several studies and to undertake an appropriate pooled analysis. This same need is also faced in health-services and socio-economic research. When a pooled analysis is required, analytic efficiency and flexibility are often best served by combining the individual-level data from all sources and analysing them as a single large data set. But ethico-legal constraints, including the wording of consent forms and privacy legislation, often prohibit or discourage the sharing of individual-level data, particularly across national or other jurisdictional boundaries. This leads to a fundamental conflict in competing public goods: individual-level analysis is desirable from a scientific perspective, but is prevented by ethico-legal considerations that are entirely valid.

METHODS

Data aggregation through anonymous summary-statistics from harmonized individual-level databases (DataSHIELD), provides a simple approach to analysing pooled data that circumvents this conflict. This is achieved via parallelized analysis and modern distributed computing and, in one key setting, takes advantage of the properties of the updating algorithm for generalized linear models (GLMs).

RESULTS

The conceptual use of DataSHIELD is illustrated in two different settings.

CONCLUSIONS

As the study of the aetiological architecture of chronic diseases advances to encompass more complex causal pathways-e.g. to include the joint effects of genes, lifestyle and environment-sample size requirements will increase further and the analysis of pooled individual-level data will become ever more important. An aim of this conceptual article is to encourage others to address the challenges and opportunities that DataSHIELD presents, and to explore potential extensions, for example to its use when different data sources hold different data on the same individuals.

Mendelian randomisation and causal inference in observational epidemiology

Nuala Sheehan and colleagues describe how Mendelian randomization provides an alternative way of dealing with the problems of observational studies, especially confounding.

Adjusting for founder relatedness in a linkage analysis using prior information

In genetic linkage studies, while the pedigrees are generally known, background relatedness between the founding individuals, assumed by definition to be unrelated, can seriously affect the results of the analysis. Likelihood approaches to relationship estimation from genetic marker data can all be expressed in terms of finding the most likely pedigree connecting the individuals of interest. When the true relationship is the main focus, the set of all possible alternative pedigrees can be too large to consider. However, prior information is often available which, when incorporated in a formal and structured way, can restrict this set to a manageable size thus enabling the calculation of a posterior distribution from which inferences can be drawn. Here, the unknown relationships are more of a nuisance factor than of interest in their own right, so the focus is on adjusting the results of the analysis rather than on direct estimation. In this paper, we show how prior information on founder relationships can be exploited in some applications to generate a set of candidate extended pedigrees. We then weight the relevant pedigree-specific likelihoods by their posterior probabilities to adjust the lod score statistics.

Family based studies and genetic epidemiology: theory and practice

Family based studies have underpinned many successes in uncovering the causes of monogenic and oligogenic diseases. Now research is focussing on the identification and characterisation of genes underlying common diseases and it is widely accepted that these studies will require large population based samples. Population based family study designs have the potential to facilitate the analysis of the effects of both genes and environment. These types of studies integrate the population based approaches of classic epidemiology and the methods enabling the analysis of correlations between relatives sharing both genes and environment. The extent to which such studies are feasible will depend upon population- and disease-specific factors. To review this topic, a symposium was held to present and discuss the costs, requirements and advantages of population based family study designs. This article summarises the features of the meeting held at The University of Sheffield, August 2006.

Structured Incorporation of Prior Information in Relationship Identification Problems

The objective of this paper is to show how various sources of information can be modelled and integrated to address relationship identification problems. Applications come from areas as diverse as evolution and conservation research, genealogical research in human, plant and animal populations, and forensic problems including paternity cases, identification following disasters, family reunions and immigration issues. We propose assigning a prior probability distribution to the sample space of pedigrees, calculating the likelihood based on DNA data using available software and posterior probabilities using Bayes' Theorem. Our emphasis here is on the modelling of this prior information in a formal and consistent manner. We introduce the distinction between local and global prior information, whereby local information usually applies to particular components of the pedigree and global prior information refers to more general features. When it is difficult to decide on a prior distribution, robustness to various choices should be studied. When suitable prior information is not available, a flat prior can be used which will then correspond to a strict likelihood approach. In practice, prior information is often considered for these problems, but in a generally ad hoc manner. This paper offers a consistent alternative. We emphasise that many practical problems can be addressed using freely available software.

Adjusting for treatment effects in studies of quantitative traits: antihypertensive therapy and systolic blood pressure

A population-based study of a quantitative trait may be seriously compromised when the trait is subject to the effects of a treatment. For example, in a typical study of quantitative blood pressure (BP) 15 per cent or more of middle-aged subjects may take antihypertensive treatment. Without appropriate correction, this can lead to substantial shrinkage in the estimated effect of aetiological determinants of scientific interest and a marked reduction in statistical power. Correction relies upon imputation, in treated subjects, of the underlying BP from the observed BP having invoked one or more assumptions about the bioclinical setting. There is a range of different assumptions that may be made, and a number of different analytical models that may be used. In this paper, we motivate an approach based on a censored normal regression model and compare it with a range of other methods that are currently used or advocated. We compare these methods in simulated data sets and assess the estimation bias and the loss of power that ensue when treatment effects are not appropriately addressed. We also apply the same methods to real data and demonstrate a pattern of behaviour that is consistent with that in the simulation studies. Although all approaches to analysis are necessarily approximations, we conclude that two of the adjustment methods appear to perform well across a range of realistic settings. These are: (1) the addition of a sensible constant to the observed BP in treated subjects; and (2) the censored normal regression model. A third, non-parametric, method based on averaging ordered residuals may also be advocated in some settings. On the other hand, three approaches that are used relatively commonly are fundamentally flawed and should not be used at all. These are: (i) ignoring the problem altogether and analysing observed BP in treated subjects as if it was underlying BP; (ii) fitting a conventional regression model with treatment as a binary covariate; and (iii) excluding treated subjects from the analysis. Given that the more effective methods are straightforward to implement, there is no argument for undertaking a flawed analysis that wastes power and results in excessive bias.

Association of WNK1 gene polymorphisms and haplotypes with ambulatory blood pressure in the general population

BACKGROUND

Blood pressure (BP) is a heritable trait of major public health concern. The WNK1 and WNK4 genes, which encode proteins in the WNK family of serine-threonine kinases, are involved in renal electrolyte homeostasis. Mutations in the WNK1 and WNK4 genes cause a rare monogenic hypertensive syndrome, pseudohypoaldosteronism type II. We investigated whether polymorphisms in these WNK genes influence BP in the general population.

METHODS AND RESULTS

Associations between 9 single-nucleotide polymorphisms (SNPs) in WNK1 and 1 in WNK4 with ambulatory BP were studied in a population-based sample of 996 subjects from 250 white European families. The heritability estimates of mean 24-hour systolic BP (SBP) and diastolic BP (DBP) were 63.4% and 67.9%, respectively. We found statistically significant (P<0.05) associations of several common SNPs and haplotypes in WNK1 with mean 24-hour SBP and/or DBP. The minor allele (C) of rs880054, with a frequency of 44%, reduced mean 24-hour SBP and DBP by 1.37 (95% confidence interval, -2.45 to -0.23) and 1.14 (95% confidence interval, -1.93 to -0.38) mm Hg, respectively, per copy of the allele.

CONCLUSIONS

Common variants in WNK1 contribute to BP variation in the general population. This study shows that a gene causing a rare monogenic form of hypertension also plays a significant role in BP regulation in the general population. The findings provide a basis to identify functional variants of WNK1, elucidate any interactions of these variants with dietary intake or with response to antihypertensive drugs, and determine their impact on cardiovascular morbidity and mortality.

Association and linkage for age at onset of a common oligogenic disease using genetic variance component models

The aims of our analysis were: (1) to investigate association of single nucleotide polymorphisms (SNPs) and other covariates with age at onset in the simulated Genetic Analysis Workshop (GAW) 12 general population data, and (2) to use the polygenic random effects estimated during model fitting (sigma squared A random effects) as input to a Haseman-Elston linkage analysis. The association analyses used genetic variance component models in a generalized linear mixed models framework and were fitted using Gibbs sampling. This method successfully detected the only three sequenced genes that were also major genes. The single-point linkage analysis used all markers provided. Regions of linkage were found close to all four of the sites of major genes that explained a non-trivial component of the variance of age at onset. In all four cases the linkage peak fell within 5 cM of the true location. In three cases the peak significance was p < 0.01.