Genetics Studies of Comorbidity Heping Zhang Department of Epidemiology and Public Health Yale University School of Medicine Presented at Science at the Edge Michigan State University January 27, 2012 Heping Zhang (C 2 S 2 , Yale University) MSU 1 / 67
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Genetics Studies of Comorbidity
Heping Zhang
Department of Epidemiology and Public HealthYale University School of Medicine
Presented atScience at the Edge
Michigan State University
January 27, 2012
Heping Zhang (C2S2, Yale University) MSU 1 / 67
Collaborators
Dr. Xiang Chen, St. Jude HospitalDr. Kelly Cho, Harvard UniversityDr. Yuan Jiang, Yale UniversityDr. Ching-Ti Liu, Boston UniversityDr. Xueqin Wang, Sun Yat-Sen University, ChinaDr. Wensheng Zhu, Northeastern Normal University, China
Heping Zhang (C2S2, Yale University) MSU 2 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 3 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 4 / 67
Comorbidity
Multiple disorders or illnesses occur in the same person,simultaneously or sequentially
Comorbidity is a topic that our stakeholders––patients, family members, health care professionals, and others––frequently ask about. It is also a topic about which we have insufficient information, so it remains a research priority for NIDA. This Research Report provides information on the state of the science in this area. Although a variety of diseases commonly co-occur with drug abuse and addiction (e.g., HIV, hepatitis C, cancer, cardiovascular disease), this report focuses only on the comorbidity of drug use disorders and other mental illnesses.*
To help explain this comorbidity, we need to first recognize that drug addiction is a mental illness. It is a complex brain disease characterized by compulsive, at times uncontrollable drug craving, seeking, and use despite devastating consequences—behaviors that stem from drug-induced changes in brain structure and function. These changes occur in some of the same brain areas that are disrupted in other mental disorders, such as depression, anxiety, or schizophrenia. It is therefore not surprising that population surveys show a high rate of co-occurrence, or comorbidity, between drug addiction and other mental illnesses. While we cannot always prove a connection or causality, we do know that certain mental disorders are established risk factors for subsequent drug abuse—and vice versa.
It is often difficult to disentangle the overlapping symptoms of drug addiction and other mental illnesses, making diagnosis and treatment complex. Correct diagnosis is critical to ensuring appropriate and effective treatment. Ignorance of or failure to treat a comorbid disorder can jeopardize a patient’s chance of recovery. We hope that our enhanced understanding of the common genetic, environmental, and neural bases of these disorders—and the dissemination of this information—will lead to improved treatments for comorbidity and will diminish the social stigma that makes patients reluctant to seek the treatment they need.
Nora D. Volkow, M.D. Director National Institute on Drug Abuse
Comorbidity: Addiction and Other Mental Illnesses
Is there a relationship between childhood ADHD and later drug abuse? See page 2.
When two disorders or illnesses occur in the same person, simultaneously or sequentially, they are described as comorbid. Comorbidity also
implies interactions between the illnesses that affect the course and prognosis of both.
*Since the focus of this report is on comorbid drug use disorders and other mental illnesses, the terms “mental illness” and “mental disorders” will refer here to disorders other than substance use disorders, such as depression, schizophrenia, anxiety, and mania. The terms “dual diagnosis,” “mentally ill chemical abuser,” and “co-occurrence” are also used to refer to drug use disorders that are comorbid with other mental illnesses.
continued inside
Dr. Volkow, Director, NIDA:Comorbidity is a topic thatour stakeholders–patients,family members, health careprofessionals, andothers–frequently ask about.It is also a topic about whichwe have insufficientinformation, so it remains aresearch priority for NIDA.Source: www.nida.nih.gov
Heping Zhang (C2S2, Yale University) MSU 7 / 67
Possible Mechanisms for Comorbidity
Mental disorder⇒ drug use disorderDrug use disorder⇒ mental disorder
Common etiology⇒{
mental disorderdrug use disorder
Source: www.nida.nih.gov
Heping Zhang (C2S2, Yale University) MSU 8 / 67
Possible Mechanisms for Comorbidity
Mental disorder⇒ drug use disorderDrug use disorder⇒ mental disorder
Common etiology⇒{
mental disorderdrug use disorder
Source: www.nida.nih.gov
Heping Zhang (C2S2, Yale University) MSU 8 / 67
Possible Mechanisms for Comorbidity
Mental disorder⇒ drug use disorderDrug use disorder⇒ mental disorder
Common etiology⇒{
mental disorderdrug use disorder
Source: www.nida.nih.gov
Heping Zhang (C2S2, Yale University) MSU 8 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 9 / 67
Genotypes and Covariates
Source: en.wikipedia.org; 2010.census.gov
Heping Zhang (C2S2, Yale University) MSU 10 / 67
Disorders, Genes and Covariates
Covariates: interact or confound genetic effectsFailure to account for covariates: bias or reduced power
Heping Zhang (C2S2, Yale University) MSU 11 / 67
Study Design
Population-based studies
Family-based studies
Heping Zhang (C2S2, Yale University) MSU 12 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 13 / 67
Notation and Hypothesis
n study subjects, from a population-based study or family-basedstudyFor each subject:
A vector of traits T = (T(1), . . . ,T(p))′
Marker genotype MParental marker genotypes Mpa (only available in a family-basedstudy)A vector of covariates Z = (Z(1), . . . ,Z(l))′
Null hypothesis: no association between marker alleles and anylinked locus that influences traits T
Heping Zhang (C2S2, Yale University) MSU 14 / 67
Typical Response
Fagerstrom Test for Nicotine Dependence
Heping Zhang (C2S2, Yale University) MSU 15 / 67
Multivariate Distributions
∏t
nt!∏a nt,a!
∏a
pnt,at,a
exp {−12(x− µ)′Σ−1(x− µ)}√
(2π)n|Σ|
Heping Zhang (C2S2, Yale University) MSU 16 / 67
Kendall’s Tau
A nonparametric statistic measuring the rank correlation betweentwo variablesPairs of observations: {(Xi,Yi) : i = 1, . . . , n}(Xi,Yi) and (Xj,Yj):
Concordant, if Xi − Xj and Yi − Yj have the same signDisconcordant, if Xi − Xj and Yi − Yj have the different sign
Kendall’s tau:τ = 2(A− B)/{n(n− 1)}
A and B: numbers of concordant and disconcordant pairsOr
τ =
(n2
)−1∑i<j
sign{(Xi − Xj)(Yi − Yj)}
Heping Zhang (C2S2, Yale University) MSU 17 / 67
Generalized Kendall’s Tau
Fij = {f1(T(1)i − T(1)
j ), . . . , fp(T(p)i − T(p)
j )}′
fk(·): identity function for a quantitative or binary traitfk(·): sign function for an ordinal trait
Dij = Ci − Cj. C: number of any chosen allele in marker genotypeM
Genaralized Kendall’s tau (Zhang, Liu and Wang, 2010):
U =
(n2
)−1∑i<j
DijFij
Special cases:FBAT-GEE (Lange et al. 2003)Test for a single ordinal trait (Wang, Ye and Zhang, 2006)
Heping Zhang (C2S2, Yale University) MSU 18 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 19 / 67
Hypothesis with Covariates
New null hypothesis: no association between marker alleles andany linked locus that influences traits T conditional on covariates Z
Heping Zhang (C2S2, Yale University) MSU 20 / 67
Weighted Test
A weight function w(Zi,Zj) imposes a relatively large weight whenZi is close to Zj, and a relatively small weight when Zi and Zj arefar awayWeighted U-statistic:
S =
(n2
)−1∑i<j
DijFijw(Zi,Zj)
Weighted test statistic:
χ2τ = {S− E0(S)}′Var−1
0 (S){S− E0(S)}
Heping Zhang (C2S2, Yale University) MSU 21 / 67
Weight Function–I: Distance
Write Z = (Zco′,Zca′)′, with Zco for the continuous covariates andZca for the categorical covariates
Propensity score: probability of a unit being assigned to aparticular treatment given a set of covariatesCausal effect analysis: match subjects according to theirpropensity scores (Rosenbaum and Rubin, 1984)Genomic propensity score: p(z) = {p1(z), p2(z)}′,pc(z) = P(C = c|Z = z)
Genetic association analysis: match subjects according to theirgenomic propensity scoresWeight function:
w(Zi,Zj) = Wh{‖p(Zi)− p(Zj)‖},
with Wh(u) = exp(−u2/2h2), h > 0
Heping Zhang (C2S2, Yale University) MSU 23 / 67
Asymptotic Distribution: Setting
Treating the offspring genotype as randomConditioning on all phenotypes and parental genotypes (ifavailable)Eliminates the assumptions about phenotype distribution, geneticmodel and parental genotype distributionRobust and less prone to population stratificationIn addition, conditioning on covariates
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 38 / 67
Maximum Weighted Test
Fixed-(h, q) test: how to choose optimal parameters h and q?Choose a grid of h and q values and maximize the weighted teststatistic over those choices{h1, . . . , hL1}: pre-specified grid points of h
{q1, . . . , qL2}: pre-specified grid points of q
χ2τ,max = max
1≤l1≤L1,1≤l2≤L2χ2τ (hl1 , ql2)
Approximate the optimal weighting scheme, yielding the strongestassociation measure
Heping Zhang (C2S2, Yale University) MSU 39 / 67
Resampling Approach
Population-based studies: restricted permutation in Yu et al.(2010)Family-based studies: children’s genotypes solely determined bytheir parents’ marker alleles, resample the children’s genotype byMendelian lawsCalculate M resampling test statistics χ2
τ,max,1, . . . , χ2τ,max,M using M
resampled dataResampling p-value: the proportion of the resampling teststatistics that exceed our observed test statistic, i.e.,M−1∑M
m=1 I(χ2τ,max,m ≥ χ2
τ,max)
Heping Zhang (C2S2, Yale University) MSU 40 / 67
Asymptotic Distribution: Joint Distribution
Equivalently,χ2τ,max = max
1≤l1≤L1,1≤l2≤L2‖Rl1,l2‖
2
R = Var−1/20D (S){S− E0(S)}
S = {S′(h1, q1), . . . ,S′(hL1 , qL2)}′Var0D(S) = diag[Var0{S(h1, q1)}, . . . ,Var0{S(hL1 , qL2)}]: the diagonalblocks of Var0(S)
Var−1/20 (S){S− E0(S)} D−→ N(0, IpL1L2)
R = Var−1/20D (S)Var1/2
0 (S)G, G ∼ N(0, IpL1L2)
Heping Zhang (C2S2, Yale University) MSU 41 / 67
Asymptotic Distribution: Uniform Approximation
TheoremAssume that the eigenvalues of Var0D(S) and Var0(S) are uniformlybounded from both above and below, i.e., there exist two positivenumbers c and C such that c ≤ λmin{Var0D(S)} ≤ λmax{Var0D(S)} ≤ Cand c ≤ λmin{Var0(S)} ≤ λmax{Var0(S)} ≤ C uniformly for all n, whereλmin and λmax denote the smallest and largest eigenvalues respectively.Then for any x ∈ R, as n→∞,
supx∈R
∣∣∣P(χ2τ,max ≤ x
)− P
(max
1≤l1≤L1,1≤l2≤L2‖Rl1,l2‖
2 ≤ x)∣∣∣→ 0.
Heping Zhang (C2S2, Yale University) MSU 42 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 43 / 67
Aims
Compare the performance of:Maximum weighted testNon-weighted test
Compare the performance of:Maximum weighted testOther covariate-adjusted tests
Heping Zhang (C2S2, Yale University) MSU 44 / 67
Simulation I: Data Generation
Generate the parents’ disease and marker genotypes via thehaplotype frequenciesGiven the parental genotypes, generate the offspring genotypeusing 1cM between the two lociTwo covariates are generated: Zco ∼ N(1, 2)
FBAT-GEE (Lange et al. 2003) adjusting for covariates:Fit the regression model g(E[T(j)]) = αj + λ′jZ, with g(·) anappropriate link functionReplace the original traits T(j) with the residuals T(j) − g−1(αj + λ′jZ)in the FBAT-GEE test statistic
Ordinal trait test (Wang, Ye and Zhang, 2006):Deal with a single ordinal trait at a timeApply the Bonferroni correction for multiple trait testing
Heping Zhang (C2S2, Yale University) MSU 50 / 67
Simulation II: Data Generation
Continuous covariate: Zco ∼ N(1, 2)
Bivariate quantitative traits:
Y(j) = µ+ βgG + βcoZco + εj, j = 1, 2,
with (ε1, ε2)′ ∼ 2φ2(x;Σ)Φ(α′x), x ∈ R2 (bivariate skew normaldistribution)Bivariate ordinal traits: discretizing quantitative traits by (50%,67%) and (33%, 54%, 75%) percentiles
FBAT-GEE 0.608 0.355 0.137Wang et al.’s Test 0.448 0.236 0.081
400 χ2τ,max 0.930 0.815 0.518
FBAT-GEE 0.902 0.758 0.499Wang et al.’s Test 0.775 0.590 0.320
600 χ2τ,max 0.991 0.961 0.817
FBAT-GEE 0.982 0.938 0.787Wang et al.’s Test 0.925 0.807 0.585
Heping Zhang (C2S2, Yale University) MSU 52 / 67
Outline
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 53 / 67
Collaborative Studies on Genetics of Alcoholism
A large scale study to map alcohol dependence susceptible genes
Heping Zhang (C2S2, Yale University) MSU 54 / 67
COGA Data
The data include 143 families with a total of 1,614 individualsMultiple Traits:
ALDX1 (the severity of the alcohol dependence): pure unaffected,never drunk, unaffected with some symptoms, and affectedMaxDrink (maximum number of drinks in a 24 hour period): 0-9,10-19, 20-29, and more than 30 drinksTimeDrink (spent so much time drinking, had little time for anythingelse): “no”, “yes and lasted less than a month”, and “yes and lastedfor one month or longer”
Genotypes: markers on chromosome 7Covariates: age at interview and gender
1 BackgroundComorbidityDisorders, Genes and Covariates
2 Weighted Association TestGeneralized Kendall’s TauAsymptotic Distribution and PowerApplication to WTCCC Bipolar Disorder Data
3 Maximum Weighted Association TestAsymptotic DistributionSimulations
4 Analysis of ComorbidityApplication to COGA Family DataApplication to SAGE GWAS Data
5 Conclusions
Heping Zhang (C2S2, Yale University) MSU 57 / 67
Study of Addiction: Genetics and Environment (SAGE)
The data were from SAGE (Bierut et al. 2010), a case-controlstudy of mostly unrelated individuals aimed at identifying geneticassociations for addiction.We included 4,121 subjects for whom the addiction to the sixcategories of substances and genomewide SNP data (ILLUMINAHuman 1M platform) were available.We defined the outcome as to whether a subject was addicted tosubstances in at least two of the six addiction categories (nicotine,alcohol, marijuana, cocaine, opiates or others).
PKNOX2 is a novel TALE homeodomain-encoding gene, locatedat 11q24 in humansIt functions as a nuclear transcription factor indicated by itsstructure and sub-cellular localizationOne of the cis-regulated genes for alcohol addiction in mice(Mulligan et al. 2006)Confirmed by multiple studies
Heping Zhang (C2S2, Yale University) MSU 61 / 67
Conclusions: Method
Developed a nonparametric weighted test to adjust for covariatesthat accommodates multiple traitsProvided its asymptotic distribution and analytical powercalculationRefined the weighted test by proposing the idea of maximumweighting over the grid points of parametersProposed an asymptotic approach to assess its significance
Heping Zhang (C2S2, Yale University) MSU 62 / 67
Conclusions: Application
WTCCC bipolar disorder data: not only confirmed SNP rs420259on Chromosome 16 reported by the WTCCC (2007), but alsoidentified two regions (rs9378249 on chr 6; rs12938916 on chr 17)at the genome-wide significance levelThe identified haplotype block is near the RPGRIP1L gene thatwas reported to be associated with bipolar disorder (O’Donovan etal., 2008; Riley et al., 2009)COGA data: confirmed and strengthened the top signal; providedevidences for the advantage of maximum weighted test overnon-weighted testSAGE data: identified PKNOX2 for addiction, which has beenconfirmed by other studies
Heping Zhang (C2S2, Yale University) MSU 63 / 67
Other Ongoing/Future Work
Incorporating genetic prior information into a current studyGenetic association analysis for rare variantsNonparametric test for gene-environment interactionsGenetic test for multiple trait covariance structure
Heping Zhang (C2S2, Yale University) MSU 64 / 67
Acknowledgment
Supported by grant R01DA016750 from National Institute on DrugAbuseThe SAGE data were obtained from dbGaP(http://www.ncbi.nlm.nih.gov)The COGA data were provided by COGAThe views expressed here are those of the authors.
Heping Zhang (C2S2, Yale University) MSU 65 / 67
References
W. Zhu and H. Zhang (2009) Why do we test multiple traits in geneticassociation studies? (with discussion). J. Korean Statist. Soc., 38:1-10.
H. Zhang, C.-T. Liu and X. Wang (2010) An association test for multipletraits based on the generalized Kendall’s tau. J. Amer. Statist. Assoc.,105:473-481.
Y. Jiang and H. Zhang (2011) Propensity Score-Based NonparametricTest Revealing Genetic Variants Underlying Bipolar Disorder. Genet.Epidemiol., 35:125-132.
H. Zhang (2011) Statistical Analysis in Genetic Studies of MentalIllnesses, Statistical Science, in press.
W. Zhu, Y. Jiang, and H. Zhang (2011) Covariate-Adjusted AssociationTests and Power Calculations Based on the Generalized Kendall’s Tau.J. Amer. Statist. Assoc.