Machine Learning in Computational Biology CSC 2431

Lecture 4: Missing Heritability Instructor: Anna Goldenberg

Heritability (of a trait)

�  Fraction of phenotypic variability attributable to genetic variation

� NOT: how much genetics influences trait in one person

� Relative to specific population in a particular environment (since contribution of genetic factors is relative to contribution of other factors such as environment)

Heritability Phenotype P, Genotype G, Environment E G: Additive A, Dominant D, Epistatic J Var(P) = Var(G)+Var(E)+2Cov(G,E) Var(G) = Var(A) + Var(D) + Var(J)

Broad Sense Heritability: (includes additive, epistatic, dominant, maternal, paternal)

H2 =V ar(G)

V ar(P )

h2 =V ar(A)

V ar(P )Narrow Sense Heritability (only additive effects)

Regress offspring value on midparent value

← Slope = h2

Example of a height trait

Parent-offspring regression

Heritability = slope Problem: Parents and children share other factors besides genome

Heritability estimates from other regression analyses

Comparison Slope

Midparent-offspring h2

Parent-offspring 1/2h2

Half-sibs 1/4h2

First cousins 1/8h2

• as the groups become less related, the precision of the h2 estimate is reduced.

Estimating Heritability

Falconer’s formula: Twin studies heritability = 2(r(MZ)-r(DZ))

Estimating Heritability

� Tetrachoric correlation: correlation of disease among relatives of particular type vs random pair from population

� Twin Method: resemblance between MZ twins vs DZ twins

�  Falconer’s method � Mixed Linear Models – uses Bayesian

method or MLE to estimate variances from families and pedigrees

Tenesa, Albert, and Chris S. Haley. "The heritability of human disease: estimation, uses and abuses." Nature Reviews Genetics 14.2 (2013): 139-149.

Examples of estimated heritability Trait/Disease Estimated heritability

Alcoholism 50-60%

Alzheimers 58-79%

Asthma 30%

Bipolar Disorder 70%

Depression 50%

Hair Curliness 85-95%

Lung Cancer 8%

Height 81%

Obesity 70%

Longetivity 26%

Sexual Orientation 60%

Schizophrenia 81%

Type 1 diabetes 88%

Type 2 diabetes 26%

http://snpedia.com/index.php/Heritability

Genetically Explained Heritability Disease # of

Loci Heritability Explained

Heritability Estimated

Measure of Heritability

Age related macular degeneration

5 50% 46-71% Sibling recurrent risk

Crohn’s Disease 32 20% 50-60% Genetic risk (liability)

Systemic Lupus Erithematosus

6 15% 44-66% Sibling recurrent risk

Type 2 diabetes 18 6% 26% “

HDL Cholesterol 7 5.2% “

Height 40 5% 81% Phenotypic Variance

Fasting glucose 4 1.5% “

Manolio, Teri A., et al. "Finding the missing heritability of complex diseases." Nature 461.7265 (2009): 747-753.

Important question: how is the genetic heritability estimated from GWAS?

Typically: add up the estimated heritability contributed by each of the genetic variants that have achieved clear genome-wide statistical significance Problem: this is just a lower bound Solution: estimate common variant heritability without identifying the exact loci

Disease # of Loci

Heritability Explained

Heritability Estimated

Measure of Heritability

Type 2 diabetes 18 6% 26% “

Height 40 5% 81% Phenotypic Variance

Miscalculated heritability estimates 1

�  Yang … Visscher, Nature Genetics, 2010: ◦  Problem: Given SNPs do not account for rare

variants, so genetic heritability is under computed ◦ Method: linear mixed models, REML ◦  Fix: model the extent to which the phenotypic

similarity across pairs of individuals in a sample is explained by their genotypic similarity at common variants. ◦  Results: using all SNPs found genetic estimate of

heritability of height to be 45% (compared to 5% before)

Miscalculated heritability estimates 2

� Golan, Lander and Rosset, PNAS, 2014: ◦  Problem: small sample size, small effect size,

true heritability, number of genotyped SNPs ◦ Method: Phenotype-correlation genotype-

correlation (PCGC) ◦  Fix: regress pairs of phenotypes to pairs of

genotypes

Miscalculated heritability estimates

Missing heritability continued �  Much larger numbers of variants of smaller

effects �  Rarer variants not present on arrays �  Structural variants �  Low power to detect gene-gene interactions �  Inadequate accounting for shared environment

by twins

Manolio, Teri A., et al. "Finding the missing heritability of complex diseases." Nature 461.7265 (2009): 747-753.

Missing heritability continued �  Much larger numbers of variants of smaller

effects �  Rarer variants not present on arrays �  Structural variants �  Low power to detect gene-gene interactions �  Inadequate accounting for shared environment

by twins Manolio, Teri A., et al. "Finding the missing heritability of complex diseases." Nature 461.7265 (2009): 747-753.

�  Heterogeneity of phenotype in complex diseases (our inability to distinguish between multiple less common but similarly manifesting diseases)

Missing heritability continued Problem: Much larger numbers of variants of smaller effects Solution: Bigger cohorts (number of people)

Rare variants

Low: 0.5% < MAF < 5% of the population Rare: MAF < 0.5%

Example: 20 variants with MAF < 1% and risk of 3 would account for most variation in Type 2 diabetes! But they were not found yet.

Reason: Small sample sizes or insufficiently large arrays

Solution: pooling (collapsing)

Rare variants �  CAST - cohort allelic sum test, collapses information on all rare variants within a

region (e.g., the exons of a gene) into a single dichotomous variable for each subject by indicating whether or not the subject has any rare variants within the region and then applies a univariate test (Morris and Zeggini, Gen Epi, 2010)

�  Calpha - non-burden-based test, robust to the direction and magnitude of effect. For case-control data, it compares the expected variance to the actual variance of the distribution of allele frequencies (Neale et al, PloS Genetics, 2011)

�  RWAS - Rare variant Weighted Aggregate Statistic –groups variants and computes a weighted sum of differences in mutation counts between case and control individuals. Weights of RWAS are estimated from data to achieve nearly optimal power under a disease model in which all variants make an equally small contribution to population disease risk (Sul et al, Genetics)

�  SKAT – sequence kernel association test: supervised, flexible, computationally efficient regression method to test for association between genetic variants (common and rare) in a region and a continuous or dichotomous trait while easily adjusting for covariates (Wu et al, AJHG, 2011)

�  SKAT+dmGWAS – SKAT + network aggregation (Jia, Bioinformatics, 2011)

Rare variants

Packages and meta-packages!

Lee, Seunggeung, et al. "Rare-variant association analysis: study designs and statistical tests." The American Journal of Human Genetics 95.1 (2014): 5-23.

Structural Variations � Copy number variants (CNVs) – insertions

and deletions � Copy neutral variations – inversions and

translocations – largely unstudied with respect to complex diseases

� Common CNVs are large – 600kb-3Mb � Disease associated CNPs – 20-40kb �  de novo CNVs are shown to be important in

neuropsychiatric and developmental conditions

Examples of identified CNVs

Similar to SNPs – rare variants have large effects common variants have small effects

Problem with studying structure

� Technical – several hundred genes that map to commonly duplicated regions are considered ‘inaccessible’ by most existing genotyping and sequencing technologies due to multicopy nature

� Need – characterize sequence content in highly variable regions

Evan Eichler et al. Nat. Rev. Gen. 2010. Missing Heritability and strategies for finding underlying causes of complex disease

Epistasis �  The departure from the independence of the

effects of different genetic loci

�  AB = Ab + aB – ab – no epistasis �  AB > Ab + aB – ab – synergistic epistasis (SE) �  AB < Ab + aB – ab – antagonistic epistasis

�  E.g. Synthetic lethality – synergistic epistasis of harmful mutations (combined together they kill the organism)

Parent of origin effect

� Example – an allele if inherited from father – hurts, from mother – helps (T2D)

� Variants can increase a recombination rate for fathers and reduce – for mothers

Epistasis method review

Wei et al, Detecting epistasis in human complex traits, Nature Genetics, 2014

Interesting findings �  Hemani et al. Nature 508, 249–253 (2014) Found: found 501 significant pairwise interactions between common SNPs influencing the expression of 238 genes (P < 2.91 × 10−16). Replication of these interactions in two independent data sets11, 12 showed both concordance of direction of epistatic effects (P = 5.56 × 10−31) �  Wood et al: Another explanation for apparent epistasis Found: Using whole-genome sequencing data from 450 individuals we strongly replicated many of the reported interactions but, in each case, a single third variant captured by our sequencing data could explain all of the apparent epistasis.

Phenotypic heterogeneity

Phenotypic heterogeneity

0   0   0   0   0  0   1   1   1   0  1   0   0   0   1  0   2   0   0   0  0   0   0   1   0  1   0   0   0   1  

0   0   2   0   0  0   1   2   1   0  1   0   0   2   0  0   2   0   2   2  0   0   0   1   2  1   0   0   0   2  

CASES

CONTROL

Phenotypic heterogeneity

0   0   0   0   0  0   1   1   1   0  1   0   0   0   1  0   2   0   0   0  0   0   0   1   0  1   0   0   0   1  

0   0   2   0   0  0   1   2   1   0  1   0   0   2   0  0   2   0   2   2  0   0   0   1   2  1   0   0   0   2  

CASES

CONTROL

Age of onset

Warde-Farley, David, et al. ”Mixture model for subphenotyping in GWAS." Pac. Symp. Biocomput. Vol. 17. 2012.

Phenotypic heterogeneity

Next class presentations �  Methods for Rare Variants - Liu, Dajiang J., and Suzanne M. Leal. "Estimating genetic effects and quantifying missing heritability explained by identified rare-variant associations." The American Journal of Human Genetics 91.4 (2012): 585-596.

�  Methods for Epistasis – Schwarz, Daniel F., Inke R. König, and Andreas Ziegler. "On safari to Random Jungle: a fast implementation of Random Forests for high-dimensional data." Bioinformatics 26.14 (2010): 1752-1758.

REMINDER: Project Proposals are due by the end of the week