Mendelian randomization in health research: using appropriate genetic variants and avoiding biased estimates.

Mendelian randomization methods, which use genetic variants as instrumental variables for exposures of interest to overcome problems of confounding and reverse causality, are becoming widespread for assessing causal relationships in epidemiological studies. The main purpose of this paper is to demonstrate how results can be biased if researchers select genetic variants on the basis of their association with the exposure in their own dataset, as often happens in candidate gene analyses. This can lead to estimates that indicate apparent "causal" relationships, despite there being no true effect of the exposure. In addition, we discuss the potential bias in estimates of magnitudes of effect from Mendelian randomization analyses when the measured exposure is a poor proxy for the true underlying exposure. We illustrate these points with specific reference to tobacco research.

Introduction

Proving how exposures affect health outcomes can be problematic in observational studies. Even if an exposure and an outcome are associated, the direction of causality can be difficult to ascertain because health outcomes can lead to changes in behaviour which can affect exposures (Munafò and Araya, 2010). Mendelian randomization studies may help to shed light on these relationships by using genetic variants, such as single nucleotide polymorphisms (SNPs) (see Table 1 for definition), as instrumental variables for measured lifestyle exposures (Davey Smith and Ebrahim, 2003). Mendelian randomization studies can be used for two related purposes: (1) to provide evidence for the existence of causal associations, and (2) to enable accurate estimation of the magnitude of the effect of lifelong exposure to a risk factor on an outcome (Davey Smith and Ebrahim, 2004).

Table 1

Definitions of genetic terms for Mendelian randomization.

Term	Definition
Allele	One form of a genetic variant
Canalization	Process of developmental compensation for the effects of a genetic variant which may disrupt normal development
Genetic variant	Part of the genetic code for which there is more than one form in the population. This can be a single nucleotide polymorphism but other forms of variation exist
Genome wide association study (GWAS)	Hypothesis-free study which investigates associations of a large number of genetic variants across the whole genome with a trait of interest
Linkage disequilibrium	Non-random association between genetic variants at different positions along the chromosome
Pleiotropic	Influencing more than one phenotypic trait
Single nucleotide polymorphism (SNP)	Variation at a single nucleotide base pair in the DNA sequence

As is the case for instrumental variable methods generally, for Mendelian randomization studies to be useful genetic variants must be robustly associated with the exposure of interest (Davey Smith and Ebrahim, 2005; Lawlor et al., 2008b). Despite this, recent Mendelian randomization studies conducted by Wehby et al. (2011a,b, 2012) have used genetic variants as instruments for smoking heaviness which were not shown to be associated with smoking phenotypes in large genome wide association studies. Whilst the authors acknowledge that these variants have not been consistently associated with smoking phenotypes, they suggest that the variants provide evidence of causal effects of smoking on body weight (Wehby et al., 2012) and smoking in pregnancy on birthweight (Wehby et al., 2011b) and risk of orofacial clefts in offspring (Wehby et al., 2011a). In addition, the authors use the genetic variants to estimate the magnitude of effect of smoking heaviness on their outcomes of interest (Wehby et al., 2011a,b, 2012). Even if the variants they use are truly associated with smoking behaviour, this is likely to produce incorrect estimates of the effect size of smoking on the outcome.

Aims

In this paper, we aim: (1) to illustrate, using a data simulation, why inferences based on the results of Mendelian randomization studies using genetic variants selected based on their association in a single sample are likely to be misleading and (2) to demonstrate why estimating the magnitudes of causal effects in cases where the measured exposure is not the same as the underlying exposure captured by the variant is problematic. We discuss these issues with reference to the specific case of tobacco as an exposure, but these principles can be applied more widely to Mendelian randomization and instrumental variable analyses.

Assumptions of Mendelian randomization

The principle of Mendelian randomization relies on the basic (but approximate) laws of Mendelian genetics (segregation and independent assortment). If these two laws hold, then at a population level, genetic variants will not be associated with the confounding factors that generally distort conventional observational studies (Davey Smith and Ebrahim, 2003; Davey Smith, 2011). In addition, genetic variants will not be affected by reverse causality (Davey Smith and Ebrahim, 2003). Epidemiological studies increasingly use Mendelian randomization to provide robust evidence of underlying causal mechanisms in a number of areas of health research including cardiovascular disease, cancer and mental health (Casas et al., 2005; Davey Smith et al., 2005; Benn et al., 2011; Scott et al., 2011; Interleukin-6 Receptor Mendelian Randomisation Analysis et al., 2012; Nordestgaard et al., 2012; Voight et al., 2012; Carslake et al., 2013).

For a SNP to be a valid instrumental variable, the following assumptions must hold: (1) the SNP should be reliably associated with the exposure, (2) the SNP should only be associated with the outcome through the exposure of interest (the “exclusion restriction”) and (3) the SNP should be independent of other factors affecting the outcome (confounders) (Angrist et al., 1996; Lawlor et al., 2008b; Wehby et al., 2008; Clarke and Windmeijer, 2012). Moreover, to use Mendelian randomization for accurate estimation of effect sizes in mediation analysis using a measured exposure, the measured exposure should accurately capture the true causal exposure (Lawlor et al., 2008a; Pierce and VanderWeele, 2012).

Use of genetic variants selected in a single sample

Genetic variants for tobacco research

Large consortium-based genome wide association studies have found genetic variants robustly associated with smoking behaviours (Thorgeirsson et al., 2008; Furberg et al., 2010; Liu et al., 2010). One genetic variant that has been highlighted by these studies, amongst others, is located in the nicotinic receptor gene cluster CHRNA5–A3–B4 on chromosome 15. Two SNPs within this region, rs16969968 and rs1051730, which are in linkage disequilibrium and can be used interchangeably in studies on Europeans, consistently associate with measures of heaviness of smoking (e.g., cigarettes per day or biomarkers of nicotine exposure) (Freathy et al., 2009; Munafò et al., 2012). Smokers with a single copy of the smoking increasing allele smoke on average one extra cigarette per day compared to those with no copies. The effects of the SNP are additive, so people with two copies of the smoking increasing allele on average smoke two additional cigarettes a day (Ware et al., 2011). The strength and consistency of this association make these variants suitable instruments for use in Mendelian randomization studies. The second assumption of instrumental variable analysis, that the SNP should only be associated with the outcome through the exposure of interest, is rarely fully testable (Glymour et al., 2012). In Mendelian randomization, this assumption may be violated if the genetic variant has pleiotropic effects, is in linkage disequilibrium with another variant of differing function or if its effects are buffered by canalization (Davey Smith and Ebrahim, 2003). However, the biological function of the nicotinic receptor gene cluster and evidence from epidemiological studies suggest that this variant is likely to affect outcomes only through tobacco exposure (for a further discussion of this see Section 3). In addition, if the variant is associated with an outcome in smokers or former smokers but not never smokers, this is a good indication that the association is fully mediated through tobacco exposure (Freathy et al., 2011). The rs1051730 SNP has been used in Mendelian randomization studies to investigate the causal effect of cigarette smoking on body mass index, depression anxiety and birthweight of offspring (Freathy et al., 2011; Lewis et al., 2011; Bjorngaard et al., 2013; Tyrrell et al., 2012).

Despite the identification of variants in the CHRNA5–A3–B4 gene cluster as suitable instruments, Wehby et al. (2011a,b, 2012) use other variants (in DRD2, MAOA, DRD4, 5HTT, GABBR2, CYP2D6) as instruments for smoking heaviness in their Mendelian randomization studies. The authors justify this approach by emphasizing the plausible biological roles of their chosen variants in smoking behaviour. However, this justification is questionable given that the candidate gene approach for finding functional genetic variants has had limited success, yielding few replicable associations and many false positives (Colhoun et al., 2003; Sleiman and Grant, 2010; Lawlor et al., 2008b). If these common variants are truly associated with the exposure, these associations should have been detected in the large genome wide association studies of smoking behaviour. We calculated that the largest of these studies, conducted by the TAG consortium, which included 74,000 smokers had 80% power to detect variants explaining as little as 0.05% of the variance in cigarettes per day (Furberg et al., 2010). Genetic variation in the CHRNA5–A3–B4 gene cluster explains about 1% of the variance in cigarettes per day (Munafò et al., 2012).

Data simulation

Below, we show why selecting variants based on their association in a single sample can introduce bias into Mendelian randomization studies. We generated continuous exposure (X) and outcome (Y) variables for 10,000 individuals using the following formulae:where Z is a binary instrument with a frequency of 0.3 and e and u (the error terms) are jointly normally distributed continuous variables with a correlation coefficient of (ρ) of 0.6:To illustrate an example where the association of the SNP and the exposure is well established, and where the observational association is biased, but estimates from Mendelian randomization are unbiased, we set α1 = 0.5 and β1 = −0.3, the raw association between X and Y from linear regression was positive (beta α = 0.26, 95% CI: 0.25, 0.28) (see Table 2). However, as we know from the negative value of β1, the true effect of X on Y is negative. Hence the linear regression estimate was biased and confounded by the error terms. In contrast, the estimate of the effect of X on Y from a two-stage least-squares regression, using the instrument Z, was negative and equal to the “true” value of β1 (beta coefficient −0.29, 95% CI: −0.37, −0.21). This demonstrates that in the presence of confounding, when there is a robust relationship between the instrument and the exposure, Mendelian randomization, and more broadly instrumental variable analysis, can give an unbiased estimate.

Table 2

Results of data simulation showing unbiased estimate from two-stage least-squares regression in the presence of confounding.

Model	Beta (95% CI)a
Y on X (linear regression)	0.26 (0.25, 0.28)
Y on X (two stage least squares)	−0.29 (−0.37, −0.21)

True value of beta from simulation is −0.3.

We next expand our simulation to demonstrate how biases can occur if instruments are selected based on their observed associations with the exposure in the sample within which the Mendelian randomization experiment is being carried out. To simulate an example in which there is no effect of the exposure on the outcome, we set β1 = 0, so the outcome and exposure were only correlated (correlation = 0.6) due to the error terms. Thus the association of the exposure and outcome is confounded. This means that if our estimation model (estimator) is correct, then it should find no effect of the exposure on the outcome. If our estimator is incorrect and we find a relationship between the outcome and the exposure, then it suggests our estimator is biased.

Next, to simulate the selection of genetic instruments within a sample, we randomly generated 1000 binary variables (Z) to simulate the SNPs (all had a frequency of 0.3). Since these instruments were randomly generated, there was no underlying effect of the SNPs on the exposure (α1 = 0). We used a binary instrument in a one instrument and one exposure example for simplicity, but these results are generalizable to additive genetic models or Mendelian randomization studies using multiple genetic variants (Pierce et al., 2011; Clarke and Windmeijer, 2012). We estimated the association of each SNP with the exposure, X, using robust linear regression. As expected, by chance, roughly 5% of these SNPs were associated with the exposure (using a p-value cut-off of 0.05).

We selected the ten instruments most strongly associated with the exposure and ran a two stage least squares regression on the outcome using each of these instruments in turn. Table 3 presents the effect sizes and p-values for the association of the instrument with the exposure and the outcome along with the F-statistic (a measure of the strength of the association of instrument and exposure).

Table 3

Regression statistics of 10 most strongly associated randomly generated instruments.

	Association of instrument with exposurea			Association of exposure with outcomeb			F statisticc
	Beta	SE	p-Value	Beta	SE	p-Value
Instrument 1	−0.078	0.021	<0.001	0.436	0.222	0.05	13.66
Instrument 2	0.072	0.021	0.001	0.902	0.255	<0.001	11.48
Instrument 3	0.070	0.021	0.001	0.304	0.260	0.24	10.89
Instrument 4	0.064	0.021	0.002	0.123	0.305	0.69	9.31
Instrument 5	0.065	0.021	0.002	0.488	0.265	0.07	9.58
Instrument 6	−0.063	0.021	0.003	0.757	0.280	0.007	8.79
Instrument 7	0.062	0.021	0.003	1.024	0.314	0.001	8.55
Instrument 8	0.059	0.021	0.005	0.04	0.352	0.91	7.92
Instrument 9	0.060	0.021	0.005	0.97	0.319	0.002	7.96
Instrument 10	0.058	0.021	0.006	0.934	0.320	0.003	7.53

From linear regression of exposure on instrument.

From 2-stage least squares regression of outcome on exposure using the instrument.

F-statistic for strength of instrument.

Of the ten instruments selected, three had an F-statistic above the commonly used cut off point of 10, suggesting that the associations of instruments and exposure were strong enough for the instrumental variable estimates to be unbiased (Stock et al., 2002). Using two-stage least-squares regression, five of the instruments showed strong or moderate evidence for associations with the outcome (p values <0.01), and two further instruments were weakly associated (p values <0.1). However, we know that no “true” relationship exists, because of how we generated the data. Therefore, these instruments, and specifically how we selected the instruments biased the two-stage least squares estimates of the effect of the exposure on the outcome.

Use of inappropriate genetic variants is not a problem specific to studies of tobacco research (Fletcher and Lehrer, 2011), but this example illustrates this problem well because of the availability of good instruments for smoking behaviour. The importance of this issue more generally in Mendelian randomization studies has been highlighted previously by Lawlor et al. (2008b) with reference to smoking- and obesity-related variants.

The Beavis effect

Even when a variant discovered in a single sample is truly associated with an exposure, the effect sizes of variants identified within a single sample are, by the nature of their discovery, likely to be larger than in the overall population (the Beavis effect, or Winner's Curse) (Goring et al., 2001; Ioannidis, 2008; Burgess et al., 2011).

For example, suppose a variant is associated with a one unit increase in an exposure variable and a two fold increase in the risk of a disease outcome. The estimate from a two stage least squares regression will imply that a one unit increase in the exposure doubles the risk of disease. However, in a sample where the effect of the variant on the exposure is inflated and is associated with a two unit increase in the exposure, the two stage least squares regression will imply that a one unit increase in the exposure would increase disease risk by fold. Thus, using genetic variants which have not demonstrated consistently strong associations with the exposure of interest is likely to bias instrumental variable estimates, with the Beavis effect leading to an underestimation of the strength of exposure–outcome associations.

Mathematically, this is explained by the following formula. The instrumental variable estimator is the association of the outcome and the instrument divided by the association of the exposure and the instrument:Thus, if the denominator, cov(x, z) is larger, and the numerator cov(y, z) remains constant, the estimated effect, β, will be smaller.

Biases in magnitudes of effects from instrumental variable analysis

Mendelian randomization can provide very good estimates of the magnitude of effects of long term exposure to a risk factor on outcomes (Davey Smith and Ebrahim, 2005; Ference et al., 2012). However, when the phenotypic exposure of interest (e.g., cigarettes per day) does not adequately capture the “causal” exposure through which the genetic variant operates (e.g., lifetime exposure to tobacco), estimates from two-stage least-squares regression may be biased. In such cases, the second assumption of instrumental variable analysis (the exclusion restriction assumption) is violated. The genetic variant is still a valid instrument for the underlying phenotype of interest and can therefore still provide evidence of causality. However, it is not a valid instrument for the effect of the measured phenotype on the outcome and so magnitudes of effect are likely to be incorrect (Glymour et al., 2012). This principle also applies more widely to instrumental variable analyses using non genetic instruments, but this issue has not been well-developed in the econometrics or statistics literatures.

In tobacco research, self-reported measures of smoking behaviour (such as number of cigarettes smoked per day) may be inadequate phenotypes because people smoke cigarettes differently. For example, there is variation in the number of puffs taken, volume of smoke inhaled or how far down the cigarette is smoked before it is discarded (Strasser et al., 2007; McNeill and Munafò, 2013). Objective measures of tobacco exposure (e.g., level of cotinine, the primary metabolite of nicotine) are likely to provide more valid assessment of actual biological exposure (i.e., the amount of smoked inhaled). For example, the rs1051370/rs16969968 variants are considerably more strongly associated with circulating levels of cotinine, than with self-reported daily cigarette consumption, explaining 4% and 1% of the variance in these phenotypes respectively (Keskitalo et al., 2009; Munafò et al., 2012). Researchers rarely have data on phenotypes such as cotinine, and often use a proxy measure such as self-reported cigarette smoking rates.

This issue is illustrated in Fig. 1. We are particularly interested in the effect (a) of lifetime exposure to tobacco smoke (X) on an outcome measure (Y) (see Fig. 1A). Unfortunately, we may only have data on cigarettes smoked per day (X2), which is associated with but does not fully capture lifetime exposure (see Fig. 1B). The raw association of smoking on the outcome is confounded by the unobserved variable U (the error terms in our simulations). The genetic variant (Z), not only affects the total lifetime exposure (b), but also the number of cigarettes smoked (c). According to the second assumption of instrumental variable analysis, Z should only affect the outcome through its effect on the number of cigarettes smoked per day (X2) but in this case it also affects the outcome through lifetime exposure to tobacco smoke (X).

Fig. 1

Directed acyclic graphs for Mendelian randomization analyses of (A) total lifetime exposure to tobacco smoke and (B) reported number of cigarettes smoked per day with outcome measures. Observed variables are denoted using squares, unobserved variables are denoted using circles, causal effects have arrows. Dashed lines represent non-causal associations. X: total lifetime exposure to tobacco smoke, X2: reported number of cigarettes smoked per day, a genetic variant (Z), outcome (Y), and an unobserved confounder (U).

In the example above, if we adjust the association of the variant (Z) with the outcome (Y) for the measured phenotype (X2) we would not expect the association to disappear because Z still affects Y through lifetime exposure to tobacco smoke (X). This issue has generated debate in the literature; the residual association observed between the CHRNA5–A3–B4 variants and lung cancer following adjustment for cigarettes per day has led to suggestions of a direct effect of the variant on lung cancer which does not operate though smoking (Lips et al., 2010; Wang et al., 2010a). However, Munafò et al. (2012) calculated that association between the variant and lung cancer was consistent with full mediation through tobacco exposure if cotinine were used as an intermediate measure of tobacco exposure rather than cigarettes per day. Therefore, the apparent direct association between these variants and lung cancer is likely to be a function of poor tobacco exposure measurement. This has important implications for the use of two-stage least-squares regression in Mendelian randomization analyses of smoking. If the measured exposure does not capture all dimensions of the relevant exposure domain, we can still infer a causal relationship, but cannot obtain an accurate estimate of the effect size of the underlying causal exposure. Thus the effect sizes presented in papers using cigarettes per day as the measured exposure of interest are likely to be subject to bias and should be interpreted with caution. It should be noted that this differs from the issue of random and systematic measurement error in the exposure phenotype, as discussed by Pierce and VanderWeele (2012). This is because even if cigarettes per day were measured perfectly, this phenotype would not adequately capture tobacco exposure.

Whilst this is a particular issue for studies of tobacco use, this is also relevant for Mendelian randomization studies of other exposures. For example, estimates from Mendelian randomization studies using variants which affect caffeine consumption may be biased if the measured phenotype is number of cups of coffee consumed per day because this measure does not account for caffeine content of each cup. Glymour et al. (2012) also discuss this issue in relation to incorrect specification of the appropriate causal time period for an exposure, using body mass index as an example.

Conclusions

The results of Mendelian randomization studies, based on genetic variants chosen because of their association with the exposure in any one sample, do not contribute useful evidence of the effects of exposures on health outcomes. It is essential for Mendelian randomization studies to use genetic variants that are robustly associated with the exposure of interest. Fortunately, this is now possible for a number of exposures, including tobacco, generally because of variants identified in large genome wide association studies and replicated in independent samples (Timpson et al., 2005; Frayling et al., 2007; Hazra et al., 2008; Furberg et al., 2010; Wang et al., 2010b; Voight et al., 2012). Mendelian randomization studies, as well as establishing causal associations, can provide good estimates of the magnitudes of effect between exposures and outcomes as they are free from bias by confounding. However, estimates may be biased if the measured exposures are not the same underlying exposure as that represented by the genetic variant. Crucially, even if the underlying causal exposure is perfectly measured, if the variant additionally affects the outcome through a different pathway, neither causality nor strength of associations can be estimated. Mendelian randomization has the potential to be a valuable tool to further our understanding of the aetiology of disease. Researchers will only realize this potential if they base their studies on well-characterized variants and are cautious about making inferences about magnitudes of the relationships between observed phenotypes and outcomes.

Financial support

Amy Taylor, Jennifer Ware and Marcus Munafò are members of the UK Centre for Tobacco and Alcohol Studies, a UKCRC Public Health Research: Centre of Excellence. Funding from British Heart Foundation, Cancer Research UK, Economic and Social Research Council, Medical Research Council, and the National Institute for Health Research, under the auspices of the UK Clinical Research Collaboration, is gratefully acknowledged. This work was supported by the Wellcome Trust (grant number 086684) and the Medical Research Council (grant numbers MR/J01351X/1, G0800612, G0802736, G0600705, MC_UU_12013/1-9). George Davey Smith and Neil Davies are supported by the European Research Council DEVHEALTH grant (269874). Jennifer Ware is supported by a Post-Doctoral Research Fellowship from the Oak Foundation. Tyler VanderWeele is supported by an NIH grant (R01 ES017876).