MENDELIAN

RANDOMIZATIONMaria 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

observed x

expected

96 (non-

genetic) traits4560 45.6 (1%) 2036 (44.6%) < 0.000001

23 SNPs 253 2.5 (1%) 4 (1.6%) 0.33

96 traits x 23

SNPs2208 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

of 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 YZ

• 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 YZ

• 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 YZ

• Z is independent of U

IV2

Z: genetic IV

X: exposure

Y: outcome

U: confounder

Population stratification

Balding, 2006

U

X YZ

U: genetic ancestry

Instrumental variable (IV) assumptions

U

X YZ

• 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….

or 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 sizeK: number of IvsR2: variance of X by IVs

SD: standard deviation

α: SNP-exposure association in SD unitsMAF: 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 pleiotropyIV3

Heterogeneity & Asymmetry

Heterogeneity

rs1

rs2

rs3

rs4

rs5

rs6

Causal estimate (βIV = βzy /βzx)

0 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)

Pre

cis

ion (

1/S

E)

Causal estimate (βxy)

Pre

cis

ion (

1/S

E)

Funnel plot symmetric:

Balanced pleiotropy (IVW OK)Funnel plot asymmetric:

Directional pleiotropy (IVW biased)

MR estimates: single instrument

• For a single instrument → Wald ratio

መ𝛽𝐼𝑉 =መ𝛽𝑍𝑌መ𝛽𝑍𝑋

• Where both 𝛽’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)

0 1-1

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

βzyβzy

βzxβzx

βIVWβIVW

βEgger

βEgger

regress βzy βzx [aw=1/seβzy^2]

αEggerαEgger=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 parameterHartwig 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

overcome 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.

ReferencesWeak 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

of 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.

ReferencesTwo-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