Complex Adaptive Systems and Human Health: Statistical Approaches in Pharmacogenomics Kim E. Zerba, Ph.D. Bristol-Myers Squibb FDA/Industry Statistics Workshop Statistics: From Theory to Regulatory Acceptance September 2003 Bethesda, Maryland Disclaimer The views presented are my own and do not necessarily represent those of Bristol-Myers Squibb

Outline l Complex Adaptive Systems and Human Health l Approach and Some Key Statistical Issues with Genetic Polymorphisms in Pharmacogenomics l 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 Load

GENOME TYPE UNIQUE (Initial Conditions) UNIQUE ENVIRONMENTAL HISTORY HISTORY FUTURE NORM OF NORM OF REACTION PHYSIOLOGICAL FITNESS, HEALTH - + TIME-SPACE CONTINUUM INDIVIDUAL NOW BLOOD PRESSURE PRESSURE REGULATION REGULATION LIPID METABOLISM CARBOHYDRATE METABOLISM HAEMOSTASIS Risk of Disease Agents participate in dynamic Agents participate in dynamic network and are not direct causes network and are not direct causes Each individual is a complex Each 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: , Zerba et al. 2000, Human Genetics 107: for more detail Network organized hierarchically Network organized hierarchically and heterarchically into fields and heterarchically into fields Health or disease is Health 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 environments environments Fields are domains of relational Fields are domains of relational order among agents order 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 change conditions and capacity for change Context and time are key to understanding influence of genetic variation Context and time are key to understanding influence of genetic variation Complex Adaptive Systems and Human Health

Genes Biomarkers Endpoints ? ? ? Complex Adaptive Systems Approach to PGx

Some Key Statistical Issues for Pharmacogenomics Studies Using Genetic Polymorphisms  Gene/Polymorphism Selection  Linkage Disequilibrium  Admixture and Population Stratification  Invariance  Context Dependence  Time

Gene/Polymorphism Selection  Genome Scan – Genes not identified a priori – Genotyping – 25K - 500K polymorphisms genotyped for each subject (not practical yet) for each subject (not practical yet) – DNA Pooling – 25K million polymorphisms – Case-control allele frequency differences for each polymorphism  Candidate Genes

F SiSiSiSi Candidate Genes Unknown and unmeasured functionalpolymorphism One of numerous non-functionalpolymorphisms  Assume that any association of S i with phenotype, P, is because of linkage disequilibrium between F and S i is because of linkage disequilibrium between F and S i P FS = p F p S + D FS FPCandidateGeneRegion

Admixture SNP+- p + = 0.8 p + = 0.2 p + = 0.5 Population IPopulation II II AdmixedPopulation  = proportion of population I = 0.5

Consider two subpopulations, I and II: For each subpopulation, there is linkage equilibrium between a disease allele, F, and a marker allele, S, P F I S I = p F I p S I ; P F II S II = p F II p S II ; D F I S I = D F II S II = 0. P F I S I = p F I p S I ; P F II S II = p F II p S II ; D F I S I = D F II S II = 0. In the admixed population (I + II), there is linkage disequilibrium between F and S, P FS = p F p S +  p F I - p F II )(p S I - p S II ) P FS = p F p S +  p F I - p F II )(p S I - p S II ) SubpopulationsProportions Disease Allele FrequencyDifference Marker Allele FrequencyDifference AdmixtureLinkageDisequilibrium

Admixture and Population Stratification  Admixture linkage disequilibrium dissipates quickly in a randomly mating population quickly in a randomly mating population  Common clinical trial feature: > 1 ethnic group – Population stratification  Ethnicity is a confounder – Population stratification can create linkage disequilibrium just like admixture only spurious – Type I or Type II error inflation

False-Positive Endpoint Association Example  Unbalanced design – Unequal numbers of each group:  I = 0.67 – Marker allele: p + = 0.8 in ethnic group I p + = 0.2 in ethnic group II p + = 0.2 in ethnic group II – Disease risk: p F = 0.8 for ethnic group I p F = 0.2 for ethnic group II p F = 0.2 for ethnic group II Not considered in analysis

Population Genetic Structure and the Search for Functional Mutations: Quantitative Traits FREQUENCY and SCALE contribute to inferences about SNP- phenotype associations: SCALE Genotype Phenotype(Biomarker) ? SNP FREQUENCY AA Aa aa FunctionalMutation? SSR =  f i (Y i - Y) 2 Analysis of Variance Approach ?

papapapa pApApApA AA Aa aa P Aa Aa SNP Population Stratification and Genotype Frequencies  Stratification can result in decreased heterozygote decreased heterozygote frequencies relative to frequencies relative to expectation: expectation: Ethnic Group II Ethnic Group I AverageGenotypeFrequencies P aa P AA P Aa = 2p A p a - 2D A (D A positive in example)

DADADADA Sum of Squares Bias + -  Population stratification can result in overestimation of quantitative phenotypic overestimation of quantitative phenotypic variation associated with genetic variation relative variation associated with genetic variation relative to Hardy-Weinberg equilibrium expectation to Hardy-Weinberg equilibrium expectation D A --> +

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 Arg AA 158 Cys Arg ArgSNP SNP Invariance, Context and Time 5’ 3’ Note: combination of SNPs involved

Quebec, Canada N = 201 Nancy, France N = 223 Munster, Germany N = 1000 Helsinki, Finland N=207 Rochester, MN, USA N=226 Cholesterol (mg/dL) 22 33 44 Invariance Alleles From Sing et al. (1996) Genetic architecture of common multifactorial diseases, pp In:Chadwick and Cardew (eds.) Variation in the human genome, Ciba Foundation Symposium 197, John Wiley & Sons, New York

Variance x Age Window Midpoint (years) Age Window Midpoint (years) Bootstrap Significance Tests 2222A > P P < 0.10  P < 0.05 Changes in ApoE Additive Genetic Variance with Age Context and Time Rochester, MN Males, N=1035 From Zerba et al. 1996, Genetics 143:

Where Do We Go From Here?  Study design in genetic setting  Genetic stratification  Genomic control  Ascertainment bias correction in choice of which polymorphisms to study  Contexts/Interactions-- which ones are important?  New analytical methods needed – Combinations of SNPs within and among genes and environments may be involved may be involved – Haplotype Reconstruction – Combinatorial Partitioning  Missing genotypes for individual polymorphisms  Sampling vs technical variability in DNA pooling studies  Multiplicity-- p-value adjustment not a trivial problem Some Additional Statistical Challenges