Probing genetic overlap among complexhuman phenotypesAndrey Rzhetsky*†‡, David Wajngurt*, Naeun Park*, and Tian Zheng§

*Department of Biomedical Informatics, Center for Computational Biology and Bioinformatics and Joint Centers for Systems Biology,and †Judith P. Sulzberger, M.D., Columbia Genome Center, Columbia University, New York, NY 10032; and §Department of Statistics,Columbia University, New York, NY 10027

Communicated by Michael H. Wigler, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, May 24, 2007 (received for review November 21, 2006)

Geneticists and epidemiologists often observe that certain hereditarydisorders cooccur in individual patients significantly more (or signif-icantly less) frequently than expected, suggesting there is a geneticvariation that predisposes its bearer to multiple disorders, or thatprotects against some disorders while predisposing to others. Wesuggest that, by using a large number of phenotypic observationsabout multiple disorders and an appropriate statistical model, we caninfer genetic overlaps between phenotypes. Our proof-of-conceptanalysis of 1.5 million patient records and 161 disorders indicates thatdisease phenotypes form a highly connected network of strongpairwise correlations. Our modeling approach, under appropriateassumptions, allows us to estimate from these correlations the size ofputative genetic overlaps. For example, we suggest that autism,bipolar disorder, and schizophrenia share significant genetic overlaps.Our disease network hypothesis can be immediately exploited in thedesign of genetic mapping approaches that involve joint linkage orassociation analyses of multiple seemingly disparate phenotypes.

autism � bipolar disorder � harmful genetic polymorphisms �schizophrenia � shared genes

In ‘‘simple’’ disorders with proven Mendelian inheritance, asingle-nucleotide aberration in the genome can cause one disease

while protecting against another; one nucleotide substitution canalso manifest in multiple physiological systems. For example, asingle-nucleotide substitution in a human �-globin gene (HBB)triggers in its bearer a drastic change of erythrocyte shape (sickle-cell anemia) but protects against invasion of the protozoan parasite(Plasmodium falciparum) that causes malaria. When designing amathematical model that describes pairs of disease phenotypes, wecan think of sickle-cell anemia and malaria as competing for thesame nucleotide site in the human genome. In another example, asingle-nucleotide polymorphism in the CFTR gene profoundlyaffects the bearer’s digestive, reproductive, and respiratory systemsand causes excessive loss of salt through sweating (a group ofsymptoms collectively known as cystic fibrosis). By analogy with ourmetaphor of phenotype competition for genes, we will say that thesedisparate phenotypic manifestations in cystic fibrosis cooperativelyshare the same nucleotide substitution (i.e., the substitution has apleiotropic effect).

Does this logic of competitive or pleiotropic genetic polymor-phisms extend to human disorders that have more complex (andlargely unknown) genetics? We think it does. Here, we suggest amethod for assessing such overlaps between complex phenotypes (areframed comorbidity analysis), then demonstrate its application toa set of 161 disorders described in 1.5 million patient records froma clinical database at the Columbia University Medical Center.

We selected disorders that represent a broad spectrum of mal-adies, from common to rare, affecting diverse physiological systems,yet we also placed special emphasis on neurological phenotypes[Fig. 1 gives a complete account of phenotypes that we analyzed; weprovide information on symptoms and patient statistics for eachphenotype in supporting information (SI)]. Our choice of pheno-types reflect a view that the etiology of every human malady, evenone as recently encountered and as clearly linked to an environ-

mental cause as AIDS, includes a significant component of hered-itary predisposition and/or resistance. For example, a series ofrecent studies showed that a significant proportion of people arepartially or completely resistant to HIV infection, whereas otherpeople have a predisposition to rapid AIDS progression once HIVinfection has occurred (1).

Results and DiscussionOutline of Our Approach. We developed a probabilistic model linkingthe unobserved genetic variation in human genomes to the ob-served succession of healthy and disease phenotypes in individualhumans. Before formulating the model’s assumptions and explain-ing details of its implementation, let us briefly outline its maincomponents (Fig. 2B). In our description, when we consider a pairof disorders (D1 and D2), we model an individual’s phenotype at orbefore a certain age (Fig. 2C). A person is born with (or without)a set of disease-predisposing variations (represented by randomvariables k1, k2, and k12 in Fig. 2B); these variations determine theprobability that the person eventually will be diagnosed with thedisease (age-integrated phenotype; see Fig. 2 B and C). Given thatthe age-integrated phenotype involves disease Di and the individ-ual’s life span, the individual can manifest symptoms of Di at anytime during his/her lifetime with probability specified by the time-of-onset function specific to this disease and possibly by theindividual’s ethnicity and gender (see Fig. 2 B and C). We need totake into account the time course of each disorder to ‘‘subtract’’ allcorrelations between disorder pairs that are merely due to acommonality or a difference in their onset times. Without this ageadjustment, an early-onset disease, such as autism, and a late-onsetdisease, such as Parkinson’s disease, would misleadingly appear asnegatively correlated.

To implement the model, we need a set of assumptions makingour computation tractable.

Assumptions. Environmental factors (such as physiological stress,diet, lifestyle, and exposure to pathogens) affect human phenotypesthrough the action of numerous molecules that are produced,distributed within cells and tissues, and used according to gene-encoded scripts. Therefore, our first assumption here is that, if thesame environmental effect triggers two (or more) different mala-dies, it typically does so through molecular mechanisms that arecommon between these two maladies. Although this assumption islikely to be violated for some pairs of disorders, it is a reasonablestarting point for the model. This assumption allows us to develop

Author contributions: A.R. designed research; A.R., D.W., and N.P. performed research;D.W. contributed new reagents/analytic tools; A.R., D.W., N.P., and T.Z. analyzed data; andA.R. and T.Z. wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.

‡To whom correspondence should be addressed at the present address: Department ofMedicine, University of Chicago, Chicago, IL 60637. E-mail: ar345@columbia.edu.

This article contains supporting information online at www.pnas.org/cgi/content/full/0704820104/DC1.

© 2007 by The National Academy of Sciences of the USA

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a probabilistic model linking the unobserved genetic variation to theobserved phenotypes. We take into account environmental influ-ence via a data-derived function that approximates the classicalage-of-onset distribution, the cumulative probability that a diseasemanifests itself before or at any given age and given that the personwill eventually get the disease (see Fig. 1). Note that these disease-specific functions are highly informative on their own and wouldmerit careful examination. For example, allergic rhinitis, breastcancer, and especially viral infections have markedly differentpatterns of incidence in males and females; the function shapes arenotably variable across disorders.

Our second assumption is that, for each phenotype pair (D1 andD2), the whole human genome can be divided into four disjoint setsof nucleotide sites (Fig. 2A). One set (S0) comprises nucleotide sitesthat can affect neither of the two phenotypes, regardless of eachsite’s state. Sites within another set (S12) can affect both phenotypes

simultaneously, either via a competitive or a cooperative mecha-nism. The remaining two site sets have the potential of predisposingthe bearer exclusively to either phenotype D1 (set S1) or D2 (set S2)(see Fig. 2A). Depending on our choice of phenotypes, some ofthese four site sets may be empty.

Our third assumption involves a spectrum of hypothetical mech-anisms that connect genetic variation within the four sets ofnucleotide sites to the disease phenotype (genetic penetrance). Allmechanisms we consider here have in common an intuitive prop-erty that, the larger the number of genetic aberrations within thedisease-predisposing set of sites, the more likely the disease phe-notype will manifest itself. We consider here two families ofgenetic-penetrance functions: sharp and soft threshold. With asharp-threshold function, the bearer must have at least � disease-related polymorphisms (where � is a positive integer) if she/he iseventually to manifest symptoms of the disease. With � � 1, we

Aciduria18/7

Alopecia3,011/967

Aortic aneurysm999/1,987

Brucellosis147/151

Cerebral palsy

1,354/1,609

Dejerine−Sottas d.251/228

Epilepsy6,285/5,807

Gout53/139

Hereditary spastic paraplegia25/28

Keratoderma412/257

Meningococcus2,738/1,985

Multiple sclerosis9,451/5,506

Osteopetrosis45/19

Pneumonia4,979/8,206

Psoriasis2,397/2,175

Scleroderma533/147

Tuberculosis37,755/28,768

AA metabolism (aromatic)43/36

Actinomycosis

758/708

Alopecia areata539/281

Aplastic anemia2,621/2,569

Budd−Chiari s.88/64

Cervical rib22/22

Depression17,272/9,792

Erythematosquamous dermatosis

1,481/1,012

HIV2,557/3,580

Hodgkins disease86/90

Klippel−Feil s.

29/22

Migraine6,432/1,616

Mumps3,070/828

Parkinsons d.2,829/3,280

Poliomyelitis2,104/1,476

Reiters s.56/80

Shigella2,648/3,665

Tuberous sclerosis

97/105

AA metabolism (branched)

9/7

Acute leukemia68/64

Alzheimers6,097/2,971

Attention deficit

1,861/5,100

Bundle branch block5,216/6,626

Charcot−Marie−Tooth s.127/119

Dermatomyositis- polymyosistis

454/188

Food poisoning660/523

Helicobacter pilori2,878/1,840

Hyperosmolality1,549/1,359

Leprosy307/172

Mineral met. (Fe)188/272

Muscular distrophy314/432

Pataus s.

52/23

Polyarteritis nodosa93/68

Renal glycosuria17/12

Sjogrens s.297/51

Tularemia228/28

AA metabolism (Lowe)

11/13

Acute promyelocytic leukemia84/87

Amebiasis59/51

Autism

107/374

Buphthalmos198/113

Cholelithiasis11,157/4,185

Diabetes type 110,690/8,670

Friedreichs ataxia26/20

Hemivertebra

35/25

Hypoosmolality6,736/6,195

Lethal midline granuloma22/7

Mineral met. (Cu)27/26

Mycoplasma

10/6

Pertussis

227/198

Polyostotic fibrous dysplasia of bone

8/2

Reticulosarcoma297/314

Spina bifida occulta

20/20

Typhoid

30/24

AA metabolism (sulfur−bearing)

311/515

Ainhum12/14

Amyotrophic lateral sclerosis910/1,271

Behcets s.26/27

Burkitt s lymphoma39/65

Cholera18/11

Diabetes type 233,128/27,635

Fragile X s.

0/9

Hepatitis A613/517

Hypersensitivity angiitis1,241/250

Leukodystrophy

121/102

Mineral met. (Mg)601/530

Myotonic disorders

93/108

Pervasive dev. dis.

379/782

Prader−Willi s.

23/33

Rheumatoid arthritis5,719/1,609

Spondylolisthesis669/354

Urea cycle met.44/30

AA metabolism (straight-chain)29/26

Albright−Sternberg s.

92/104

Anaerobes398/311

Benign neoplasms55,523/21,698

Carcinoma in situ18,392/12,735

Chondrodystrophy

105/101

Diphtheria23/28

Giant cell arteritis625/203

Hepatitis B2,792/2,958

Hypertrophic cardiomyopathy

323/279

Lown−Ganong−Levine s.12/8

Mineral met. (Ca)2,367/1,561

Neuromyelitis optica23/24

Phenylketonuria

9/6

Primary cerebellar degeneration45/46

Systemic lupus erythematosus

2,642/551

Staphilococcus9,764/13,817

Virus99,279/36,422

AA transport90/69

Alcoholism6,979/20,623

Aniridia

6/5

Bipolar disorder7,009/5,354

Carbohydrate transport and metabolism

428/350

Congenital absence of vertebra

19/11

E. coli intestinal47/55

Gram−negative bacteria10,931/6,618

Hepatitis C9,639/8,766

Hypoglycemia216/156

Lumbosacral spondylolysis

258/157

Mitochondrial d.11/20

Neurofibromatosis

348/290

Picks d.5/6

Prion−related d.1,472/852

Salmonella326/367

Streptococcus16,257/11,378

Vitamin deficiency491/285

Acanthosis nigricans

270/161

Allergic rhinitis12,515/6,690

Ankylosing spondylitis257/253

Breast cancer F15,351/0

Cardiomyopathy4,405/7,046

Congenital spinal fusion26/18

Edwards s.

51/23

Goiter9,034/1,773

Hepatitis D29/17

Ichthyosis congenita

91/79Lymphosarcoma

169/234

Moyamoya84/46

Ornithosis27/17

Plague58/60

CNS viral d.

41,988/34,769

Schilders s.

8/5

Takayasus arteritis51/23

WPW s.329/410

Acidosis3,195/3,033

Alkalosis884/717

Anthrax2,677/27

Breast cancer M

0/700

Celiac sprue1,272/682

Cystic fibrosis

859/879

Enzyme-deficiency (hemolytic anemia)

35/22

Goodpastures s.9/12

Hepatitis E16/16

Kawasakiʼ s d.

181/313

Lipid metabolism d.32,148/25,149

Multiple epiphyseal dysplasia

9/5

Osteogenesis imperfecta

66/59

Plasma cell leukemia5/2

Progeria59/30

Schizophrenia5,084/6,157

Thrombotic thrombocytopenic purpura74/38

Wegenerʼsgranulomatosis

118/73

Fig. 1. Probability that a person manifests symptoms of a disorder before or at age t (given that she/he will be eventually diagnosed with the disease Di [P(Ti

� t � Ti � �, e, g; �) � 1 � Fi(t � e, g; �)]) for the 161 disorders we consider in this study. Each graph has the same format: the x axis represents the individual’sage (bounded by 0 and 100 years); the y axis represents the probability that the individual is diagnosed with the specific disorder before or at age t (boundedby 0 and 1). The red and blue curves represent data for female and male patients, respectively. The numbers shown in red and blue indicate the number of recordsdescribing female and male patients, respectively, that we used to estimate each disorder-specific curve.

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obtain the classic multilocus heterogeneity model, whereas largervalues of the parameter represent more complex epistatic geneinteraction models (2). With a soft-threshold function (see SI), the

relationship between the number of deleterious polymorphisms andthe time-integrated phenotype is more complicated: the likelihoodthat an individual’s age-integrated phenotype will include a specific

Fig. 2. Model assumptions, definitions,and results of the following analysis. (A–C)The structure and main concepts associatedwith our model, which describes a pair ofdisorders, D1 and D2. (A) We partition allnucleotide sites in the human genome intofour disjoint sets, S0, S1, S2, and S12. (B)Structure of our probabilistic model. Ar-rows indicate the sequence of probabilisticconditioning in computation of the likeli-hood under our model (see Methods). (C)Time course of phenotype change as theperson ages, as described by our model. Inthis example, the person starts as a healthyindividual at t1 (phenotype �0); at timepoints t2 and t3, the person displays D1 andD2, respectively, so �(t2) � �1, and �(t3) ��12. (D–G) Two hypothetical models ofgene-disease mappings (D and E) and esti-mates of the proportion of autism-specificnucleotide sites that autism ‘‘shares’’ withschizophrenia (F) and bipolar disorder (G).(D) A simple hypothetical model, probablymost appropriate for Mendelian disorders,where different disorders are mapped todisjoint sets of genes, with a deterministicrelationship between genetic polymor-phism and phenotype. (E) A more compli-cated hypothetical model, probably appli-cable to common (highly prevalent)disorders, where multiple genes determinepredisposition to a disease in a probabilisticand combinatorial fashion. (F) Posterior dis-tribution for estimate of relative size ofgenetic overlap of autism with schizophre-nia under three different models of geneticpenetrance (we used an uninformativeprior distribution). Parameter � representsthe smallest number of deleterious poly-morphisms in disease-specific nucleotidesites required for the disease phenotype tomanifest itself. (G) Similar estimate of ge-netic overlap between autism and bipolardisorder, relative to the genetic basis ofautism. (H–J) Significant correlations be-tween pairs of disorders. In each of the fourplots, we compare one disorder (in the cen-ter of the plot) against the other 160 disor-ders that we selected for this study. Thecolor of the arc, with corresponding num-ber, represents the value of the � statistic.The warm-colored edges have the highest� values, and those in the colder part of thecolor spectrum represent smaller � values.All values of � �8 are highly significant. Thewhite and turquoise labels indicate disor-ders that are positively and negatively cor-related, respectively, with the disorder inthe center of the subplot. The size of a nodeindicates the number of the disorder-specific patient records in our data set (notethat the node scale is different for differentplots). (H) Autism, data for male patientsonly (see SI for analogous analyses of fe-male patients and joint analysis of bothmale and female patients). (I and J) Bipolardisorder and schizophrenia, joint analysesof both genders.

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disorder at the end of the individual’s life is nonzero for any numberof the disease-related variations in her/his genome but growsquickly with an increase in the number of deleterious variationsrelated to the disorder (see SI for details).

Competing Models. In our data analysis, for every pair of disorders,we choose one of three competing models (hypotheses): (i) thedisorders are uncorrelated (which we interpret as a lack of a geneticoverlap), (ii) the disorders are significantly negatively correlated(which we interpret as a genetic overlap via competition), or (iii) thedisorders are significantly positively correlated (genetic overlap viacooperation; see Methods). The cooperative model is slightly moregeneral than the standard genetic pleiotropy model. The twomodels are identical when two phenotypes are caused by exactly thesame set of genetic polymorphisms; however, unlike the pleiotropymodel, the cooperation model allows each phenotype (in additionto the shared polymorphisms) to be associated with a pool ofgenetic polymorphisms that does not affect the other phenotype.The independence model is a special case of both overlap models,so we can represent results of our analysis with the two log-likelihood-ratio statistics (�), comparing both overlap models to themodel of independence (Figs. 2 H–J and 3). Furthermore, ourparametric model provides an estimate of the size of the hypothet-ical genetic overlap (Fig. 2E and SI).

Correlations and Overlaps. Our analysis of genetic overlap revealsnumerous correlations among disorders, many of which are wellestablished (e.g., see refs. 3–8), whereas other correlations appearpreviously undescribed.

It is not surprising that autism is strongly correlated with perva-sive developmental disorders and fragile X syndrome (Fig. 2H),

because autism is included (along with several other disorders) inthe formal definition of pervasive developmental disorders, andfragile X syndrome has autism as one of its manifestations. How-ever, it is less obvious why autism, which typically manifests beforethe affected child is 3 years old, has a strong positive correlationwith a number of neurological disorders, some of which have alate-age onset (ordered by decreasing statistical significance; seealso Fig. 2H): attention deficit, epilepsy, cerebral palsy, depression,schizophrenia, bipolar disorder, neurofibromatosis, Parkinson’sdisease, and migraine. Our estimated significant overlap betweenautism and tuberculosis may indicate that both diseases are asso-ciated with genetic changes weakening the immune system.

Another group of phenotypes that overlaps with the most highlyprevalent neurological disorders comprises various bacterial, viral,and protozoan infections. In the case of autism, the most stronglypositively correlated phenotypes of this group include viral infec-tions of the central nervous system (such as viral encephalitis),tuberculosis, viral infections of other systems, and staphylococcaland Helicobacter pylori infections (phenotypes are sorted here bydecreasing significance of correlation). The third group of pheno-types, comorbid with autism and with many highly prevalentneurological disorders, includes allergies and autoimmune disor-ders, such as allergic rhinitis. Schizophrenia and bipolar disorderare positively correlated with many additional disorders of thisgroup, including diabetes, rheumatoid arthritis, and psoriasis (seeFigs. 2 I and J and 3). The fourth group of autism-correlateddisorders includes both benign and malignant neoplasms. Autism isalso comorbid with Kawasaki’s disease [a relatively rare phenotypewhose etiology is ill-understood and that probably relies on anunknown pathogen; similar to autism, it affects male individualssignificantly more frequently than females (see SI)], acanthosis

Fig. 3. Significant correlations (that weinterpret as genetic overlap) among threeneurodevelopmental disorders (autism, bi-polar disorder, and schizophrenia; corre-sponding nodes are shown in yellow) andall other disorders in our data set (bluenodes). The volume of each sphere (dis-ease) is proportional to the number of pa-tient records annotated with the corre-sponding phenotype, as explained in thekey. The arcs represent significant correla-tions among phenotypes, with negativecorrelations shown in blue and positive cor-relations shown in red. Thicker arcs repre-sent stronger correlations; see key.

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nigricans, and aberrations of carbohydrate metabolism. Similargroups of highly correlated phenotypes are visible in our analysesof schizophrenia and bipolar disorder (see Fig. 2 I and J), with theimportant addition that female breast cancer shows strong negativecorrelations with both schizophrenia and bipolar disorder (unlikeother malignancies, including male breast cancer; see SI). Thisnegative correlation is highly significant even when only femalepatients are analyzed (see SI). The negative correlation mayindicate in the framework of our model a competition for genes inthe cell cycle/cell death regulation: both schizophrenia and bipolardisorder under this explanation are associated with genetic poly-morphisms that increase the probability of abnormal cell death insome tissues, whereas breast cancer is linked to (only partiallyknown) genetic variation leading to an increased probability ofabnormal cell proliferation. Although the competitive geneticoverlap between bipolar disorder and female breast cancer has notbeen reported, there is recent indirect evidence that supports it: awell established breast cancer-treatment drug, tamoxifen, wasrecently discovered to be effective in treating symptoms of bipolardisorder (9).

We show a composite representation of correlations (interpretedas genetic overlaps) for autism, bipolar disorder, and schizophrenia(yellow spheres) and the rest of 158 disorders (blue spheres) in Fig.3. All blue spheres have one, two, or three incoming arcs, indicatingthey correlate significantly with one, two, or all three of theyellow-sphere disorders. For example, acanthosis nigricans andcerebral palsy are positively correlated with every member of theyellow-sphere disease triplet. Female breast cancer is significantlynegatively correlated with bipolar disorder and schizophrenia (bluearcs) but shows no significant correlation with autism. Neurofibro-matosis is significantly positively correlated with autism and bipolardisorder (red arcs) but not with schizophrenia. Aortic aneurysm isnegatively correlated with schizophrenia but is independent ofautism and bipolar disorder.

Proportion of Autism-Predisposing Polymorphisms That Also Contrib-ute to Schizophrenia or Bipolar Disorder. So long as our model isdesigned for estimating the mean number of disease-related poly-morphisms (per a randomly sampled human genome) in disease-specific site sets and in genetic overlap among disease pairs, we canuse such estimates to assess the proportion of autism-predisposingvariation that is shared with bipolar disorder and with schizophrenia(see Fig. 2 F and G).

Despite the fact that the absolute estimates of the expectednumber of disease-related polymorphisms are different underdifferent models of genetic penetrance (see the model descriptionand tables in SI), the proportion of the polymorphisms that autismshares with bipolar disorder and schizophrenia is consistent acrossdifferent models (Fig. 2 F and G): we estimate that 20–60% ofautism-predisposing variations also predispose the bearer to bipolardisorder, and 20–75% of autism-predisposing variations also pre-dispose the bearer to schizophrenia. It is therefore extremely likelythat there is a three-way positive correlation among autism, bipolardisorder, and schizophrenia, a correlation that probably arises froma genetic variation that predisposes to all three disorders.

Corollaries. Our analysis suggests that, instead of following thefamiliar model of ‘‘unique malady–unique (disjoint with others) setof broken genes’’ applicable to most Mendelian disorders (Fig. 2D),most complex phenotypes are probably rooted in genetic variationthat is significantly shared (in either a competitive or cooperativemanner) by multiple disease phenotypes (Fig. 2E).

Phenotypes of non-Mendelian disorders are often defined witha considerable degree of fuzziness, especially those that are neu-rological: it is not uncommon to define a neuropsychiatric diseasephenotype as comprising, for example, at least five of a list of 10symptoms (4). This fuzziness arises because, in many cases, theobserved disease is a heterogeneous collection of multiple maladies

that have partially similar symptoms and potentially differentgenetic causes. However, these genetically heterogeneous maladiesare combined because of the history of disease identification andthe incompleteness of our knowledge about the disease causes.

Our interpretation of genetic overlap among pairs of disordersdoes not exclude the possibility that one disorder can cause theother. For example, it is possible that comorbidity of autism (orschizophrenia, or bipolar disorder) with infectious and autoimmunemaladies indicates that the neurodevelopmental disorder can betriggered by different developmental insults, including viral orbacterial infection, or an autoimmune disease launched by a benignallergen. Another possibility is that the same molecular featuresthat make a child more susceptible to infection or to autoimmuneattack have a pleiotropic effect on brain development and function.

Our analysis has immediate practical implications for the designof gene-mapping studies that examine complex phenotypes. Imag-ine that we can study a set of families (pedigrees) whose membersare affected by multiple disorders (for example, autism, bipolardisorder, schizophrenia, diabetes, and psoriasis). If we have reasonsto believe that these disorders overlap in terms of disease-predisposing genetic variation, to extract maximum informationfrom available data, we might be able to design genetic linkage orassociation strategies that analyze multiple complex disordersjointly. Furthermore, by selecting different sets of seemingly dis-parate disorders, we might be able to examine systematically thegenetic background of a wide spectrum of complex phenotypes. Inaddition, we hope that the estimated disease overlaps will be usefulin defining sharper (more specific) phenotypes that are also moregenetically homogeneous.

MethodsData. Our input data comprise anonymized statistics about patientsin the Columbia University Medical Center clinical database (1.5million records). This database was designed for pragmatic pur-poses (such as billing) rather than for basic research; thus, in thisstudy, we used a predefined data representation not specificallyoptimized for our purposes (see SI). With respect to the twodiseases, D1 and D2, the ith patient (H in the notation Hi stands forhuman) is described with the following pentaplet of variables.

Hi � �Ai, Gi, Ei, O1.i, O2.i� i�1...., N, [1]

where N is the total number of patients in the database, Ai is thepatient’s age, Gi is the patient’s gender, Ei is his/her ethnicity, andO1,i and O2,i are the patient’s ages at the time she/he was firstdiagnosed with diseases D1 and D2, respectively. For the sake ofencoding simplicity, we set Ok,i to infinity (�) for patients who werenever diagnosed with disease Dk.

The ethnicity, Ei, attributed to the ith patient in our data can haveone of the following codes: A, B, D, E, H, I, M, N, L, O, P, U, W,or X. A table in SI provides the key to these codes.

Variable Gi takes values F (female), M (male), O (other, usuallyindicating an ambiguity/difficulty in gender assignment), and U(unknown, usually indicating missing data).

Models. Let us focus on two human diseases, D1 and D2, each ofwhich has a distinct hereditary component. We can divide the wholegenome into four disjoint sets of nucleotide sites, S0, S1, S2, and S12(see Fig. 2A). The first set, S0, comprises genomic sites that have nopotential to contribute to either of the two diseases. The second andthe third sets of sites, S1 and S2, include genomic loci that, when theyharbor deleterious polymorphisms, predispose the polymorphisms’bearers to D1 and D2, respectively (see Fig. 2A). Finally, the fourthset of sites, S12, involves portions of the genome that predispose anindividual who bears mutations in them to both D1 and D2simultaneously. Although here we focus on point mutations, ourapproach can be extended to other types of genetic polymorphism,such as insertions, deletions, inversions, and translocations.

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Phenotypes. We define the following four phenotypes withrespect to diseases D1 and D2: �1, �2, �12, and �0 correspondto ‘‘affected by disease D1 but not by disease D2,’’ ‘‘affected bydisease D2 but not by disease D1,’’ ‘‘affected by both diseasesD1 and D2,’’ and ‘‘affected by neither disease D1 nor D2,’’respectively.Genotypes: Probability of Gi � {ki,1, ki,2, ki,12}. We denote the totalnumber of deleterious polymorphisms that fall into S1, S2, and S12for individual i with a triplet of random variables {ki,1, ki,2, ki,12}. Inour model, these three variables completely describe the individu-al’s genotype, Gi, with respect to diseases D1 and D2. We assumethat the random variables ki,1, ki,2, and ki,12 independently followPoisson distributions (10) with rates �1, �2, and �12, respectively. Ifa disease-related nucleotide site set Sk is small, as in the case ofsickle-cell anemia (just two sites), we can assume that the observednumber of disease-relevant polymorphisms per genome follows abinomial distribution instead of a Poisson distribution (see SI).Probability of �(�) given Gi � {ki,1, ki,2, ki,12} (penetrance function). Weuse the notation �(�) to denote an individual’s phenotype withrespect to diseases D1 and D2 at the end of his/her life (eventual orage-integrated phenotype; see Fig. 2B). We consider here twodefinitions of the penetrance function. The first definition postu-lates that disease D1 manifests itself only if the number of delete-rious variations in S1 and S12, ki,1 � ki,12 is equal or greater than athreshold, �1 (similarly, D2 develops eventually if ki,2 � ki,12 � �2).The second definition postulates that the threshold value itself is arandom variable, so that the probability of developing a diseasegradually increases with the number of deleterious polymorphisms(see SI for details).Probability of �(t) given �(�). We use the notation �(t) to indicate anindividual’s phenotype at or before age t. Let T1 and T2 be the agesat onset (or first diagnosis) of diseases D1 and D2, respectively.�(t) � �1 is then equivalent to {T1 � t, T2 � t}. Thus, the likelihoodof the two-disease phenotype status can be studied using the jointfailure time model (11) for T1 and T2, based on the genetic factorsand covariates such as age and gender. We then define the followingconditional distributions for T1 and T2,

Fk�tk�e, g; �� � P�Tk � tk�Tk �,e, g; ��, [2]

where k � 1, 2. Note that we can estimate Fk(tk � e, g; �) directlyfrom our data (estimates of 1 � Fk(tk � e, g; �) are shown in Fig. 1).Finally, we define the probability of �(t) given �(�) in terms ofprobabilities Fk(tk � e, g; �), as shown in Table 1.Two genetic overlap models: Cooperation and competition. In the co-operation (generalized pleiotropy) model, the overlap genes can

simultaneously contribute to both diseases, whereas in the compe-tition model, the overlapped genes can contribute to only one of thediseases (the choice is made stochastically with probability specificto each pair of diseases; see SI).

Likelihood and Likelihood Ratio Test. To compute a likelihood valuefor data representing the ith patient, we need to sum the probabilityof the observed phenotype [given ki,1, ki,2, ki,12, and �(�)] over alladmissible values of ki,1, ki,2, ki,12 (ki,j � 0, 1, . . . , �), and �(�) (seeSI for description of an efficient computation of this value). If weassume that the vector of parameters, �, is the same for all valuesof e (ethnicity) and g (gender), then the likelihood function is justa product (over all patients) of probabilities of the observedphenotypes given common parameter values (see SI). (Alterna-tively, we subdivide the data by ethnicity and gender and estimatea separate set of parameters for each data subset.)

At its heart, our analysis is a model selection problem. First, wehave two versions of the same model where two disorders have anarbitrarily large genetic overlap (via either a cooperation or com-petition scenario). Second, we have a simpler model that is nestedin both former models, where the two disorders are geneticallyindependent. Put differently, the model where two disorders, D1and D2, are genetically independent (the genetic overlap, nucleotideset S12, is empty [�12 � 0]) is a special case of the two models wherethe same two disorders are either genetically overlapping or inde-pendent (S12 � � [�12 � 0] or S12 � � [�12 � 0]). Therefore, we canuse a standard log-likelihood ratio statistic, �, for nested models.This � statistic asymptotically (as the sample size grows) follows a2 distribution with the number of degrees of freedom equal to thedifference in the number of parameters between the two models (1,in our case) (12).

In the presence of a statistical signal, we can distinguish amongthe three models (independence, cooperation, and competition) bycomputing two statistics: �cooperation and �competition.

Availability. Detailed information on estimated disease overlaps forall pairs of disorders mentioned in this study is available as SI.

We thank Murat Cokol, Lyn Dupre Oppenheim, Ivan Iossifov, IgorFeldman, Richard Friedman, George Hripcsak, Marianthi Markatou,Rita Rzhetsky, and Chani Weinreb for very helpful comments on theearlier version of this manuscript. This work was supported by NationalInstitutes of Health Grants GM61372 and U54 CA121852–01A1 (toA.R.) and GM070789 (to T.Z.), National Science Foundation Grants0438291 and 0121687 (to A.R.) and 0532231 (to T.Z.), the Cure AutismNow Foundation (A.R.), and Defense Advanced Research ProjectsAgency Grant FA8750-04-2-0123 (to A.R.).

1. O’Brien SJ, Nelson GW (2004) Nat Genet 36:565–574.2. Risch N (1990) Am J Hum Genet 46:222–228, 229–241.3. Richardson AJ, Ross MA (2000) Prostaglandins Leukot Essent Fatty Acids 63:

1–9.4. Sutker PB, Adams HE (2001) Comprehensive Handbook of Psychopathology (Kluwer/

Plenum, New York), 3rd Ed.5. Wiznitzer M (2004) J Child Neurol 19:675–679.6. Stahlberg O, Soderstrom H, Rastam M, Gillberg C (2004) J Neural Transm

111:891–902.

7. Cohen D, Pichard N, Tordjman S, Baumann C, Burglen L, Excoffier E, Lazar G,Mazet P, Pinquier C, Verloes A, Heron D (2005) J Autism Dev Disord 35:103–116.

8. Newcomer JW (2006) J Clin Psychiatry 67(Suppl 9):25–30; discussion 36–42.9. Kulkarni J, Garland KA, Scaffidi A, Headey B, Anderson R, de Castella A, Fitzgerald

P, Davis SR (2006) Psychoneuroendocrinology 31:543–547.10. Sawyer SA, Hartl DL (1992) Genetics 132:1161–1176.11. Kalbfleisch JD, Prentice RL (2002) The Statistical Analysis of Failure Time Data

(Wiley, Hoboken, NJ), 2nd Ed.12. Neyman J, Pearson ES (1928) Biometrika 20-A, 175–240, 263–294.

Table 1. Conditional probability of the age-t phenotype [�(t)] given the ultimatephenotype [�(�)]

P(�(t)��(�), e, g; �)

�(�)

�0 �1 �2 �12

�0 1 F1(t�e, g; �) F2(t�e, g; �) F1(t�e, g; �) F2(t�e, g; �)�(t) �1 0 1 � F1(t�e, g; �) 0 (1 � F1(t�e, g; �))F2(t�e, g; �)

�2 0 0 1 � F2(t�e, g; �) F1(t�e, g; �)(1 � F2(t�e, g; �))�12 0 0 0 (1 � F1(t�e, g; �))(1 � F2(t�e, g; �))

Total 1 1 1 1

Rzhetsky et al. PNAS � July 10, 2007 � vol. 104 � no. 28 � 11699

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