Discovering Mechanistic Heterogeneity using Mendelian Randomization - PowerPoint PPT Presentation

Discovering Mechanistic Heterogeneity using Mendelian Randomization Qingyuan Zhao Statistical Laboratory, University of Cambridge Joint work with Daniel Iong (who made most of the slides) and Yang Chen September 26, 2020 @ PCIC Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 1 / 21

Outline Motivation 1 Mechanistic Heterogeneity in MR 2 MR-PATH 3 Model Assumptions Statistical inference Results 4 HDL-CHD BMI-T2D Conclusion 5 Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 2 / 21

Motivation Mendelian randomization (MR) MR = Using genetic variation as instrumental varibles. Surging interest in epidemiology and genetics. Number of publications in MR by year (Source: Web of Science). Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 3 / 21

Motivation Example: Causal effect of the LDL-cholesterol Basic idea: People who inherited certain alleles of rs17238484 and rs12916 have naturally higher concentration of LDL cholesterol. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 4 / 21

Motivation Example: Causal effect of the LDL-cholesterol Basic idea: People who inherited certain alleles of rs17238484 and rs12916 have naturally higher concentration of LDL cholesterol. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 4 / 21

Motivation Motivation for this work Exclusion restriction : Instruments (genetic variants) can only affect the outcome through the risk exposure. In MR, this assumption may be violated due to pleiotropy . Many pleiotropy-robust MR methods (e.g. MR-RAPS) have been developed. Most robust MR methods rely on the “effect homogeneity” assumption : the risk exposure has the same causal effect for every individual. Our contributions 1 A novel concept— Mechanistic heterogeneity . 2 A transparent mixture model— MR-PATH . Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 5 / 21

Mechanistic Heterogeneity in MR Review : Linear structural equation model for MR U α 1 Z 1 θ X 1 β X Y . . . θ X p Z p α p For exposure X , outcome Y , unobserved confounding variables U , and SNPs Z 1 , . . . , Z p , the commonly assumed linear structural equation model is given by p � X = θ X i Z i + η X U + E X , i =1 p � Y = β X + α i Z i + η Y U + E Y i =1 Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 6 / 21

Mechanistic Heterogeneity in MR Review : Linear structural equation model for MR p � X = θ X i Z i + η X U + E X , i =1 p � Y = β X + α i Z i + η Y U + E Y i =1 If Z i is a valid instrument, θ X i � = 0, Z i = { U , E X , E Y } , and α i = 0. | However, it is often the case that α i � = 0 due to pleiotropy and multiple causal pathways. If α i � = 0 for some SNPs, then the causal effect β cannot be estimated consistently without further assumptions on α i . e.g. α i ∼ N (0 , τ 2 ) for most SNPs. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 7 / 21

Mechanistic Heterogeneity in MR Two scenarios of mechanistic heterogeneity Z 1 , 1 θ 1 M 1 X 1 . . Z 1 , 1 . U M 1 Z 1 , p 1 . . . β 1 Z 1 , p 1 θ 1 U Z 2 , 1 θ 2 β 2 Z 2 , 1 M 2 X 2 Y . . θ 2 β . M 2 X Y . . . Z 2 , p 2 β 3 Z 2 , p 2 α 2 θ 3 α 3 Z 3 , 1 Z 3 , 1 θ 3 M 3 X 3 . M 3 . . . . . Z 3 , p 3 Z 3 , p 3 X = X 1 + X 2 + X 3 (a) Scenario 1: Multiple pathways of (b) Scenario 2: Multiple mechanisms horizontal pleiotropy. for the exposure X . Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 8 / 21

Mechanistic Heterogeneity in MR Two scenarios of mechanistic heterogeneity If we interpret the diagrams in the previous slide as linear structural equations as before, we can derive the Wald estimands for each pathway. Instruments Z Pathway M Effect of M on X Effect of M on Y Wald estimand Scenario 1 Z 1 , 1 , . . . , Z 1 , p 1 M 1 θ 1 θ 1 β β Z 2 , 1 , . . . , Z 2 , p 2 M 2 θ 2 θ 2 β + α 2 β + α 2 /θ 2 Z 3 , 1 , . . . , Z 3 , p 3 M 3 θ 3 θ 3 β + α 3 β + α 3 /θ 3 Scenario 2 Z 1 , 1 , . . . , Z 1 , p 1 M 1 θ 1 θ 1 β 1 β 1 Z 2 , 1 , . . . , Z 2 , p 2 M 2 θ 2 θ 2 β 2 β 2 Z 3 , 1 , . . . , Z 3 , p 3 M 3 θ 3 θ 3 β 3 β 3 SNPs on the same pathway have the same Wald estimand, while SNPs across different pathways generally have different estimands. Mechanistic heterogeneity can arise even when all SNPs are valid instruments (Scenario 2). Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 9 / 21

Mechanistic Heterogeneity in MR Mechanism-specific causal effect The same clustering phenomenon also occurs in nonlinear models. It is well known that assuming monotonicity , IV nonparametrically estimates the complier average treatment effect (Angrist et al., JASA , 1996). By assuming monotonicity and Pearl’s nonparametric structural equation model with independent errors ( NPSEM-IE ), our paper showed that (if X , Z , M are all binary variables) E [ Y ( X = 1) − Y ( X = 0) | X ( Z kj = 1) > X ( Z kj = 0)] = E [ Y ( X = 1) − Y ( X = 0) | X ( M k = 1) > X ( M k = 0)] , where k indexes the mechanism and j indexes the gene within. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 10 / 21

MR-PATH Model Assumptions MR-PATH : Model Assumptions Assumption (Error-in-variables regression) The observed SNP-exposure and SNP-outcome associations are distributed as � � θ X i � ˆ � σ 2 � � 0 � � θ X i indep. X i ∼ N , , i = 1 , . . . , p , ˆ σ 2 β i θ X i 0 θ Y i Y i where σ X i , σ Y i are (fixed) measurement errors. Assumption (Mixture model for mechanistic heterogeneity) Z i ∼ Categorical ( π 1 , . . . , π K ) , β i | Z i = k ∼ N ( µ k , σ 2 k ) , k = 1 , . . . , K . Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 11 / 21

MR-PATH Statistical inference MR-PATH : Statistical Inference 1 Monte-Carlo EM algorithm for obtaining model parameter estimates 2 Approximate confidence intervals for quantifying uncertainty of the estimates 3 Modified Bayesian Information criterion (BIC) for selecting number of clusters We perform simulation studies to verify the efficacy of these inference procedures. See paper for implementation details. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 12 / 21

Results HDL-CHD Example : HDL-CHD Data (Three-sample MR design) Selection dataset : Teslovich et al. 2010 1 Exposure dataset : Kettunen et al. 2016 2 Outcome dataset : Nikpay et al. 2015 3 1 Tanya M Teslovich et al. “Biological, clinical and population relevance of 95 loci for blood lipids”. In: Nature 466.7307 (2010), pp. 707–713. 2 Johannes Kettunen et al. “Genome-wide study for circulating metabolites identifies 62 loci and reveals novel systemic effects of LPA”. In: Nature communications 7.1 (2016), pp. 1–9. 3 Majid Nikpay et al. “A comprehensive 1000 Genomes–based genome-wide association meta-analysis of coronary artery disease”. In: Nature Genetics 47.10 (2015), p. 1121. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 13 / 21

Results HDL-CHD Example : HDL-CHD SNP association with CHD 0.00 −0.05 −0.10 0.00 0.05 0.10 0.15 SNP association with HDL−C Results of MR-RAPS. Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 14 / 21

Results HDL-CHD Example : HDL-CHD SNP association with CHD 0.00 −0.05 −0.10 1 2 0.00 0.05 0.10 0.15 SNP association with HDL−C Results of MR-PATH ( http://danieliong.me/mr-path/ .) Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 14 / 21

Example : HDL-CHD Qingyuan Zhao (Cambridge) Cluster membership prob. 95% Posterior Credible Interval 0.00 0.25 0.50 0.75 1.00 −1.0 −0.5 0.0 rs838880 rs4846914 rs2954029 rs2814944 rs12678919 rs2241770 rs9326246 rs863750 rs2943634 rs643531 rs17782313 Results rs11869286 MR-PATH rs4731702 rs8071366 rs7134375 HDL-CHD rs2243976 rs4969178 rs4939883 rs4841132 rs2293889 rs4660293 rs3136441 rs2923084 September 26, 2020 @ PCIC rs7679 rs9989419 rs3890182 rs16942887 rs11067231 rs174546 1 rs588136 rs1532085 2 15 / 21

Results HDL-CHD Example : HDL-CHD z−score −7 −5 −3 0 3 5 7 S−HDL−L S−HDL−P S−HDL−TG M−HDL−C M−HDL−CE M−HDL−FC M−HDL−L M−HDL−P M−HDL−PL L−HDL−C L−HDL−CE L−HDL−FC L−HDL−L L−HDL−P L−HDL−PL XL−HDL−C XL−HDL−CE XL−HDL−FC XL−HDL−L XL−HDL−P XL−HDL−PL XL−HDL−TG APOA1 HDL−C HDL−D IDL−C IDL−FC IDL−L IDL−P IDL−PL IDL−TG S−LDL−C S−LDL−L S−LDL−P M−LDL−C M−LDL−CE M−LDL−L M−LDL−P M−LDL−PL L−LDL−C L−LDL−CE L−LDL−FC L−LDL−L L−LDL−P L−LDL−PL APOB LDL−C LDL−D XS−VLDL−L XS−VLDL−P XS−VLDL−PL XS−VLDL−TG S−VLDL−FC S−VLDL−L S−VLDL−P S−VLDL−PL S−VLDL−TG M−VLDL−C M−VLDL−CE M−VLDL−FC M−VLDL−L M−VLDL−P M−VLDL−PL M−VLDL−TG L−VLDL−C L−VLDL−CE L−VLDL−FC L−VLDL−L L−VLDL−P L−VLDL−PL L−VLDL−TG XL−VLDL−L XL−VLDL−P XL−VLDL−PL XL−VLDL−TG XXL−VLDL−L XXL−VLDL−P XXL−VLDL−PL XXL−VLDL−TG VLDL−D rs12678919 rs17782313 rs11869286 rs16942887 rs11067231 rs4846914 rs2954029 rs2814944 rs2241770 rs9326246 rs2943634 rs4731702 rs8071366 rs7134375 rs2243976 rs4969178 rs4939883 rs4841132 rs2293889 rs4660293 rs3136441 rs2923084 rs9989419 rs3890182 rs1532085 rs838880 rs863750 rs643531 rs174546 rs588136 rs7679 Qingyuan Zhao (Cambridge) MR-PATH September 26, 2020 @ PCIC 16 / 21