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

4 Why Mendelian randomization?

Causal inference & Epidemiology Confounding Bias Reverse causation ?

6 P value for Expected Observed N pair-wise observed x associations ( P ≤ 0.01) ( P ≤ 0.01) expected 96 (non- 4560 45.6 (1%) 2036 (44.6%) < 0.000001 genetic) traits 23 SNPs 253 2.5 (1%) 4 (1.6%) 0.33 96 traits x 23 2208 22.1 (1%) 27 (1.1%) 0.29 SNPs

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 Randomized randomization controlled trial Random Random segregation of allocation alleles Exposed: Control: Exposed: Control: Allele A Other allele Intervention No intervention Confounders Confounders equal between equal between groups groups Outcomes compared Outcomes compared between groups between groups Adapted from Ebrahim, Davey-Smith, 2008

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

Hypothetical example: LDL-c → CHD Instrumental variable: randomization to HMGCR variant (rs12345) U X: LDLc Y: CHD Z: rs12345 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)

ASSUMPTIONS

Instrumental variable (IV) assumptions Z: genetic IV U X: exposure IV2 Y: outcome Y X Z U: confounder IV1 IV3 • Z is strongly associated with X • Z is independent of U • Z is independent of Y, given X & U

Instrumental variable (IV) assumptions Z: genetic IV U X: exposure Y: outcome Y X Z U: confounder IV1 • Z is strongly associated with X

Weak instruments • 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) Burgess et al., 2011; 2016

Instrumental variable (IV) assumptions Z: genetic IV U X: exposure IV2 Y: outcome Y X Z U: confounder • Z is independent of U

Population stratification U X Z Y U: genetic ancestry Balding, 2006

Instrumental variable (IV) assumptions Z: genetic IV U X: exposure Y: outcome Y X Z U: confounder IV3 • Z is independent of Y, given X & U

Violations of exclusion restriction VanderWeele et al. 2014

Phenotype Abbreviation Neurological phenotypes The ubiquity of pleiotropy 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

What is the underlying causal model? ✓ Vertical pleiotropy X Horizontal pleiotropy (mediation) Z X Y Z X Y Z X Y

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 U β ZX X Z Y β ZY One-sample MR

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

26 Identifying genetic instruments SNPs with well understood functions…. or via GWAS

Explore violations of IV assumptions Instrument strength IV1 Endogeneity IV2 Overidentification IV3 Burgess et al., 2011; Davies et al., 2013

One-sample MR estimates Outcome Exposure Instruments (37 SNPs) Common one-sample MR estimator Overidentification test

First stage regression Instrument strength Endogeneity test

One-sample MR using polygenic score - Increases variance explained (compared to single SNPs) Polygenic score - Avoid many weak instrument bias (compared to many separate SNPs)

TWO-SAMPLE MR

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

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 U β ZX X Z Y β ZY 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 IV1 Instrument strength • F-statistics N: sample size K: number of Ivs R 2 : variance of X by IVs For each IV*: α : SNP-exposure association in SD units MAF: minor allele frequency *If multiple & independent SNPs are available, R 2 can be added up to calculate F statistics SD: standard deviation Burgess et al., 2016

Explore violations of IV assumptions Explore presence of horizontal pleiotropy IV3 Heterogeneity & Asymmetry

Substantial heterogeneity indicates that either Heterogeneity modelling or IV assumptions are violated rs1 Cochran’s Q statistic rs2 rs3 rs4 rs5 rs6 m : number of IVs -1 0 1 Causal estimate ( β IV = β zy / β zx ) Del Greco et al., 2015; Burgess et al., 2017

Asymmetry Precision (1/SE) Precision (1/SE) Causal estimate ( β xy ) Causal estimate ( β xy ) Funnel plot symmetric: Funnel plot asymmetric: Balanced pleiotropy (IVW OK) Directional pleiotropy (IVW biased)

MR estimates: single instrument • For a single instrument → Wald ratio መ 𝛾 𝑎𝑍 መ 𝛾 𝐽𝑊 = መ 𝛾 𝑎𝑌 • Where both 𝛾 ’s on the right hand side are regression coefficients Assumption: no invalid instruments

MR estimates: multiple instruments • Pooled Wald ratios (fixed- vs random effects) rs1 rs2 rs3 rs4 rs5 rs6 -1 0 1 Causal estimate ( β IV = β zy / β zx ) Assumption: no invalid instruments Del Greco et al., 2015; Burgess et al., 2017

MR estimates: multiple instruments • Inverse variance weighted (IVW) method β IVW regress β zy ~ β zx [weigths=1/se β zy ^2] *** β zy *** With intercept constraint to be zero β zx 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 regress β zy β zx [aw=1/se β zy ^2] β Egger β IVW β IVW β zy β zy β Egger α Egger α Egger =0 β zx β zx IVW OK IVW biased MR-Egger OK MR-Egger OK α Egger → non-zero estimate is evidence for directional pleiotropy β Egger → causal effect estimate adjusted for directional pleiotropy Bowden et al., 2015, 2016; Burgess, Thompson, 2017