Complex Adaptive Systems and Human Health: Complex Adaptive Systems and Human Health: Statistical Approaches in PharmacogenomicsStatistical Approaches in Pharmacogenomics

Kim E. Zerba, Ph.D.Kim E. Zerba, Ph.D.

Bristol-Myers SquibbBristol-Myers Squibb

FDA/Industry Statistics WorkshopFDA/Industry Statistics Workshop

Statistics: From Theory to Statistics: From Theory to Regulatory AcceptanceRegulatory Acceptance

18-19 September 200318-19 September 2003

Bethesda, MarylandBethesda, Maryland

Disclaimer Disclaimer The views presented are my own and do not necessarily represent those of Bristol-Myers SquibbThe views presented are my own and do not necessarily represent those of Bristol-Myers Squibb

OutlineOutline

Complex Adaptive Systems and Human HealthComplex Adaptive Systems and Human Health Approach and Some Key Statistical Issues with Approach and Some Key Statistical Issues with

Genetic Polymorphisms in PharmacogenomicsGenetic Polymorphisms in Pharmacogenomics Where Do We Go from Here?Where Do We Go from Here?

The Genetic Paradigm

DNA

RNA

Protein

Gene

Phenotype

Gene

Disease

Simple,Monogenic

< 2%

Complex,Multifactorial

> 98%

Non-Infectious Human Disease LoadNon-Infectious Human Disease Load

GENOME TYPEGENOME TYPEUNIQUEUNIQUE

(Initial Conditions)(Initial Conditions)

UNIQUEUNIQUEENVIRONMENTALENVIRONMENTAL

HISTORYHISTORY

FUTUREFUTURE NORM OFNORM OFREACTIONREACTION

PH

YS

IOL

OG

ICA

L

PH

YS

IOL

OG

ICA

L

FIT

NE

SS

, HE

AL

TH

FIT

NE

SS

, HE

AL

TH

--

++TIME-SPACE CONTINUUMTIME-SPACE CONTINUUM

INDIVIDUALINDIVIDUAL

NOWNOW

BLOODBLOOD

PRESSUREPRESSURE

REGULATIONREGULATION

LIPID LIPID

METABOLISMMETABOLISMCARBOHYDRATECARBOHYDRATE

METABOLISMMETABOLISM

HAEMOSTASISHAEMOSTASIS

Risk of DiseaseRisk of Disease

• Agents Agents participateparticipate in dynamic in dynamic network and are network and are notnot directdirect causescauses

• Each individual is a complexEach individual is a complex adaptive system and the adaptive system and the fundamental unit of organization fundamental unit of organization

See : Zerba and Sing, 1993, Current Opinion in Lipidology 4: 152-162, Zerba et al. 2000, Human Genetics 107: 466-475 for more detail

• Network organized hierarchicallyNetwork organized hierarchically and heterarchically into fieldsand heterarchically into fields

• Health or disease isHealth or disease is an emergent feature based on an emergent feature based on interactions among many interactions among many agents, including genes and agents, including genes and environmentsenvironments

• Fields are domains of relationalFields are domains of relational order among agentsorder among agents

• Stronger relationships within fields,Stronger relationships within fields, weaker relationships among fields weaker relationships among fields

• Unique genome type provides initial Unique genome type provides initial conditions and capacity for changeconditions and capacity for change

• Context and time are key to understanding influence of genetic variationContext and time are key to understanding influence of genetic variation

Complex Adaptive Systems and Human HealthComplex Adaptive Systems and Human Health

Genes

Biomarkers

Endpoints

1

3

2 ?

?

?

Complex Adaptive Systems Approach to PGx Complex Adaptive Systems Approach to PGx

Some Key Statistical Issues for Some Key Statistical Issues for Pharmacogenomics Studies Using Genetic Pharmacogenomics Studies Using Genetic

PolymorphismsPolymorphisms

Gene/Polymorphism SelectionGene/Polymorphism Selection Linkage Disequilibrium Linkage Disequilibrium Admixture and Population Stratification Admixture and Population Stratification InvarianceInvariance Context DependenceContext Dependence TimeTime

Gene/Polymorphism SelectionGene/Polymorphism Selection

Genome ScanGenome Scan– Genes not identified Genes not identified a prioria priori – Genotyping Genotyping

– 25K - 500K polymorphisms genotyped25K - 500K polymorphisms genotyped forfor eacheach subjectsubject (not practical yet) (not practical yet)

– DNA Pooling DNA Pooling – 25K - 1.5 million polymorphisms 25K - 1.5 million polymorphisms – Case-control allele frequency differences Case-control allele frequency differences for each polymorphismfor each polymorphism

Candidate GenesCandidate Genes

FF SSii

Candidate GenesCandidate Genes

UnknownUnknownand unmeasuredand unmeasuredfunctionalfunctionalpolymorphismpolymorphism

One of numerousOne of numerousnon-functionalnon-functionalpolymorphismspolymorphisms

Assume that any association of SAssume that any association of Sii with phenotype, P, with phenotype, P,

is because of linkage disequilibrium between F and Sis because of linkage disequilibrium between F and Sii

PPFSFS = p = pFFppSS + + DDFSFS

FF

PP CandidateCandidateGeneGene

RegionRegion

AdmixtureAdmixture

++

++

++++

++

++++

++--

--++

++

----

--

--

--

--

--

--

++

++

++

++

----

------++

SNPSNP

++

--

pp++ = 0.8 = 0.8 pp++ = 0.2 = 0.2

pp++ = 0.5 = 0.5

PopulationPopulation II

PopulationPopulation IIII

AdmixedAdmixedPopulationPopulation

= proportion= proportionof population Iof population I= 0.5= 0.5

Consider two subpopulations, I and II:Consider two subpopulations, I and II:

For each subpopulation, there is linkage equilibrium For each subpopulation, there is linkage equilibrium between a disease allele, F, and a marker allele, S,between a disease allele, F, and a marker allele, S,

PPFFIISSII = p = pFFII

ppSSII; P; PFFIIIISSIIII

= p = pFFIIIIppSSIIII

; D; DFFIISSII = D = DFFIIIISSIIII

= 0. = 0.

In the admixed population (I + II), there is linkage In the admixed population (I + II), there is linkage disequilibrium between F and S,disequilibrium between F and S,

PPFSFS = p = pFFppSS + + ppFFII - p - pFFIIII

)(p)(pSSI I - p- pSSIIII

))

SubpopulationsSubpopulationsProportionsProportions

Disease AlleleDisease AlleleFrequencyFrequencyDifferenceDifference

Marker AlleleMarker AlleleFrequencyFrequencyDifferenceDifference

AdmixtureAdmixtureLinkage Linkage DisequilibriumDisequilibrium

Admixture and Population StratificationAdmixture and Population Stratification Admixture linkage disequilibrium dissipates Admixture linkage disequilibrium dissipates quickly in a randomly mating populationquickly in a randomly mating population Common clinical trial feature: > 1 ethnic groupCommon clinical trial feature: > 1 ethnic group

– Population stratificationPopulation stratification Ethnicity is a confounderEthnicity is a confounder

– Population stratification can create linkage Population stratification can create linkage disequilibrium just like admixture only disequilibrium just like admixture only spuriousspurious– Type I or Type II error inflationType I or Type II error inflation

False-Positive Endpoint Association ExampleFalse-Positive Endpoint Association Example

Unbalanced designUnbalanced design

– Unequal numbers of each group: Unequal numbers of each group: II = 0.67 = 0.67

– Marker allele: pMarker allele: p++ = 0.8 in ethnic group I = 0.8 in ethnic group I

pp++ = 0.2 in ethnic group II = 0.2 in ethnic group II

– Disease risk: pDisease risk: pFF = 0.8 for ethnic group I = 0.8 for ethnic group I

ppFF = 0.2 for ethnic group II = 0.2 for ethnic group II

Not considered in analysisNot considered in analysis

+ Carriers -

+ Carriers -

+ Carriers -

Cases 13 3 0 2 13 5Controls 3 1 2 6 5 7

Ethnic Group I Ethnic Group II Margin

OR = 3.6

Population Genetic Structure and Population Genetic Structure and the Search for Functional Mutations:the Search for Functional Mutations:

Quantitative TraitsQuantitative Traits

FREQUENCYFREQUENCY andand SCALESCALE contribute to inferences about SNP-contribute to inferences about SNP-phenotype associations:phenotype associations:

SCALESCALE

GenotypeGenotype

PhenotypePhenotype(Biomarker)(Biomarker)

??

SNPSNP

FR

EQ

UE

NC

YF

RE

QU

EN

CY

AAAA AaAa aaaa

FunctionalFunctionalMutation?Mutation?

SSR = SSR = ffii (Y(Yii - Y) - Y)22

Analysis of VarianceAnalysis of VarianceApproachApproach

??

ppaa ppAA

AAAA

AaAa

aaaa

PPAaAa

AA

aaSNPSNP

Population Stratification andPopulation Stratification andGenotype FrequenciesGenotype Frequencies

Stratification can result inStratification can result in decreased heterozygotedecreased heterozygote frequencies relative to frequencies relative to expectation:expectation:

Ethnic Group IIEthnic Group IIEthnic Group IEthnic Group IAverageAverageGenotypeGenotypeFrequenciesFrequencies

PPaaaaPPAAAA

PPAaAa = 2p = 2pAAppaa - 2D - 2DAA

(D(DA A positive in example)positive in example)

DDAA

++-- 00

00

Sum

of

Squ

ares

Bia

sS

um o

f S

quar

es B

ias ++

--

Population stratification can result in Population stratification can result in overestimation of quantitative phenotypic overestimation of quantitative phenotypic variation associated with genetic variation relativevariation associated with genetic variation relative to Hardy-Weinberg equilibrium expectationto Hardy-Weinberg equilibrium expectation

DDAA --> + --> +

An example from Apolipoprotein E Biology Molecular weight: 34 kD

Synthesized in most organs– liver, brain, gonads, kidney, spleen, muscle

Key physiological role in lipid transport– ligand for the LDL (ApoB-E) receptor

Structural gene on chromosome 19– polymorphic with three common alleles 2 3 4

AA 112 Cys Cys ArgAA 158 Cys Arg Arg

SNPSNPSNPSNP

Invariance, Context and TimeInvariance, Context and Time

5’5’

3’3’

Note: combination of SNPs involvedNote: combination of SNPs involved

-20

-10

0

10

Quebec,CanadaN = 201

Nancy,FranceN = 223

Munster,GermanyN = 1000

Helsinki,FinlandN=207

Rochester,MN, USA

N=226

Ch

ole

ster

ol

(mg

/dL

)

234

Invariance

Alleles

From Sing From Sing et alet al. (1996) Genetic architecture of common multifactorial diseases, pp. 211-232 . (1996) Genetic architecture of common multifactorial diseases, pp. 211-232 InIn:Chadwick and :Chadwick and Cardew (eds.) Variation in the human genome, Ciba Foundation Symposium 197, John Wiley & Sons, New YorkCardew (eds.) Variation in the human genome, Ciba Foundation Symposium 197, John Wiley & Sons, New York

1010 2020 3030 4040 5050 6060 707000

44

88

1212

1616

1010 2020 3030 4040 5050 6060 70701010

2020

3030

4040

5050

6060

7070

Var

ian

ce x

10

Var

ian

ce x

10-

4-4

Ag

e W

ind

ow

Mid

po

int

Ag

e W

ind

ow

Mid

po

int

(yea

rs)

(yea

rs)

Age Window Midpoint (years)Age Window Midpoint (years)

BootstrapBootstrapSignificance TestsSignificance Tests

22

AA

+ + 0.05 0.05 >> P < P < 0.100.10P < 0.05P < 0.05

Changes in Changes in ApoEApoE Additive Genetic Variance with Age Additive Genetic Variance with AgeContext and TimeContext and Time

Rochester, MN Rochester, MN Males, N=1035Males, N=1035

From Zerba From Zerba et alet al. 1996, Genetics . 1996, Genetics 143143:: 463-478. 463-478.

Where Do We Go From Here?Where Do We Go From Here?

Study design in genetic settingStudy design in genetic setting Genetic stratificationGenetic stratification Genomic controlGenomic control

Ascertainment bias correction in choice of which Ascertainment bias correction in choice of which polymorphisms to studypolymorphisms to study

Contexts/Interactions-- which ones are important?Contexts/Interactions-- which ones are important? New analytical methods needed New analytical methods needed

– Combinations of SNPs within and among genes and environmentsCombinations of SNPs within and among genes and environments

may be involvedmay be involved– Haplotype ReconstructionHaplotype Reconstruction– Combinatorial PartitioningCombinatorial Partitioning

Missing genotypes for individual polymorphismsMissing genotypes for individual polymorphisms Sampling vs technical variability in DNA pooling studiesSampling vs technical variability in DNA pooling studies Multiplicity-- p-value adjustment not a trivial problemMultiplicity-- p-value adjustment not a trivial problem

Some Additional Statistical ChallengesSome Additional Statistical Challenges