MENDELIAN RANDOMIZATION Maria Carolina Borges Research Fellow MRC - - PowerPoint PPT Presentation

MENDELIAN RANDOMIZATION

Maria Carolina Borges

Research Fellow MRC Integrative Epidemiology Unit University of Bristol UK

Outline

• Motivation
• Assumptions
• One-sample MR
• Two-sample MR
• Recent extensions
• MR-Base

MOTIVATION

Why Mendelian randomization?

4

Causal inference & Epidemiology

Confounding Bias

?

Reverse causation

6 N pair-wise associations Expected (P ≤ 0.01) Observed (P ≤ 0.01) P value for

• bserved x

expected 96 (non- genetic) traits 4560 45.6 (1%) 2036 (44.6%) < 0.000001 23 SNPs 253 2.5 (1%) 4 (1.6%) 0.33 96 traits x 23 SNPs 2208 22.1 (1%) 27 (1.1%) 0.29

Bone Marrow Transplant. 1991;7 Suppl 3:9-12. Lancet 1986;i:507–08

Mendel’s Second Law: independent assortment

Gregor Mendel (1822–1884): “the behavior of each pair of differentiating characteristics in hybrid union is independent of the other differences between the two original plants, and, further, the hybrid produces just so many kinds of egg and pollen cells as there are possible constant combination forms...”

Inheritance of one trait is independent

• f the inheritance of other traits

Randomization

Mendelian randomization Randomized controlled trial

Random segregation of alleles Random allocation Exposed: Allele A Control: Other allele Control: No intervention Exposed: Intervention Outcomes compared between groups Outcomes compared between groups Confounders equal between groups Confounders equal between groups

Adapted from Ebrahim, Davey-Smith, 2008

Mendelian randomization

X Y U Z

Z: genetic instrument X: exposure Y: outcome U: confounder

Z: rs12345 X: LDLc Y: CHD U Z → X: 0.05 mmol/L of LDLc per T allele Z → Y: 0.03 log odds CHD per T allele X → Y: 0.03/0.05=0.6 log odds CHD per 1 mmol/L of LDLc (OR=1.82)

Instrumental variable: randomization to HMGCR variant (rs12345)

Hypothetical example: LDL-c → CHD

ASSUMPTIONS

Instrumental variable (IV) assumptions

U X Y Z

• Z is strongly associated with X
• Z is independent of U
• Z is independent of Y, given X & U

IV1 IV2 IV3 Z: genetic IV X: exposure Y: outcome U: confounder

Instrumental variable (IV) assumptions

U X Y Z

• Z is strongly associated with X

IV1 Z: genetic IV X: exposure Y: outcome U: confounder

• Loss of power
• Bias
• Finite samples: confounders will not be perfectly balanced between

genotypic subgroups

• If IV weak, this may explain more of phenotypic differences than IV
• Bias towards confounded estimate (one-sample MR) or towards null

(two-sample MR with no sample overlap)

Weak instruments

Burgess et al., 2011; 2016

Instrumental variable (IV) assumptions

U X Y Z

• Z is independent of U

IV2 Z: genetic IV X: exposure Y: outcome U: confounder

Population stratification

Balding, 2006

U X Y Z

U: genetic ancestry

Instrumental variable (IV) assumptions

U X Y Z

• Z is independent of Y, given X & U

IV3 Z: genetic IV X: exposure Y: outcome U: confounder

Violations of exclusion restriction

VanderWeele et al. 2014

Phenotype Abbreviation Neurological phenotypes Alzheimer disease AD Migraine MIGR Parkinson disease PD Photic sneeze reflex PS Schizophrenia SCZ Anthropometric and social traits Beighton hypermobility BHM Breast size CUP Body mass index BMI Bone mineral density (femoral neck) FNBMD Bone mineral density (lumbar spine) LSBMD Chin dimples DIMP Educational attainment EDU Height HEIGHT Male-pattern baldness MPB Nearsightedness NST Nose size NOSE Waist–hip ratio WHR Unibrow UB Immune-related traits Any allergies ALL Asthma ATH Childhood ear infections CEI Crohn's disease CD Hypothyroidism HTHY Rheumatoid arthritis RA Tonsillectomy TS Ulcerative colitis UC Metabolic phenotypes Age at menarche AAM Age at menarche (23andMe) AAM (23) Age at voice drop AVD Coronary artery disease CAD Type 2 diabetes T2D Fasting glucose FG Low-density lipoproteins LDL High-density lipoproteins HDL Triglycerides TG Total cholesterol TC Hematopoietic traits Hemoglobin HB Mean cell hemoglobin concentration MCHC Mean red blood cell volume MCV Packed red blood cell volume PCV Red blood cell count RBC Platelet count PLT Mean platelet volume MPV

Pickrell et al., 2016; Visscher, Yang, 2016

The ubiquity of pleiotropy

What is the underlying causal model?

Z X Y Z X Y Z Y X

✓ Vertical pleiotropy

(mediation) X Horizontal pleiotropy

ONE-SAMPLE MR

One-sample Mendelian randomization (MR)

Definition

Genotypes (Z), exposure (X), and outcome (Y) available from individuals in the same sample

One-sample MR

Z X Y U

βZX βZY

One-sample MR

Key aspects

• Identify genetic instruments for the exposure
• Explore violations of IV assumptions
• Generate MR estimates
• Run sensitivity analyses

Identifying genetic instruments

SNPs with well understood functions….

• r via GWAS

26

Explore violations of IV assumptions

Instrument strength Endogeneity Overidentification

Burgess et al., 2011; Davies et al., 2013

IV1 IV2 IV3

One-sample MR estimates

Common one-sample MR estimator

Outcome Exposure Instruments (37 SNPs) Overidentification test

First stage regression

Instrument strength Endogeneity test

One-sample MR using polygenic score

Polygenic score

• Increases variance explained (compared to single SNPs)
• Avoid many weak instrument bias (compared to many separate SNPs)

TWO-SAMPLE MR

SNP-exposure association SNP-outcome association Effect of exposure on outcome Underlying population

Two-sample Mendelian randomization (MR)

Definition

SNP-exposure and SNP-outcome association estimates from two independent samples from the same underlying population

Two-sample MR

Z X Y U

βZX βZY

One-sample MR Two-sample MR

Hartwig et al., 2017

Why did two-sample MR become so popular?

Genome-wide association studies (GWAS)

Key aspects

• 1. Identify genetic instruments for the exposure
• 2. Extract summary data
• 3. Harmonise the two datasets
• 4. Explore violations of IV assumptions
• 5. Generate MR estimates
• 6. Run sensitivity analyses

Harmonise datasets

• Ensure that all instruments in dataset 1 are associated with exposure in the

same direction

• Ensure datasets 1 and 2 are identically coded
• Check and correct palindromic SNPs
• Check quality of harmonisation

Hartwig et al., 2017

Explore violations of IV assumptions

• F-statistics

Burgess et al., 2016 N: sample size K: number of Ivs R2: variance of X by IVs SD: standard deviation α: SNP-exposure association in SD units MAF: minor allele frequency

For each IV*:

*If multiple & independent SNPs are available, R2 can be added up to calculate F statistics

Instrument strength IV1

Explore violations of IV assumptions

Explore presence of horizontal pleiotropy IV3

Heterogeneity & Asymmetry

Heterogeneity

rs1 rs2 rs3 rs4 rs5 rs6 Causal estimate (βIV = βzy /βzx) 1

• 1

Del Greco et al., 2015; Burgess et al., 2017

Substantial heterogeneity indicates that either modelling or IV assumptions are violated

m: number of IVs

Cochran’s Q statistic

Asymmetry

Causal estimate (βxy) Precision (1/SE) Causal estimate (βxy) Precision (1/SE)

Funnel plot symmetric: Balanced pleiotropy (IVW OK) Funnel plot asymmetric: Directional pleiotropy (IVW biased)

MR estimates: single instrument

• For a single instrument → Wald ratio

መ 𝛾𝐽𝑊 = መ 𝛾𝑎𝑍 መ 𝛾𝑎𝑌

• Where both 𝛾’s on the right hand side are regression

coefficients

Assumption: no invalid instruments

• Pooled Wald ratios (fixed- vs random effects)

MR estimates: multiple instruments

rs1 rs2 rs3 rs4 rs5 rs6 Causal estimate (βIV = βzy /βzx) 1

• 1

Del Greco et al., 2015; Burgess et al., 2017

Assumption: no invalid instruments

• Inverse variance weighted (IVW) method

MR estimates: multiple instruments

βzy βzx βIVW

regress βzy ~ βzx [weigths=1/seβzy^2] *** *** With intercept constraint to be zero Assumption: no invalid instruments

Sensitivity analyses

• Many new methods relax the assumption of no invalid
• instruments. E.g:
• MR-Egger
• Median-based estimator
• Mean-based estimator
• And many others ...
• Consistency of results across methods is key (≠ methods,

≠ assumptions)

MR-Egger

IVW OK MR-Egger OK IVW biased MR-Egger OK βzy βzy βzx βzx βIVW βIVW βEgger βEgger

regress βzy βzx [aw=1/seβzy^2]

αEgger αEgger=0

αEgger → non-zero estimate is evidence for directional pleiotropy βEgger → causal effect estimate adjusted for directional pleiotropy

Bowden et al., 2015, 2016; Burgess, Thompson, 2017

MR-Egger

• MR-Egger allows 100% of invalid IVs, but requires InSIDE
• INSIDE (Instrument Strength Independent of Direct Effect) assumption: SNP-

exposure effects should NOT correlate with the horizontal pleiotropic effects

• Low power particularly when the SNP-exposure effect sizes are

relatively homogeneous

• SNP-exposure estimates have to be oriented to be positive (and the

SNP-outcome effects flipped accordingly)

• More susceptible to regression dilution bias
• Individual outliers can have a large influence on causal estimates

Bowden et al., 2016; Burgess, Thompson, 2017

Median based estimators

Bowden et al., 2016

βzy βzx βzy βzx

• InSIDE not required
• If true, the median ratio estimate is a reliable estimate for the causal effect
• More efficient to use weighted analysis (assumption: set of instruments accounting for

50% or more of the total weight is valid)

Hypothetical example – finite sample Hypothetical example – infinite sample

Mode based estimators (MBE)

βzy βzx βzy βzx

Hypothetical example: Truth=MBE Hypothetical example: Truth≠MBE

• InSIDE not required
• Zero Modal Pleiotropy Assumption (ZEMPA)
• Current implementation requires specification of smoothing parameter

Hartwig et al., 2017

RECENT EXTENSIONS

Zheng et al., 2017

Multivariable MR Factorial MR Two-step MR (mediation) Bidirectional MR

MR-BASE

What is MR-Base?

Web server Web-based API GWAS database

• Web interface
• www.mrbase.org/beta
• R package
• TwoSampleMR

MR-Base access

Information on two-sample MR R package: https://github.com/MRCIEU/TwoSampleMR

Key messages

• MR uses genetic variants as proxies of modifiable exposures and can
• vercome some key limitations of observational studies
• MR can reliably test for causal relations provided that IV assumptions are met
• Horizontal pleiotropy is one of the main threats to the validity of MR studies
• Two-sample MR can be performed with free, open access, summary data

from GWAS

• Consistency of results across methods is key to reliable causal inference

Acknowledgements

• Debbie A Lawlor
• Jack Bowden
• Sarah Lewis
• Chris Zheng

References

Motivation

• Davey Smith G, Ebrahim S. Epidemiology--is it time to call it a day? Int J Epidemiol. 2001;30(1):1-

11.

• Smith GD, Lawlor DA, Harbord R, Timpson N, Day I, Ebrahim S. Clustered environments and

randomized genes: a fundamental distinction between conventional and genetic epidemiology. PLoS

• Med. 2007;4(12):e352.
• Gray R, Wheatley K. How to avoid bias when comparing bone marrow transplantation with
• chemotherapy. Bone Marrow Transplant. 1991;7 Suppl 3:9-12.
• Katan MB. Apolipoprotein E isoforms, serum cholesterol, and cancer. Lancet. 1986;1(8479):507-8.
• Smith GD, Ebrahim S. 'Mendelian randomization': can genetic epidemiology contribute to

understanding environmental determinants of disease? Int J Epidemiol. 2003;32(1):1-22.

• Ebrahim S., Davey Smith G. Mendelian randomization: can genetic epidemiology help redress the

failures of observational epidemiology? Hum. Genet. 2008;123:15–33.

References

Weak instrument bias

• Burgess S, Thompson SG; CRP CHD Genetics Collaboration.

Avoiding bias from weak instruments in Mendelian randomization studies. Int J

• Epidemiol. 2011;40(3):755-64.
• Burgess S, Davies NM, Thompson SG. Bias due to participant overlap in two-

sample Mendelian randomization. Genet Epidemiol. 2016;40(7):597-608.

Population stratification

• Balding DJ. A tutorial on statistical methods for population association studies. Nat Rev
• Genet. 2006;7(10):781-91.

Exclusion restriction assumption

• VanderWeele TJ et al. Methodological challenges in mendelian randomization.
• Epidemiology. 2014;25(3):427-35.

Pleiotropy

• Visscher PM, Yang J. A plethora of pleiotropy across complex traits. Nat Genet. 2016;48(7):707-8.
• Pickrell JK, Berisa T, Liu JZ, Ségurel L, Tung JY, Hinds DA.

Detection and interpretation of shared genetic influences on 42 human traits. Nat Genet. 2016 Jul;48(7):709-17.

References

One-sample MR

• Burgess S, Thompson SG; CRP CHD Genetics Collaboration.

Avoiding bias from weak instruments in Mendelian randomization studies. Int J

• Epidemiol. 2011;40(3):755-64.
• Davies NM, Smith GD, Windmeijer F, Martin RM. Issues in the reporting and conduct
• f instrumental variable studies: a systematic review.
• Epidemiology. 2013 May;24(3):363-9.
• Burgess S, Small DS, Thompson SG. A review of instrumental variable estimators

for Mendelian randomization. Stat Methods Med Res. 2017 Oct;26(5):2333-2355.

References

Two-sample MR

• Hartwig FP, Davies NM, Hemani G, Davey Smith G. Two-sample Mendelian randomization: avoiding

the downsides of a powerful, widely applicable but potentially fallible technique. Int J Epidemiol. 2016 Dec 1;45(6):1717-1726.

• Burgess S, Davies NM, Thompson SG. Bias due to participant overlap in two-

sample Mendelian randomization. Genet Epidemiol. 2016 Nov;40(7):597-608.

• Greco M FD, Minelli C, Sheehan NA, Thompson JR. Detecting pleiotropy in Mendelian

randomisation studies with summary data and a continuous outcome. Stat Med. 2015 Sep 20;34(21):2926-40.

• Burgess S, Bowden J, Fall T, Ingelsson E, Thompson SG. Sensitivity Analyses for Robust Causal

Inference from Mendelian Randomization Analyses with Multiple Genetic Variants.

• Epidemiology. 2017 Jan;28(1):30-42.
• Bowden J, Davey Smith G, Burgess S. Mendelian randomization with invalid instruments: effect

estimation and bias detection through Egger regression. Int J Epidemiol. 2015;44(2):512-25.

• Burgess S, Thompson SG. Interpreting findings from Mendelian randomization using the MR-

Egger method. Eur J Epidemiol. 2017;32(5):377-389.

• Bowden et al. Assessing the suitability of summary data for two-sample Mendelian randomization

analyses using MR-Egger regression: the role of the I2 statistic. Int J Epidemiol. 2016;45(6):1961- 1974.

• Bowden J et al. Consistent Estimation in Mendelian Randomization with Some Invalid Instruments

Using a Weighted Median Estimator. Genet Epidemiol. 2016;40(4):304-14.

• Hartwig FP, Davey Smith G, Bowden J. Robust inference in summary data Mendelian randomization

via the zero modal pleiotropy assumption. Int J Epidemiol. 2017;46(6):1985-1998.

References

MR extensions

• Zheng J, Baird D, Borges MC, Bowden J, Hemani G, Haycock P, Evans DM,

Smith GD. Recent Developments in Mendelian Randomization Studies. Curr Epidemiol Rep. 2017;4(4):330-345.

MR-base

• Hemani G et al. The MR-Base platform supports systematic causal inference

across the human phenome. eLife 2018. doi: https://doi.org/10.7554/eLife.34408