American Journal of Epidemiology

American Journal of Epidemiology Advance Access originally published online on January 12, 2006
American Journal of Epidemiology 2006 163(5):397-403; doi:10.1093/aje/kwj062

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American Journal of Epidemiology Copyright © 2006 by the Johns Hopkins Bloomberg School of Public Health All rights reserved; printed in U.S.A.

Special Article

Limits to Causal Inference based on Mendelian Randomization: A Comparison with Randomized Controlled Trials

Dorothea Nitsch, Mariam Molokhia, Liam Smeeth, Bianca L. DeStavola, John C. Whittaker and David A. Leon

From the Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom

Correspondence to Dr. Dorothea Nitsch, Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom (e-mail: Dorothea.Nitsch{at}lshtm.ac.uk).

Received for publication April 18, 2005. Accepted for publication October 13, 2005.

	ABSTRACT

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
"Mendelian randomization" refers to the random assortment of genes transferred from parent to offspring at the time of gamete formation. This process has been compared to a randomized controlled trial of genetic variants. This could greatly aid observational epidemiology by potentially allowing an unbiased estimate of the effects of gene products on disease outcomes. However, studies utilizing Mendelian randomization to estimate effects of gene products on outcomes should be interpreted with caution. In this paper, the authors discuss some of the challenges facing epidemiologists in the analysis and interpretation of Mendelian randomization studies, particularly those that become apparent when the analogy with randomized controlled trials is closely examined. The authors conclude that Mendelian randomization is a powerful addition to etiologic research tools. However, care must be taken, because drawing valid causal inferences from its application depends upon more extensive assumptions than are required in randomized controlled trials.

causality; epidemiologic methods; genetics; random allocation; randomized controlled trials

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Abbreviations: ITT, intention-to-treat; IV, instrumental variable; MTHFR, methylenetetrahydrofolate reductase

	INTRODUCTION

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
Randomized controlled trials can provide rigorous evidence for potentially therapeutic or disease-reducing interventions (1). However, for many types of exposure, it is neither practical nor ethical to randomize human beings for such studies. Recently, there has been considerable interest in using an approach referred to as "Mendelian randomization" to investigate the causal effects of a wide range of exposures (2–10). This approach may offer a strategy for eliminating or reducing residual confounding in observational studies.

The term "Mendelian randomization" derives from the random assortment of genes transferred from parent to offspring at the time of gamete formation (9–12). The random assortment of alleles at conception has been likened to a randomized controlled trial in which people are randomly allocated to different genotypes rather than therapeutic interventions (9, 10).

The use of Mendelian randomization is well illustrated by a recent study (8) assessing the influence of plasma homocysteine level on the risk of stroke (see figure 1). Observational studies have failed to provide unequivocal evidence of a causal role for homocysteine in stroke. Persons who are homozygous for the T allele of the methylenetetrahydrofolate reductase (MTHFR) C677T polymorphism have a higher level of plasma homocysteine than those with the CC genotype. In a study by Casas et al. (8), the observed increase in risk of stroke among persons homozygous for the MTHFR T allele was found to be close to that predicted using the association between homocysteine and stroke taken together with the differences in homocysteine conferred by this genetic variant. The authors concluded that this result supports a causal relation between plasma homocysteine concentration and stroke. This could be seen as analogous to a randomized controlled trial in which participants were randomized to an intervention that affected plasma homocysteine level.

View larger version (13K): [in this window] [in a new window]   FIGURE 1. Relations between the methylenetetrahydrofolate reductase (MTHFR) C677T polymorphism, homocysteine level, and stroke.

 
While we acknowledge the potential contribution of Mendelian randomization studies to resolving some of the problems of observational epidemiology, in this paper we introduce a cautionary note. To clarify the main interpretational differences and assumptions needed to interpret the causality of observed associations, we adopt the device of comparing Mendelian randomization studies with randomized controlled trials. We focus on the difference between intention-to-treat (ITT) effects and the biologic effects of the treatment actually received. We show that this distinction is important for the interpretation of genetic association studies.

	RANDOMIZED CONTROLLED TRIALS

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
ITT analyses assess allocated treatment as a predictor of outcome (upper portion of figure 2). ITT effects are unconfounded because of randomization, despite the fact that not every participant will adhere to the allocated treatment (13). ITT analyses therefore reflect the effect of allocating a treatment rather than the biologic effect of treatment. Under three conditions—1) patients do not change their allocated treatment, 2) there is no differential loss to follow-up, and 3) there is a single common biologic effect of treatment—ITT effects may be similar to biologic treatment effects. Hence, reports on randomized controlled trials should include information on losses to follow-up and the occurrence of other potentially biasing factors, such as unblinding (14, 15).

View larger version (30K): [in this window] [in a new window]   FIGURE 2. Conceptual graph highlighting a randomized controlled trial (upper portion) and its analogous Mendelian randomization approach (lower portion). The intention-to-treat effect and the genetic effect on the outcome are represented by the large open arrows.

 
If we are interested in the biologic effects of received treatment, comparisons of patients who did or did not receive treatment are confounded, because factors such as compliance with medication may be associated with other factors causally related to the outcome (16–19). However, as is discussed below, assuming knowledge of compliance mechanisms, instrumental variable methods can be used to estimate unconfounded biologic effects (16, 20–23).

	ANALOGIES BETWEEN A RANDOMIZED CONTROLLED TRIAL AND MENDELIAN RANDOMIZATION STUDIES

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
In Mendelian randomization studies, a distinction is made between genotype (e.g., the MTHFR polymorphism), intermediate phenotypes (e.g., homocysteine level), and disease outcomes (e.g., stroke). Within a randomized controlled trial, random allocation can only have an effect through treatment, because received treatment is necessarily on any causal pathway between allocation and outcome (figure 2, upper portion). In a Mendelian randomization setting, this corresponds to the assumption of effects of a gene on a distal outcome only acting via the intermediate phenotype (figure 2, lower portion; table 1) (3, 24).

View this table: [in this window] [in a new window]   TABLE 1. Analogies between randomized controlled trials and Mendelian randomization studies

 
In most studies that use Mendelian randomization, the investigators' primary interest is in the biologic effect of the gene product (intermediate phenotype) on disease risk, rather than in assessing the effects of genetic allocation on disease outcome per se (4, 8, 25). The gene itself serves as a device to enable the estimation of unconfounded effects of the gene product on disease. This parallels the interest in the biologic effect of a treatment and is distinct from the primary interest in ITT effects in randomized controlled trials. Effects of the intermediate phenotype on outcome are usually assessed by an informal comparison of the genotypic effect on outcome (e.g., the effect of the MTHFR polymorphism on stroke) with a previously reported or concurrent intermediate effect on outcome (e.g., the effect of homocysteine level on stroke (figure 1)) (8).

However, it is not clear that a long-term genetically determined "exposure" is biologically equivalent to environmental exposures investigated in observational research or tested in intervention studies. In genetic studies, one is effectively observing the effects of long-term levels determined by a particular gene. Indeed, it has been argued that Mendelian randomization studies might have particular relevance in the assessment of the effects of long-term exposure, such as dietary intake of antioxidant vitamins, whereas randomized controlled trials (involving, for example, dietary supplements) can only examine short-term effects (26).

	CONFOUNDING

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
Confounding at the genetic level
While utilization of Mendel's laws seems to offer the prospect of studying genetic effects that are largely unconfounded by environmental exposures, genetic confounding by population stratification and linkage disequilibrium may still arise.

If the ancestral populations of persons in our sample carry different risks of disease and different genotypes, population origin can act as a confounder, a phenomenon called "population stratification" (27). Population stratification can be dealt with at the study design stage (28, 29) or by adjustment in the analyses (30, 31).

Linkage disequilibrium is the association of genetic polymorphisms, usually because the polymorphisms are close together on the genome (32). In genetic association studies, only a defined proportion of single nucleotide polymorphisms within a candidate gene may be genotyped. Interpretation of gene function on outcome based on the association of genotyped single nucleotide polymorphisms with disease might be biased because of omission of untyped disease-causing variants in linkage disequilibrium with the typed single nucleotide polymorphisms (33).

"Functional genomic" confounding
Adaptation to a genetically determined phenotype might alter the expected genotype-disease association—a phenomenon known as "canalization" (9, 10, 34–36). Mathematical modeling suggests that genetic knockouts in underlying complex functional networks can lead to compensatory alterations in other pathways which buffer or reduce the extent of phenotypic variance (35, 36). Further, there is evidence for a substantial biologic complexity underlying the response to environmental stimuli prior to overt disease manifestation (37–40) which can be difficult to assess in genetic association studies (figure 3).

View larger version (46K): [in this window] [in a new window]   FIGURE 3. Biologic model showing the sequence of events between inheritance of a disease-causing allele and the diagnosis of disease. Examples of human diseases for which the Mendelian randomization argument faces some challenges, especially in the setting of a case-control study, are given on the right side of the figure. Phenylketonuria (PKU) is an autosomal recessive inborn error of metabolism resulting in phenylalanine hydroxylase deficiency, leading to mental retardation unless it is treated with dietary intervention.

 

	STATISTICAL IMPLICATIONS

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
Instrumental variables in randomized controlled trials
In randomized controlled trials, it is common to use ITT analysis to avoid the inevitable confounding that arises when analyses are conducted by treatment received. However, the instrumental variable approach can be used to estimate the biologic effect of treatment on outcome. In using the randomized controlled trial analogy, let Z be the random allocation to treatment (Z = 1) or control (Z = 0) status; let X = 1 for those who actually receive the treatment and X = 0 for those who do not, and let Y be the outcome of interest. Random allocation (Z) affects outcome (Y) only through received treatment (X), whereas receipt of treatment may be influenced by a number of unknown or unmeasured confounders (U) (figure 4). Provided that participants are completely blinded to their assignment, we can specify the relation between allocation and compliance, ß(X, Z), in such a way that the actual received treatment has the same effect on outcome whatever the compliance behavior. Then the instrumental variable (IV) approach can be used to estimate an unconfounded biologic effect on outcome of the received treatment, denoted as ß^IV (16, 20–23), by using the estimated ITT effect ß^ITT, which depends on treatment allocation and outcome:

(1)

where E( ) denotes estimate.

View larger version (11K): [in this window] [in a new window]   FIGURE 4. Conceptual graph depicting the instrumental variable (IV) approach. ßITT represents the intention-to-treat (ITT) effect of randomized allocation (Z) on outcome (Y), where Z acts through actually received treatment (X); ßIV denotes the biologic effect of actually received treatment on outcome; and ß denotes the effect of Z on X.

 
With reference to figure 4, it can be seen that estimation of ß^IV relies on assumptions about compliance, namely blinding to allocation (i.e., Z being associated with X and independent of U) and the absence of any other pathway from allocation to outcome (i.e., Z being independent of Y given X and U).

Equation 1 concerns linear relations between X and Z, Y and X, and Y and Z. A one-unit change in Z is estimated to result in a ß increase in X, and this increase of X in turn is estimated to cause a further increase of ß^IV in Y, which, multiplied together, gives the total ß^ITT increase from Z to Y (figure 4). Another, equivalent way to obtain IV estimates is to save the residuals from the regression of X on Z and then include them in the regression of Y on X. Such residuals act as unbiased estimates of the unmeasured confounders in U and therefore lead to unbiased estimates of the causal effect from X to Y—only if the regression model for the regression of X on Z is appropriately specified, however. If it is not, biased estimates will be obtained.

Not all of the assumptions mentioned above can be easily satisfied in a Mendelian randomization setting.

Estimation of intermediate phenotype effects
In Mendelian randomization studies, ß^IV would correspond to the effect of the intermediate phenotype on disease and ß^ITT to the genetic effect on disease, while the denominator in equation 1 would capture the observed, or presumed, relation between genetic allocation, Z, and its gene product, the intermediate variable X.

Substantial uncertainty is likely to arise, because the less precisely the genetic variation predicts the gene product, the less precise the derived effect estimate for the causal association between gene product and disease will be (2, 3, 19, 41). Hence, we need a strong relation between gene and gene product to be able to use equation 1 to estimate the effects of the intermediate phenotype on outcome. This requires, for instance, that there be no substantial biologic adaptation. Furthermore, any differential measurement error, or informative missingness, affecting the observed outcome would lead to biased estimates of the numerator in equation 1 and therefore of the intermediate effect on the outcome.

When using a case-control study design, which assesses the intermediate phenotype after determination of disease status, classical ß^IV estimates would be invalid if disease influences the intermediate phenotype, while the gene-disease association, ß^ITT, is unaffected by reverse causality. Usual practice is therefore to examine the association between gene and gene product only in controls.

A gene may act via more than one pathway, a phenomenon called pleiotropy. For example, in the case of the insulin resistance syndrome, there is evidence that the same gene or set of genes that influences this syndrome also influences high density lipoprotein cholesterol level, body mass index, and subscapular:triceps skinfold ratio (42). In the case of pleiotropy of intermediate phenotypes, quantification of effects of one of these on outcome using instrumental variables may be confounded by other pathways leading from gene to outcome, thus invalidating the assumption of Z's being associated with Y only via X (and being conditional on U) (figure 4).

It follows that in Mendelian randomization studies there will be some degree of bias for estimates of the derived ß^IV when the above assumptions are not met (11). Further, because an association study with adequate statistical power to detect a genetic effect on the gene product of interest may have inadequate power to investigate the genetic effects on disease (43, 44), it is unlikely that a definitive statement on the absence of an intermediate phenotype effect on outcome can be made on the basis of the absence of significant genetic effects on the outcome in a single study.

Meta-analysis of Mendelian randomization studies
Given the large sample sizes generally required in genetic association studies (11, 44–47), a common strategy is to use meta-analysis of existing studies (7, 24).

However, in the presence of substantial gene-environment interaction, the effect of a gene on disease may be influenced by environmental factors that vary with time or between populations. Hence, case-control studies should be viewed as "snapshots" taken at one point in time in a particular population. Even when allowing for random and systematic differences across populations—that is, using a meta-analytic regression approach (24)—other sources of bias (e.g., publication bias, selection bias, or environmental exposure measurement error) might not be accounted for. It is possible to conduct structured sensitivity analyses with respect to different forms of selection mechanisms that might operate (48).

A distinguishing feature of Mendelian randomization analyses is that estimates of gene-disease, gene-intermediate phenotype, and intermediate phenotype-disease associations may come from different studies, analogous to using the results of an ITT analysis obtained from one randomized controlled trial with a measure of compliance obtained from another to obtain an estimate of the biologic treatment effect. If these summary measures were taken from different populations using different disease definitions, the resulting estimate could be prone to substantial bias (24). Hence, when using summary measures based on several different studies, investigators cannot safely claim "causal" effects of the actual intervention on a disease outcome or, if applied to genetic studies, of the intermediate phenotype.

	CONCLUSION

TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 
A randomized controlled trial is an experimental setting in which predefined simple hypotheses—the effectiveness of targeting interventions in humans—are tested. In contrast, a Mendelian randomization study is not an experimental setting: It requires instead that the settings established at conception remain when data on the intermediate and disease phenotypes are collected. This is equivalent to assuming that the relations between the gene and the intermediate phenotype, the gene and the disease, and the intermediate phenotype and the disease are all correctly specified. As we have discussed, there is no guarantee that this is the case.

Caution is therefore required in order to correctly interpret studies that utilize Mendelian randomization. Mendelian randomization studies can make important contributions to observational epidemiology with suitable attention to study design, appropriate use of statistical methods, and more explicitness about the assumptions underlying the inferences drawn.

	ACKNOWLEDGMENTS

 
Dr. Dorothea Nitsch was supported by the Swiss National Science Foundation (Young Investigator Fellowship PBBSB-100661).

Conflict of interest: none declared.

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TOP ABSTRACT INTRODUCTION RANDOMIZED CONTROLLED TRIALS ANALOGIES BETWEEN A RANDOMIZED... CONFOUNDING STATISTICAL IMPLICATIONS CONCLUSION References

 

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