family-based association tests “if you cannot get rid of the family skeleton, you may as well make...

Family-Based Association Tests

“If you cannot get rid of the family skeleton, you may as well make it

dance” (G.B. Shaw)

Outline

• Overview

• Trios: Transmission Disequilibrium Test (TDT)

• Discordant sibships: Conditional logistic regression

• General Pedigree: FBAT test

• Comparisons and extensions

Family-based designs

• Discordant sibpairs, sibships

• Affected offspring and their parents– Trios (2 parents, child) common design

• Complex nuclear families

• Extended pedigrees– Leftovers from linkage (next lecture)

Family-based vs. Case-control

Family-based vs. Case-control• Completely robust to

population substructure

• Robust to HWE failure

• More powerful for very rare highly penetrant diseases (e.g., arguments coming back for sequencing)

• Pseudo-controls (e.g., longevity study…), but much harder to recruit (esp. late onset diseases, children generally not difficult)

• Adjusting for PC’s/AIMs does well in practice, now

• Test for HWE in controls

• More powerful in most other situations

• More careful selection of good controls (sort of)

Family-based vs. Case-control• Detect genotyping

error (Mendel error)• More complex

analysis (but doable)

• Cryptics, maybe

• Standard regression methods

Mendel’s laws

• Recall the playing cards example...

• One allele from each parent for each gene– Many family based tests based on this, rather

than estimating allele frequencies (case-control)

Mendelian transmission: Ex

• E.g., parents are Aa, Aa:– P(offspring=AA | Mother=Aa,Father=Aa)=?– P(offspring=Aa | Mother=Aa,Father=Aa)=?– P(offpsring=aa | Mother=Aa, Father=Aa)=?

M\F A a

A AA Aa

a Aa aa


• E.g., parents are Aa, Aa:– P(offspring=AA | Mother=Aa,Father=Aa)=1/4– P(offspring=Aa | Mother=Aa,Father=Aa)=1/2– P(offpsring=aa | Mother=Aa, Father=Aa)=1/4

M\F A a

A AA Aa

a Aa aa

Conditioning on parents...


• E.g., parents are AA, Aa:– P(offspring=AA | Mother=AA,Father=Aa)=?– P(offspring=Aa | Mother=AA,Father=Aa)=?– P(offpsring=aa | Mother=AA, Father=Aa)=?

M\F A a

A AA Aa

A AA Aa


• E.g., parents are AA, Aa:– P(offspring=AA | Mother=AA,Father=Aa)=1/2– P(offspring=Aa | Mother=AA,Father=Aa)=1/2– P(offpsring=aa | Mother=AA, Father=Aa)=0

M\F A a

A AA Aa

A AA Aa


• E.g., parents are AA, AA:– P(offspring=AA | Mother=AA,Father=AA)=?– P(offspring=Aa | Mother=AA,Father=AA)=?– P(offpsring=aa | Mother=AA, Father=AA)=?

M\F A A

A AA AA

A AA AA


• E.g., parents are AA, AA:– P(offspring=AA | Mother=AA,Father=AA)=1– P(offspring=Aa | Mother=AA,Father=AA)=0– P(offpsring=aa | Mother=AA, Father=AA)=0

M\F A A

A AA AA

A AA AAHomozygote parents are “non-informative” (no variation in offspring’s conditional genotype distribution)

Outline

• Overview





Trios: Transmission Disequilibrium Test (TDT)

• Test based on transmissions from parents to offspring

• Assumptions– Parents’ and offspring genotypes known

– dichotomous phenotype (though Q-TDT), only affected offspring

• Count transmissions from heterozygote parents, and compare to expected transmissions– Mendel’s laws of segregation (previous slides), not control group

– test for over/under-transmission of alleles in cases (intuition…)

• Conditional test– offspring affection status

– Parental genotypes (conditions out allele frequencies, which is what case-control is based on testing)

Spielmen et al., AJHG 1993


• w AA parents (transmit one A, do not transmit other A)

• z aa parents (transmit one a, do not transmit other a)

• x Aa parents that transmit A, do not transmit a

• y Aa parents that transmit a, do not transmit A

A a

A w x

a y z

Transmitted parental allele

Non-transmitted parental allele

Possible Parental Configurations

• AA-AA, AA-Aa, AA-aa, Aa-AA, Aa-Aa, Aa-aa, aa-AA, aa-Aa, aa-aa– (Ones not bolded are symmetric for what we

will do next, e.g., AA-Aa == Aa-AA– Six possible configurations

Both parents homozygous

• Offspring genotype is deterministic, no variation, not informative!

A a

A 2 0

a 0 0


Non-transmitted parental allele AA-AA

| AA



A a

A 0 0

a 0 2


Non-transmitted parental allele aa-aa

| aa



A a

A 1 0

a 0 1


Non-transmitted parental allele AA-aa

| Aa

One parent heterozygous

• Variation from one parent

A a

A 1 1

a 0 0


Non-transmitted parental allele AA-Aa

|AA,Aa.5 .5 ← Pr

A a

A 1 0

a 1 0



One parent heterozygous

• Variation from one parent

A a

A 0 1

a 0 1


Non-transmitted parental allele Aa-aa

|Aa,aa.5 .5 ← Pr

A a

A 0 0

a 1 1



Both parents heterozygous

• Variation from both parents

A a

A 0 2

a 0 0


Non-transmitted parental allele Aa-Aa

|AA,Aa,aa.5 .5 ← Pr

A a

A 0 1

a 1 0



A a

A 0 0

a 2 1




• w AA parents (transmit one A, do not transmit other A)

• z aa parents (transmit one a, do not transmit other a)

• x Aa parents that transmit A, do not transmit a

• y Aa parents that transmit a, do not transmit A

A a

A w x

a y z



Transmission Disequilibrium Test (TDT)

• No variation in w or z (recall homozygous parents non informative)

• (x-y)2/(x+y) ~ 12; it’s just special case of McNemar’s test

• Think of it as testing are there an excess of the A allele in the affected offspring than would happen by Mendel's laws?

A a

A w x

a y z



Transmission Disequilibrium Test (TDT)

• Example from the text: 94 families, 78 parents transmit allele A, 46 transmit allele a

• (78-46)2/(78+46)=8.26, p-value=0.004

A a

A ? 78

a 46 ?



Insulin Dependent Diabetes Mellitus (IDDM)

Spielman et al., 1993

Limitations of TDT

• Only affected offspring

• Only dichotomous phenotypes

• Bi-allelic markers

• Additive genetic model

• No missing parents

• Incorporating siblings assumes no linkage (more next time)

• Can’t do multiple markers, multiple phenotypes

Key features of the TDT

• Random variable in analysis is offspring genotype

• Parental genotypes fixed

• Trait fixed (condition on affected offspring)

Outline

• Overview




• Extra

Discordant sibships

• Conditional logistic regression

– P(Y1=1|Y1+Y2=1,g1,g2,…)

– Matching each sib together, conditions on the fact that they have discordant phenotypes

– Standard model for disease as in logistic regression, just matching based on family strata

• Can also use FBAT framework– Similar power for main effects

– Greater power for GxE (Witte, AJE 1999; Chatterjee et al., Gen Epi 2005; Hoffmann et al., Biometrics 2011)

• You will go through an example in the homework

Outline

• Overview





FBAT: More general methodology

• Maintains general principals of TDT

• Other genetic models (dominant, recessive, …)

• Additional siblings, extended pedigrees, missing parents

• Multiple markers, (haplotypes)

• Test statistic intuition: covariance between offspring trait and genotype

FBAT: Extending TDT to more general families

• For the moment, assume parents are genotyped

• Let i index across families, j offspring

• Score test of f({offspring genotype}ij|traitij,parentsi), use Mendel’s laws, Bayes rule– U=i,j (traitij-offset) x ({offspring genotype}ij - E[{offspring

genotype}ij|parentsi])

– Assume trait is continuous or binary– Assume offset is mean (continuous) or population prevalence

(dichotomous)

– Condition on Parents (avoid specification of allele distribution)

– Condition on offspring phenotypes (avoid specification of trait distribution)

FBAT: Extending the TDT to more general families (cont.)

• U=i,j (traitij-offset) x ({offspring genotype}ij - E[{offspring genotype}ij|parentsi])

• Intuition: Like a sample covariance between trait and genotype

• ZFBAT=U/sqrt(var(U)) ~ N(0,1)

FBAT: Extending the TDT to more general families (cont.)

• U=i,j (traitij-offset) x ({offspring genotype}ij -E[{offspring genotype}ij|parentsi])

• Let oij={offspring genotype}ij

• Let Pi=parentsi

• E[oij|Pi]

= X(AA)P(oij=AA|Pi) + X(AA)P(oij=AA|Pi)

+ X(AA)P(oij=AA|Pi)

• Essentially using Mendel’s laws, as we calculated earlier

Seem familiar? FBAT=TDT

• If Y=affection status (1=affected, 0=unaffected), offset=0, then FBAT==TDT

• Similarly conditional logistic regression roughly equivalent to TDT in terms of power for main effects

FBAT offset for dichotomous traits

• If all offspring are affected, then it does not matter– For rare diseases, affected most informative– For more common, can get some information

from unaffecteds

• Population prevalence, allows one to gain a little information from unaffecteds

Offset choice

Disease prevalence K = 0.05, allele frequency of the disease gene p=0.05, attributable fraction of the disease due to carrying at least one disease gene AF=0.3, significance level α=10−4 and sample size 100

Lange and Laird (2002)

Disease prevalence K=0.3, allele frequency of the disease gene p=0.143, attributable fraction of the disease due to carrying at least one disease gene AF=0.25, significancelevel α=0.01 and sample size 100.

Offset choice

FBAT offset for continuous traits

• The trait mean– (Optimal choice is E(Y), depends on ascertainment)

• Residual from the trait adjusted for covariates– e.g., regress gender on bmi, use residual

– Suppose Y is your phenotype of interest, Z covariate

– Linear regression Y = 0 + 1Z

– Compute residual R=Y- (0 + 1Z)

– Use R as trait in FBAT

Continuous vs. Dichotomous trait

• Modeling as continuous trait -- more powerful

• With highly selected traits, dichotomizing may be preferable– Using mean for offset is a poor choice here– Results very sensitive to offset choice– Dichotomizing will lose power compared to

best offset choice

Offset general comments

• Very poor choice -- poor power

• More complicated slightly more efficient offsets are also available

Childhood asthma management program (CAMP) example

• 696 trios

• bi-allelic locus in IL13 gene

• five groups of 22 quantitative phenotypes

DeMeo Gen Epi, 2006

DeMeo Gen Epi, 2006

Can also do a multi-marker (gene-based) test...

Obesity GWAS example

• BMI follow-up for 24 years

• 86,604 SNPs

• 694 participants

• One of the first GWAS successes

•GWAS example uses clever screening approach, longitudinal phenotype data...

Obesity example: Longitudinal phenotype

Obesity example: Screening based on “conditional mean model”

• Prioritizes SNPs based on modeling X imputed from parental genotypes (PBAT software)– f(X,P)=f(X|P)f(P)

• Screening not robust to population substructure, but later testing is (so doesn’t matter)

Obesity example: Results

Screening based on “conditional power”...

• Started with only analyze “top k” (Lange et al.)– Criticized, not looking at all SNPs, and in

practice...

• Prior distribution for type I error (Iulianna et al, AJHG 2007)

• Bayesian (Naylor et al, Gen Epi 2010)

Critiques

• Only modeling the offspring conditional on parents, not using parents?– Other models do, not robust to population

stratification (but could adjust for covariates…)– Are used in conditional mean model screening

approach

Outline

• Overview





Power of FBAT, CACO, Rare disease

200 trios (600 genotypes)

200 DSP (400 genotypes)

200 sibtrios (3 offspring, no parents, 600 genotypes)

200 cases/200 controls (400 genotypes)

OR=1.5

In your book, but not necessarily a fair comparison...

Power of common disease200 trios (600 genotypes)

200 DSP (400 genotypes)

200 sibtrios (3 offspring, no parents, 600 genotypes)

200 cases/200 controls (400 genotypes)

OR=1.5

Final thoughts

• FBAT also extended to– X chromosome– Survival Analysis– Multi-marker– Multi-phenotype– Haplotypes– Missing parents– Gene-environment/gene-gene interactions– Meta-analysis

Final thoughts

• Other likelihood approaches, Shaid 1989, Cordell 2000, Dudbridge 2010 (software unphased)

• Other approach by Allison 1997, Abecasis 2009 for quantitative traits

• Also simultaneous modeling of family and case-control data (Sage/Mendel software)– If large enough sample, maybe cryptics?

Software

• FBAT http://www.biostat.harvard.edu/fbat/fbat.htm

• PBAT https://webapps.sph.harvard.edu/live/pbat/,– P2BAT

http://sites.google.com/site/thomashomannproject/software/pbatr-1

• Dudbridge's UNPHASED – http://homepages.lshtm.ac.uk/frankdudbridge/

software/unphased/

• Clayton's software http://www-gene.cimr.cam.ac.uk/clayton/software/

family-based association tests “if you cannot get rid of the family skeleton, you may as well make...

Documents

aa mother

homozygote parents

heterozygote parents

fbat test comparisons

casecontrolcompletely

genemany family

family skeleton

hwe failuremore powerful