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- RE: Response to Richmond et. al: "Why mediation analysis trumps Mendelian randomization in population epigenomics studies of the Dutch Famine"
- Elmar Tobi, Molecular Epidemiology, Department of Biomedical Data Sciences, Leiden University Medical Center
- Other Contributors:
- Erik van Zwet, Medical Statistics, Department of Biomedical Data Sciences, Leiden University Medical Center
- L.H. Lumey, Molecular Epidemiology, Department of Biomedical Data Sciences, Leiden University Medical Center
- Bastiaan Heijmans, Molecular Epidemiology, Department of Biomedical Data Sciences, Leiden University Medical Center
(29 August 2018)Why mediation analysis trumps Mendelian randomization in population epigenomics studies of the Dutch Famine
Elmar W. Tobi1,2, Erik W. van Zwet3, L.H. Lumey1,4, Bastiaan T. Heijmans1
1Molecular Epidemiology, Department of Biomedical Data Sciences, Leiden University Medical Center, 2300 RC Leiden, The Netherlands.
2Division of Human Nutrition, Wageningen University and Research, 6708 WE Wageningen, Netherlands.
3Medical Statistics, Department of Biomedical Data Sciences, Leiden University Medical Center, 2300 RC Leiden, The Netherlands.
4Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.
Citable as Tobi EW, Van Zwet EW, Lumey LH, Heijmans BT. BioRxiv 2018; doi: https://doi.org/10.1101/362392
Our recent analysis of genome-wide DNA methylation data in men and women exposed to the Dutch Famine met passionate criticism by several researchers active on Twitter. It also prompted a more reasoned letter by Richmond and colleagues. At the core of the debate is the proper interpretation of findings from a mediation analysis. We used this method to identify specific DNA methylation changes that statistically provide a link between prenatal exposure to famine and adult metabolic traits. Our c...
Show MoreWhy mediation analysis trumps Mendelian randomization in population epigenomics studies of the Dutch Famine
Elmar W. Tobi1,2, Erik W. van Zwet3, L.H. Lumey1,4, Bastiaan T. Heijmans1
1Molecular Epidemiology, Department of Biomedical Data Sciences, Leiden University Medical Center, 2300 RC Leiden, The Netherlands.
2Division of Human Nutrition, Wageningen University and Research, 6708 WE Wageningen, Netherlands.
3Medical Statistics, Department of Biomedical Data Sciences, Leiden University Medical Center, 2300 RC Leiden, The Netherlands.
4Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.
Citable as Tobi EW, Van Zwet EW, Lumey LH, Heijmans BT. BioRxiv 2018; doi: https://doi.org/10.1101/362392
Our recent analysis of genome-wide DNA methylation data in men and women exposed to the Dutch Famine met passionate criticism by several researchers active on Twitter. It also prompted a more reasoned letter by Richmond and colleagues. At the core of the debate is the proper interpretation of findings from a mediation analysis. We used this method to identify specific DNA methylation changes that statistically provide a link between prenatal exposure to famine and adult metabolic traits. Our critics first argue that our results do not suggest mediation but reverse-causation, where famine-induced metabolic traits drive changes in DNA methylation. We rebut this scenario in a simulation study showing that our test of mediation was unlikely to become statistically significant in the case of reverse-causation. Some critics then argue that Mendelian randomization provides the sole path to correct inference. This belief misses a crucial point: DNA methylation, especially when measured in peripheral blood, is not likely to be a causal mediator from a biological point of view. It could however be a proxy of epigenetic regulation changes in specific tissues, for example at the level of transcription factor binding. If so, a Mendelian randomization approach using genetic variants affecting local DNA methylation in blood will be disconnected from the underlying biological mechanism and is bound to yield false-negative results. Our new simulation studies strengthen the original reasoning that the relationship between prenatal famine and metabolic traits is statistically mediated by specific DNA methylation changes while the specific molecular mechanism awaits elucidation.
Introduction
Intrauterine exposure to an adverse environment has been linked to adult health1-3 and epigenetic mechanisms are widely believed to mediate this long-term effect.4,5 Analyses aimed at finding the specific epigenetic changes involved are a logical next step. Previous analyses have concentrated on the association between intrauterine exposures and either DNA methylation or adult health, but not on both. As a result, mediating epigenetic changes remain ill-defined. We recently analyzed genome-wide DNA methylation data in men and women with intrauterine exposure to the Dutch Famine.6 We used a genome-wide search for potential mediators followed by statistical mediation analysis to identify specific genomic regions at which differential epigenetic regulation could explain the observed association of prenatal famine exposure with adult metabolic traits. Our analysis identified the DNA methylation level in blood at one CpG as a candidate mediator of the association between famine exposure and adult body-mass index (BMI), and at eight CpGs as candidate mediators of the association with adult serum triglycerides levels (TG).
In a response to our work, Richmond et al7 argue that not mediation but reverse-causation is the most likely explanation for our results. In their view, the observed DNA methylation differences are secondary to changes in BMI and TG induced by prenatal famine and do not drive the observed adult metabolic traits.
Analysis
To obtain a quantitative view of the assumptions underlying the reasoning of Richmond et al. we carried out a series of simulation studies. We generated one thousand data sets according to both the mediation and the reverse-causation scenario using the data patterns as observed in our original study. We then recorded the fraction of significant results obtained by Sobel tests for mediation (computationally fast and valid, assuming that Monte Carlo procedures for estimating p-values are not critical for normally distributed simulated data). The scenarios and results of our simulations are summarized in Figure 1.
Under the scenario of mediation, our simulations show a high statistical power of the mediation test (0.87). In contrast, the test for mediation has a very low power (0.07) under the reverse-causation scenario proposed by Richmond et al. This implies that the test for mediation is very unlikely to become statistically significant when changes in DNA methylation are secondary to changes in BMI and TG induced by prenatal famine. The findings
from the simulation study agree with the results of our original analysis which effectively eliminated those CpGs as potential mediators that had been previously identified in epigenome-wide association studies of BMI and TG, but for which there was evidence of reverse-causation in 2-step Mendelian randomization analysis.8,9 Conversely, for the CpGs we identified as candidate mediators, there was no or inconclusive evidence for reverse-causation from previous studies.8-10 Richmond et al also considered a scenario in which DNA methylation and metabolic traits are linked by an unobserved confounder. The power for this scenario is low (0.19). In our original analysis was already adjusted for key potential confounders, including smoking, social-economic position, and current diet, further decreasing the likelihood of this scenario. Our new simulation study therefore effectively rebuts the comments of Richmond et al. and show that mediation by DNA-methylation changes is more likely to explain our findings than reverse-causation.
From a more general perspective however, we feel that neither of the above scenarios is likely to present a sufficiently accurate picture of the biological mechanism underlying our results. DNA methylation is known to mark the regulatory state of a genomic region but does not necessarily control that state. As an example, an extensive body of work has shown that DNA methylation changes can be the downstream effect of altered transcription factor binding.11,12,13 This suggests a scenario where the causal driver of the relationship between prenatal famine and metabolic traits could be a change in epigenetic regulation different from DNA methylation. Statistical evidence for mediation is observed if a CpG site is an adequate proxy of this causal change (Figure 2). This reasoning is not new and was already included in our mediation paper6 and also in earlier work.5 We have also simulated this driver scenario and found that a mediation analysis has considerable power to detect such effects (0.62).
The notion that DNA methylation in blood may not be the biological mediating mechanism has important implications for the application and interpretation of Mendelian randomization
analysis. Richmond et al claim that Mendelian randomization is the only viable route to valid causal inferences in population epigenomics studies. This claim is problematic however, since current Mendelian randomization approaches use local genetic instruments to predict methylation of a CpG site in blood. The findings will therefore be negative in the event that DNA methylation change is merely a proxy of underlying causal changes in the epigenetic regulation at the level of histone modifications or transcription factor binding (Figure 2). This mismatch of unsuitable statistical methods to specific biological mechanisms may explain why there currently are surprisingly few examples of Mendelian randomization studies that link CpG methylation in blood to phenotypic changes.10 By contrast, there are ample examples of reverse-causation.8-10 It is therefore not surprising that Richmond et al failed to find evidence for a directed effect of methylation on BMI and TG for our candidate mediator CpGs. It is important to realize however that despite the disappointing results of Mendelian randomization approaches in this setting, few will dispute that epigenetic regulation could be an important driver of phenotypic variation.
Conclusion
Our simulations confirm that mediation analysis is a legitimate and potentially valuable approach to identify potential causal mechanisms in population epigenomics studies. We also agree that Mendelian randomization can be a very powerful tool for causal inference in molecular data but any negative or positive findings will require cautious interpretation. Negative findings may be due to a mismatch between the statistical method and the underlying mechanism, and positive findings could be related to pleiotropy and backdoor paths.8,14,15 As in all modelling approaches to data analysis, any study result should be viewed in the broader context of the available knowledge from relevant disciplines and the relevance of study findings should not be determined by p-values from isolated statistical tests alone. In our original report6, we clearly outline the limitations of the Dutch Famine data and consider all available evidence to come to a cautious interpretation of our findings.
Identifying causal effects in observational data is challenging and results must be interpreted with caution.16,17 Causal reasoning in population epigenomics is best served by weighting evidence from alternative approaches. Essential in this field is the awareness that progress will depend on contributions from biology, epidemiology, and other disciplines. To identify molecular mechanisms in sufficient detail, population-based approaches (covering diverse study designs and analytical strategies) and experimental studies (from human cells and organoids to animal models) will be required from researchers who keep an open mind as to unexpected turns of biology and to optimal analytic methods to deal with the observed phenomena.
Simulation script
To help further discussions on mediation analysis based on empirical data, we provide a set of R Markdown scripts to perform further simulations through GitHub (https://github.com/molepi/SimulationStudy-Mediation).
References
1. Barker DJ. The fetal and infant origins of adult disease. BMJ 1990; 301: 1111.
2. Lumey LH, Stein AD, Susser E. Prenatal Famine and Adult Health. Annu Rev Public Health 2011; 32: 237–62.
3. Lumey LH, Khalangot MD, Vaiserman AM. Association between type 2 diabetes and prenatal exposure to the Ukraine famine of 1932-33: a retrospective cohort study. Lancet Diabetes Endocrinol 2015; 3: 787–94.
4. Waterland RA, Michels KB. Epigenetic Epidemiology of the Developmental Origins Hypothesis. Annu Rev Nutr 2007; 27: 363–88.
5. Mill J, Heijmans BT. From promises to practical strategies in epigenetic epidemiology. Nat Rev Genet 2013; 14: 585–94.
6. Tobi EW, Slieker RC, Luijk R, Dekkers KF, Stein AD, Xu KM, et al. DNA methylation as a mediator of the association between prenatal adversity and risk factors for metabolic disease in adulthood. Sci Adv 2018; 4: eaao4364.
7. Richmond RC, Relton CL, Davey Smith G. What evidence is required to suggest that DNA methylation mediates the association between prenatal famine exposure and adulthood disease. Sci Adv 2018; eLetter to eaao4364.
8. Dekkers KF, van Iterson M, Slieker RC, Moed MH, Bonder MJ, van Galen M, et al. Blood lipids influence DNA methylation in circulating cells. Genome Biol 2016; 17: 138.
9. Wahl S, Drong A, Lehne B, Loh M, Scott WR, Kunze S, et al. Epigenome-wide association study of body mass index, and the adverse outcomes of adiposity. Nature 2017; 541: 81–6.
10. Mendelson MM, Marioni RE, Joehanes R, Liu C, Hedman AK, Aslibekyan S, et al. Association of Body Mass Index with DNA Methylation and Gene Expression in Blood Cells and Relations to Cardiometabolic Disease: A Mendelian Randomization Approach. PLoS Med 2017; 14: e1002215–30.
11. Feldmann A, Ivanek R, Murr R, Gaidatzis D, Burger L, Schübeler D. Transcription Factor Occupancy Can Mediate Active Turnover of DNA Methylation at Regulatory Regions. PLoS Genet 2013; 9: e1003994–10.
12. Domcke S, Bardet AF, Ginno PA, Hartl D, Burger L, Schübeler D. Competition between DNA methylation and transcription factors determines binding of NRF1. Nature 2015; 528: 575–9.
13. Bonder MJ, Luijk R, Zhernakova DV, Moed M, Deelen P, Vermaat M, et al. Disease variants alter transcription factor levels and methylation of their binding sites. Nat Genet 2017; 49: 131–8.
14. Smith GD, Ebrahim S. “Mendelian randomization”: can genetic epidemiology contribute to understanding environmental determinants of disease? Int J Epidemiol 2003; 32: 1–22.
15. Luijk R, Dekkers KF, van Iterson M, Arindrarto W, Claringbould A, Hop P, et al. Genome-wide identification of directed gene networks using large-scale population genomics data. BioRxiv 2017; doi: https://doi.org/10.1101/221879.
16. Rohrer JM. Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data. Adv Methods Practices Psychol Sci 2018; 1: 27–42.
17. Pingault J-B, O'Reilly PF, Schoeler T, Ploubidis GB, Rijsdijk F, Dudbridge F. Using genetic data to strengthen causal inference in observational research. Nat Rev Genet 2018; doi: 10.1038/s41576-018-0020-3.
Show LessCompeting Interests: None declared. - Editorial Addendum(14 May 2018)
Editorial Update:
Please note that one of the author's names is listed incorrectly, and should be George Davey Smith.
The author list is:
Rebecca Richmond
Caroline Relton
George Davey Smith
Best,
The Science Advances Editorial Team.
Competing Interests: None declared. - RE: What evidence is required to suggest that DNA methylation mediates the association between prenatal famine exposure and adulthood disease?
- George Cavey Smith, Medical Research Council Integrative Epidemiology Unit, University of Bristol
- Other Contributors:
- Rebecca Richmond, Medical Research Council Integrative Epidemiology Unit at the University of Bristol
- Caroline Relton, Medical Research Council Integrative Epidemiology Unit at the University of Bristol
(29 March 2018)What evidence is required to suggest that DNA methylation mediates the association between prenatal famine exposure and adulthood disease?
Rebecca Richmond, Medical Research Council Integrative Epidemiology Unit at the University of Bristol, Bristol, UK
Caroline Relton, Medical Research Council Integrative Epidemiology Unit at the University of Bristol, Bristol, UK
George Davey Smith, Medical Research Council Integrative Epidemiology Unit at the University of Bristol, Bristol, UK
Epigenome-wide associations studies (EWAS) are a key starting point for making inferences about whether DNA methylation lies on a molecular pathway between risk factors and disease. Mediation analysis is an important next step in interpreting observational associations from EWAS but, as highlighted by the recent paper by Tobi et al1, one beset with methodological problems. In the context of a powerful natural experiment, the authors provide evidence that DNA methylation mediates associations between prenatal famine exposure and adulthood cardiometabolic disease indicators. To be a mediator a factor must be causal with respect to the outcome and be influenced by the exposure. Whilst the natural experiment utilized in the study provides strong evidence that the latter may be the case, the design does not protect the former association against confounding or reverse causation. For exampl...
Show MoreWhat evidence is required to suggest that DNA methylation mediates the association between prenatal famine exposure and adulthood disease?
Rebecca Richmond, Medical Research Council Integrative Epidemiology Unit at the University of Bristol, Bristol, UK
Caroline Relton, Medical Research Council Integrative Epidemiology Unit at the University of Bristol, Bristol, UK
George Davey Smith, Medical Research Council Integrative Epidemiology Unit at the University of Bristol, Bristol, UK
Epigenome-wide associations studies (EWAS) are a key starting point for making inferences about whether DNA methylation lies on a molecular pathway between risk factors and disease. Mediation analysis is an important next step in interpreting observational associations from EWAS but, as highlighted by the recent paper by Tobi et al1, one beset with methodological problems. In the context of a powerful natural experiment, the authors provide evidence that DNA methylation mediates associations between prenatal famine exposure and adulthood cardiometabolic disease indicators. To be a mediator a factor must be causal with respect to the outcome and be influenced by the exposure. Whilst the natural experiment utilized in the study provides strong evidence that the latter may be the case, the design does not protect the former association against confounding or reverse causation. For example, if prenatal famine exposure increases body mass index and triglycerides, and they in turn influence DNA methylation, then reverse causation can underlie the observed findings (Figure 1). Differential measurement error in DNA methylation and the outcomes can lead the sophisticated mediation methods that were applied to produce misleading findings2,3. Unfortunately, the very sophistication of the methods – and their impenetrability to many – can generate a false sense of security regarding the results obtained4,5.
Figure 1 – Directed Acyclic Graphs illustrating possible scenarios for the observed associations between DNA methylation and cardiometabolic disease
- DNA methylation mediates the association between prenatal famine and cardiometabolic disease
- Cardiometabolic disease mediates the association between prenatal famine and DNA methylation (reverse causation)
- Cardiometabolic disease risk factors mediate the association of prenatal famine with both DNA methylation and cardiometabolic disease (reverse causation and confounding)
- An unmeasured factor e.g. alcohol intake influences both DNA methylation and cardiometabolic disease, hence generating a spurious association between DNA methylation and cardiometabolic disease (confounding)
Mendelian randomization (MR) can provide powerful evidence regarding the existence and direction of causal effects6, including in the domain of DNA methylation investigations7, and in the context of mediation3,7. For example, initial claims, based on conventional mediation analysis approaches, that AHRR methylation acts as a mediator between smoking and lung cancer8 are likely erroneous9.
We have therefore reviewed existing literature and utilized Mendelian randomization to interrogate Tobi et al’s findings with respect to the CpG sites identified as mediating the effect of prenatal famine on adulthood BMI and triglycerides.
Several recent studies have undertaken Mendelian randomization analysis to appraise the causal role of differential methylation in relation to metabolic traits, including BMI and lipid levels. These analyses have involved the identification of mQTLs (methylation quantitative trait loci) which are robustly associated with levels of site specific CpG methylation and which may therefore serve as genetic instruments in Mendelian randomization analysis, in either a one- or two-sample framework 10-15.
Unlike the direction of effect presumed by Tobi et al1, where differential methylation directly influences levels of BMI and triglycerides, these previous studies have typically suggested the absence of a causal relationship between methylation and metabolic traits when using MR approaches. Instead, they have illustrated a prevailing direction of causality from metabolic trait to DNA methylation for some CpG sites, using genetic variants strongly associated with metabolic traits identified in large GWAS analyses in a bi-directional MR approach 10-15.
As several of the CpG sites identified in the study by Tobi et al have not been previously investigated within an MR framework, we chose to evaluate this using two publicly-available resources, mqtldb (http://www.mqtldb.org/)16 and MR-Base (http://www.mrbase.org/)17. Using a two-sample MR approach18, we first obtained summary statistics for cis mQTLs shown to be strongly related to the CpG sites of interest in the mQTL database (all associations with p<1x10-5, n~1,000). Within MR-Base, we next performed LD pruning of the mQTLs (r2<0.001) and then performed a look-up of the mQTL (or SNP proxies at r2>0.8) associations from genome-wide association studies of our outcomes of interest (BMI and triglycerides). The exposure and outcome datasets were harmonized within MR-Base using the default settings and MR analysis run.
Of the 9 CpGs highlighted by Tobi et al as potentially mediating the impact of prenatal famine on later metabolic health in the offspring, we identified mQTLs to serve as instruments for 5 of these (no cis mQTLs could be identified for cg09349128 (PIM3), linked with BMI, or cg19693031 (TXNIP), cg06983052 (LRRC8C) or cg07397296 (ABCG1), linked with triglycerides). Using genetic association summary statistics from triglyceride GWAS conducted by the GLGC consortium with n=187,36519, we established the causal effect estimates for increasing methylation in relation to triglyceride levels and compared these with observational estimates obtained from the analysis by Tobi et al, shown in Figure 2.
The variance explained in each CpG site by the identified mQTLs ranged from 2.5 to 23.0%, highlighting the strength of the genetic instruments in this context. There was no convincing evidence for a causal effect of methylation on triglycerides at any of the 5 CpG sites evaluated. This is in stark contrast to the observational associations presented by Tobi et al, and the mediation estimates presented in their paper.
Figure 2 – Observational vs Mendelian randomization estimates for effect of DNA methylation at famine-responsive CpG sites on triglycerides
While our approach suffers from various limitations, including the use of a single source of relatively small sample size to identify mQTLs and the lack of cis mQTLs for some of the CpG sites evaluated, with increasing availability of larger mQTL datasets and GWAS summary statistics, we would advocate that a two-sample Mendelian randomization approach be adopted when investigating the mediating role of methylation in future studies. This is due to its relative strengths of ameliorating risk of reverse causation, unobserved confounding and measurement error. This method should be triangulated with other approaches to mediation, each with relative strengths, in order to provide an overall evaluation of the mediating role of DNA methylation20.
Furthermore, while Tobi et al showed correlations between methylation at identified CpG sites across tissues, it would have been preferable to investigate mediation within those tissues of interest for pathogenesis. For MR analysis, this requires large enough samples with genetic and methylation data in the tissues of interest to demonstrate the cis mQTL effects identified in readily available samples also exist in these tissues. Evidence of a robust, tissue specific mQTL-CpG relationship would strengthen the causal inference that could be made21.
References
1. Tobi EW, Slieker RC, Luijk R, et al. DNA methylation as a mediator of the association between prenatal adversity and risk factors for metabolic disease in adulthood. Science Advances. 2018;4.
2. Phillips AN, Davey Smith G. How Independent Are Independent Effects - Relative Risk-Estimation When Correlated Exposures Are Measured Imprecisely. J Clin Epidemiol. 1991;44(11):1223-1231.
3. Richmond RC, Hemani G, Tilling K, Davey Smith G, Relton CL. Challenges and novel approaches for investigating molecular mediation. Hum Mol Genet. 2016;25(R2):R149-R156.
4. Krieger N, Davey Smith G. The tale wagged by the DAG: broadening the scope of causal inference and explanation for epidemiology. Int J Epidemiol. 2016;45(6):1787-1808.
5. Krieger N, Davey Smith G. Response: FACEing reality: productive tensions between our epidemiological questions, methods and mission. Int J Epidemiol. 2016;45(6):1852-1865.
6. Davey Smith G, Ebrahim S. 'Mendelian randomization': can genetic epidemiology contribute to understanding environmental determinants of disease? Int J Epidemiol. 2003;32(1):1-22.
7. Relton CL, Davey Smith G. Two-step epigenetic Mendelian randomization: a strategy for establishing the causal role of epigenetic processes in pathways to disease. Int J Epidemiol. 2012;41(1):161-176.
8. Fasanelli F, Baglietto L, Ponzi E, et al. Hypomethylation of smoking-related genes is associated with future lung cancer in four prospective cohorts. Nat Commun. 2015;6.
9. Battram T, Richmond RC, Baglietto L, et al. Appraising the causal relevance of DNA methylation for risk of lung cancer. bioRxiv. 2018.
10. Wahl S, Drong A, Lehne B, et al. Epigenome-wide association study of body mass index, and the adverse outcomes of adiposity. Nature. 2017;541(7635):81-+.
11. Dekkers KF, van Iterson M, Slieker RC, et al. Blood lipids influence DNA methylation in circulating cells. Genome Biol. 2016;17.
12. Richardson TG, Zheng J, Smith GD, et al. Mendelian Randomization Analysis Identifies CpG Sites as Putative Mediators for Genetic Influences on Cardiovascular Disease Risk. Am J Hum Genet. 2017;101(4):590-602.
13. Mendelson MM, Marioni RE, Joehanes R, et al. Association of Body Mass Index with DNA Methylation and Gene Expression in Blood Cells and Relations to Cardiometabolic Disease: A Mendelian Randomization Approach. Plos Med. 2017;14(1).
14. Truong V, Huang SY, Dennis J, et al. Blood triglyceride levels are associated with DNA methylation at the serine metabolism gene PHGDH. Sci Rep-Uk. 2017;7.
15. Zaghlool SB, Mook-Kanamori DO, Kader S, et al. Deep molecular phenotypes link complex disorders and physiological insult to CpG methylation. Hum Mol Genet. 2018.
16. Gaunt TR, Shihab HA, Hemani G, et al. Systematic identification of genetic influences on methylation across the human life course. Genome Biol. 2016;17:61.
17. Hemani G, Zheng J, Wade KH, et al. MR-Base: a platform for systematic causal inference across the phenome using billions of genetic associations. bioRxiv. 2016.
18. Pierce BL, Burgess S. Efficient design for Mendelian randomization studies: subsample and 2-sample instrumental variable estimators. Am J Epidemiol. 2013;178(7):1177-1184.
19. Willer CJ, Schmidt EM, Sengupta S, et al. Discovery and refinement of loci associated with lipid levels. Nat Genet. 2013;45(11):1274-1283.
20. Lawlor DA, Tilling K, Davey Smith G. Triangulation in aetiological epidemiology. Int J Epidemiol. 2016;45(6):1866-1886.
21. Davey Smith G, Hemani G. Mendelian randomization: genetic anchors for causal inference in epidemiological studies. Hum Mol Genet. 2014;23(R1):R89-98.
Show LessCompeting Interests: None declared.
