Comorbidit o Readin anMathematic DisabilitiesGeneti an Environmenta Et - PDF document

Comorbidit o Readin anMathematic DisabilitiesGeneti an Environmenta EtiologieJacquely Gilli Ligh an Joh C DeFrieAlthough disabilities frequently manifest comorbid readingmathematics this extent to which between reading deficits due tomental twin study offrom 148 fraternal pairs in which at least one the paira disability a analysis to a VOLUM 28 NUMBE 2 FEBRUAR 199ation (Kirb & Becker 1988) angeneti predispositio (Barakat 1951Burt 1949 Husen 1959 Kosc 1974)Althoug n behaviora genetistudie o mathematica disabilit havbee reporte t date result o twian famil studie o mathematic performanc sugges tha individuaference i arithmetica abilit withith norma rang o variatio ar duea leas i part t geneti influence(se Plomin DeFries & McClearn1990 Detterman1991)ComorbiditComorbidity t th co-occurrenco a leas tw differen disorder i thsam individual Th ter ha becomincreasingl commo i th psychiatriliteratur bu ha onl recentl beeapplie t learnin disabilities Fo example severa recen studie hav concerne th comorbidit betwee readin disabilit an attention-deficithyperactivit disorde (ADHD (Augus 1990 Hinshaw 1992Semrud-Clikema e al. 1992) an betwee comorbi learnin disabilitiean substanc abus disorder (Bentle & Conley 1992 Fo & Forbing1991 & Jasinski 1990)Th concep o comorbidit ha itorigin i genera medicine wherebFeinstei (1970 define comorbidit aan ''distinc additiona clinica entittha ha existe o tha ma occudurin th clinica cours o a patienwh ha th inde diseas undestudy (pp 456-457) Thus th origina ter referre t coexistin budistinc disorders—distinc i tha thdisorder ma involv separat phenomenologies pathologies o etiologie (Shea Widiger & Klein 1992)I referenc t menta disorder anlearnin disabilities however distinctnes amon coexistin disorderofte canno b assume becaus osubstantia overla i criteri anunknow etiolog o th separat disorders Thus i i difficul t determin whethe a disorde tha exist ipur for o tha coexist wit anothedisorde represent th sam syndrome Wit regar t learnin disabil­ities pertainin t thetiolog o comorbidit ma influencth remediatio strateg a wel a thfina outcome Fo example i readindisabilit cause mathematic deficitsthe readin remediatio ma alleviat th mat difficultie a well O thothe hand i readin an mathematic disabilitie coexist bu wit ncausa relation the bot disordermus b remediate (se Clarki & Kendall 1992)Th presenc o comorbi disordernecessaril complicate studie o thindividua conditions I clinica research investigator ofte limi theisample t patient wh hav jus ondisease Althoug thi approac istraightforward i ma resul i th investigatio o atypica samples Foexample i tw studie o childhoodepression onl 3 o 1 case (Anderson Williams McGee & Silva 1987an non o 1 case (Kashan e al.1987 o depressio wer "pure, thais no co-occu wit anxiet disorders conduc disorders and/oattention-defici disorders I contrastsocia an epidemiologica researcherusuall conside broade sample anthe investigat th exten o comorbidit fo variou disabilitie (Verbrugge Lepkowski & Imanaka 1989)Caro an Rutte (1992 suggestetha researchers failur t considecomorbidit i previou studie mahav resulte i misleadin findingfo tw mai reasons First a stud oon conditio (e.g. conditio X maproduc finding tha ar largel a consequenc o a ignore disorde (e.g.conditio whe comorbidit i ignored a implici assumptioi mad tha conditio X i th sameregardles o th presenc o absenco conditio Y— possibl fals assumptionObserve comorbidit ma b eithe"artifactual o "true. Fo exampleapparen comorbidit ma b du tsampl selectio method (e.g. thBerkso effect se Berkson 1946)Selectio biase ar particularl prevalen i clinicall derive sampleswhic ten t contai th mosseverel affecte

children Arti actuacomorbidit coul als occu becauso overlappin diagnosti criteria obecaus on disorde i a earl manifestatio o a secon disorde o iactuall a par o th secon disorderSevera explanation ma als exisfo tru comorbidity tha is comorbidit tha i no a statistica o diagnosti artifac (Caro & Rutter 1992)First th disorder ma shar th samris factors Man psychiatri disorderar multifactoria i origi an theicause ar no specifi t an on disorder Fo example variable suc aoveractivity shor attentio span animpulsivit hav al bee foun tinfluenc bot conduc disorder anreadin disability Thus thes variable migh accoun fo comorbiditbetwee conduc disorder an readin disability Becaus geneti influence ma b importan i hyperactivit an impulsivit (se Stevenson1992) observe comorbidit betwee conduc disorder an readindisabilit ma b due a leas i partt a share ris facto tha i geneti iorigin Alternatively share ris factor ca als originat fro environmenta circumstances Fo examplelarg famil siz an socia disadvantag ca als increas th ris fo botconduc problem an readin problem (Richman Stevenson & Graham1982 & Giller 1983)A secon possibl explanatio fotru comorbidit i tha th ris factorfo tw disorder ma co-occur Foexample Caro an Rutte (1992note tha parenta depressio i a risfacto fo severa childhoo psychopathologies Weissma e al (1987examine th occurrenc o childhoodepressio i th offsprin o depresse parent suggeste tha thris i geneticall transmitte fro paren t child Ther als appear t ba increase ris o conduc disorderamon offsprin tha seem t b a functio o famil discord whic imuc mor frequen whe on o bot 9parent ar depresse (se Rutte & Quinton 1984) Thus th comorbiditbetwee childhoo depressio anconduc disorder ma b du t bota geneti ris fo depressio an aenvironmenta ris fo conduc disorde a a resul o famil discordA thir possibl explanatio o trucomorbidit i tha th comorbi symptom represen a meaningfu syndromeFo example wit regar t readinan mathematic deficits individualma b classifie int on o thregroups (a readin an mat disable(RDMD) (b onl readin disable(RD) (c onl mat disable (MD)Result obtaine fro severa studie(e.g. Fletcher 1985 Fletche & Loveland 1986 Rourke 1985,1993 Rourk& Finlayson 1978 Rourk & Strang1983 & Linder 1984 suggestha individual wit RDM an Rhav simila cognitiv profiles whicdiffe fro tha o individual wit MDA fourt possibl explanatio fotru comorbidit i tha th presenco on disorde ma increas th riso a secon disorder Fo example thpresenc o a readin disabilit macaus a greate ris fo a mathematicadisability Individual place i remedia educatio classe ma receivremediatio i readin abilit a thexpens o tim devote t teachinmathematica concept (Kelle & Sutton 1974 McLeostrong 1982)Comorbi Readin anMathematic DeficitTh overla betwee readin anmathematic deficit ha bee weldocumente (Ackerman Anhalt & Dykman 1986 Fletche & Loveland1986 1993 McLeo & Armstrong 1982) Ackerma e al suggeste tha mos childre diagnoseearl a readin disable wil eventuall displa a seriou deficienci arithmetic despit havin nearaverag arithmeti score i th priJOURNA O LEARNIN DISABILITIEmar grades I a sampl o fifth-gradstudent wit L participatin i thFlorid Longitudina Project Fletchean Lovelan reporte tha onl 1showe specifi deficit i reading18 specifi deficit i mathematics an comorbideficit i bot readin an math Ia descriptiv stud o student servea learnin disable b Chil ServicDemonstratio Centers Norma anZigmon (1980 foun tha 8 showesever deficit solel i math whil13 thei sampl displaye deficiti bot readin an mathematics I a separat sampletha 6 o elementar an junio higschoo student experience matficulties whil a additiona 5 experience difficultie wit reading Moreover 56 o t

h childre wit readinproblem als showe poo mathematic achievement an 43 o th childre wit mat deficit als showepoo readin achievement I a serieo studie o childre wit readin disabilities Siege an colleague (Siege& Linder 1984 Siege & Ryan 19881989 foun fe childre tha di nohav accompanyin sever arithmetideficits excep a th younges agesEtiology Student wh displa comorbireadin an mathematic deficit probabl d s fo a variet o reasonsAlthoug understandin o th mechanism underlyin th observe comorbidit ma facilitat appropriatremediatio strategies littl researcha bee conducte i thi area Onpossibilit i tha poo achievemen imathematic ma b du t languagebase deficit tha als underli pooreadin achievemen (Lansdown 1978McLeo & Crump 1978 se als SatzTaylor Friel & Fletcher 1978 Share al. 1988) Rourk an Stran (1983suggeste tha childre wit RDMhav difficultie memorizin table anprocedura step i proble solvinbecaus o genera languag an verba impairments Consisten wit thiview Mut (1984 foun tha b experimentall manipulatin th computationa an readin demand o a serie o arithmeti problems 14 oth varianc explaine i performancscore wa uniquel attributabl treadin skills 8 wa attributabl tcomputationa skills an 32 waattributabl t join variance Alternativ hypothese t explai comorbireadin an mat deficit includ overal deficit i verba short-ter and/olong-ter memor retrieva (Ackerma e al. 1986 Brandy & Rourke1991 1985 Fletche & Loveland 1986 Lerner 1989 Siege & Linder 1984 Webster 1979)Th primar objectiv o th presenstud wa t asses th geneti an environmenta etiologie o comorbireadin an mathematic deficits Datfro twi pair participatin i thColorad Learnin Disabilitie Researc Cente (LDC i whic a leason membe o th pai ha a readindisabilit wer subjecte t crossconcordanc analyse an t a bivariat extensio o th basi multipleregressio mode fo th analysi oselecte twi dat (DeFrie & Fulker1985) result o thes analyseprovid evidenc concernin th exten t whic deficit i readin ardu t geneti an environmenta influence tha als caus mathematicdeficitsMethoProcedure T minimiz ascertainmen biasw systematicall identifie twi pairfro cooperatin schoo district withia 150-mil radiu o Denver Withouregar t readin status al twi pairwithi a schoo distric wer identifiedan permissio wa sough fro theiparent t revie th twins schoorecord fo evidenc o readin problems wer screene fo evidenc o readin problems whic include lo standardize achievemen VOLUM 28 NUMBE 2 FEBRUAR 1999tes scores referral t specia resourcroom o remedia readin programsan comment fro teacher o schoopsychologists Pair i whic a leason membe evidence a schoo histor o readin problem wer the invite t th Universit o Coloradowher the wer administere a batter o psychometri tests A compariso sampl o contro twi pair waals teste i whic neithe membe oa pai ha a histor o readin problem i school Contro twin wermatche t th proband b agegender an schoo district B Decembe schoo informatio fronearl 2,00 twi pair i 2 cooperatin schoo district ha bee obtainedFro tha sample 46 twi pair iwhic a leas on membe evidencereadin difficultie an 29 twi pairi whic bot twin exhibite normareadin performanc ha bee testedTh twi pair wer administere a batter o psychometri test measurin variou cognitiv abilities includin subtest (Readin RecognitionReadin Comprehension SpellingMathematics o th Peabod Individua Achievemen Tes (PIAT Dun & Markwardt 1970) an th WechsleIntelligenc Scal fo Children-Revise(WISC-R Wechsler 1974 o thWechsle Adul Intelligenc ScaleRevise (WAIS-R Wechsler 1981) A discriminan functio readin scorwa compute fo eac individualemployin discriminan weight estimate fro a analysi o PIA Readin Recognition Readin Comprehension an Spelli

n dat obtainefro a independen sampl o 14nontwi childre wit diagnose readin problem an 14 controls A composit mathematic scor wa compute b summin standardize scoreo th PIA Mathematic an WISC-Arithmeti subtestsPair wer include i th readinproban sampl i a leas on membe o th pai (th proband me thfollowin fiv criteria (a a positivhistor o readin problem i school(b a negativ discriminan readinscore (c a Verba o Performanc Io a leas 90 (d n evidenc o neurologica o sever emotiona problemsan (e n uncorrecte visua o auditor acuit deficits Criteri fo mathematic disabilit include a standardize mat composit scor o a leas1. standar deviation belo tha oth contro twi sample an criteri(c throug (e fo probandsZygosit o th twi pair wa determine usin selecte item fro thNichol an Bilbr (1966 zygositquestionnaire whic ha a reporteaccurac o 95% I doubtfu caseszygosit wa determine b th analysi o bloo samples B Decembe1992 tota o 14 pair o M twin(6 male 8 female an 11 pair osame-se D twin (6 maleme th criteri fo inclusio i thproban sampl [i.e. a leas onmembe o th pai me criteri (athroug (e) an ha complet readinan mathematic performanc measures compariso sampl o contro twin include 13 M (5 male77 female an 9 same-se D (5male 4 female pairs Th mea verba an performanc I score wer 9an 102 respectively fo probandsan 11 an 112 respectively fo thmatche contro twin rangei ag fro 8 t 2 year a th tim otestin (mea ag = 12.0 years anal ha bee raise i middl clashome i whic Englis wa th primar languag spoken Althoug mostwin i th curren sampl ar Whiterecen effort hav bee mad b LDstaf member t increas th numbeo nonwhit twi pairs i orde t obtai a mor representativ sampleAnalyses Cross-Concordanc Rates Severadifferen methodologie ca b use tasses th etiolog o comorbi disorder suc a readin an mat disabilities a a compariso o M anD concordanc rate wa employet asses geneti etiolog i earl twistudie o readin disabilit (Bakwin1973 1950 Stevenson Graham Fredman & McLpughlin 19841987 1967) a compariso o cross-concordanc rate foM an D twi pair ca b use tasses th etiolog betwee tw comorbi disorder (Gilger Pennington& DeFries 1992) A pai i define across-concordan i Twi 1 manifeston disorde an Twi 2 manifest thsecon disorder I th presen studya pai wa define a cross-concordani Twi 1 displaye a readin disabilit an Twi 2 ha a mat disabilityTh logi o thi desig relie o thfac tha M twin shar al o theigenes D twins o averageshar onl 50 o thei segregatingenes a highe cross-concordancamon M twi pair compare t Dtwi pair woul sugges a genetietiolog t th comorbidit betweeth tw disordersMultipl Regressio Analysis Aalternativ metho fo assessin thetiolog o comorbidit betwee twdisorder i a bivariat extensio o thbasi multipl regressio mode fo thanalysi o selecte twi dat (DeFrie& Fulker 1985) I th univariat casewhe proband ar selecte becaus odevian score o a continuou measure score o bot M an Dco-twin shoul regres towar thmea o th unselecte populationHowever a show i Figur 1 thregressio o M co-twin shoul bles tha tha o D co-twin i th conditio i heritable Whe th M anD proban mean ar approximatelequal a simpl t tes betwee th Man D co-twi mean provide a teso geneti etiology However DeFriean Fulke propose tha a multipleregressio analysi o suc data iwhic a co-twin' scor i regresse obot th proband' scor an th coefficien o relationship facilitate a mor flexibl an statisticall powerfutest Subsequently DeFrie an Fulke(1988 demonstrate tha a simpltransformatio o th dat prio tmultiple-regressio analysi yielde a 10JOURNA O LEARNIN DISABILITIEFIGUR 1 Hypothetica distributio fo readin performanc o a unselectesampl o twins an o th identica (MZ an fraterna (DZ co-twin o probandwit readin di

sabilities Th differentia regressio o th M an D co-twintowar th mea o th unselecte sampl (fi) provide a tes o geneti etiology(P an C th mean fo probands M co-twins an D co-twinsrespectively. Reprinte wit permissio fro Nature ("Evidenc fo a GenetiAetiolog i Readin Disabilit o Twins, b J C DeFries D W Fulker anM C LaBuda 1987 Nature, 329, p 537) Copyrigh 198 b MacmillaMagazine Limitedestimat o inde o th extent whic th observe proban deficii heritableTh basi multiple-regressio equatio formulate b DeFrie an Fulke(1985 i a followsC = B - B + A (1wher th co-twin' score P i thproband' score R i th coefficien orelationshi (R = 1. fo M twin an0. fo D twins) an A represent thregressio constant Thi th partia regressio o th co-twin'scor o th proband' score a measur o averag M an D twi resemblanc (LaBuda DeFries & Fulker1986) B i th partiaregressio o th co-twin' scor o thcoefficien o relationshi an equaltwic th differenc betwee th Man D co-twi mean afte covariancadjustmen fo an differenc betweeM an D proban means Thus thB provide a direc tes fogeneti etiology Whe th dat artransforme prio t multipl regressio analysi (eac scor i expressea a deviatio fro th mea o thunselecte populatio an the divideb th differenc betwee th probanan contro means) B estimate hi (th exten t whic th observe proban defici i heritable)Moreover th differenc betwee thtransforme M co-twi mea an hi estimate c| a measur o th extent whic th proban defici i du tenvironmenta influence share bmember o twi pairsT asses th heritabl natur oth comorbidit betwee readin anmathematic deficits w fitte th followin bivariat extensio o th basimultipl regressio mode t probandiscriminan readin score an cotwi composit mathematic score oth selecte twi sampleC B B + A (2wher Cy i th co-twin' expectecomposit mat score P th proband' discriminan readin score R ith coefficien o relationshi (th sama i th univariat case) an A i thregressio constant B\ i th partiaregressio o th co-twin' mat scoro th proband' discriminan readinscore— measur o averag MZ-Dcross-variabl twi resemblanc (i.e.th exten t whic co-twi score oY ar relate t proban score oX acros zygosity) B th partiaregressio o th co-twin' compositmat scor o th coefficien o relationship Becaus th dat wer standardize an transforme prio t multipl regressio analysis th standardeviation o bot th readin anmat variable wer equa t 1 andconsequently th B i a functio o th grou heritabilitie foreadin an mat performanc anth geneti correlatio betwee the(se Appendix se als Stevenson VOLUM 28 NUMBE 2 FEBRUAR 19910Pennington Gilger DeFries & Gillis1993) B a estimat o"bivariat heritability, a inde o thexten t whic th proban readindefici i du t geneti factor tha alsinfluenc mat disability Furthermore th rati o th B tth observe covarianc betwee readin an mat score estimate th proportio o th observe covarianc thaca b attribute t geneti factorsFo th presen analyses dat frotwi pair i whic a leas on membe o th pai me th criteri foreadin disabilit wer used Becaustruncat selectio wa employe wheascertainin th curren twi sampl(se Thompso & Thompson 1986)pair i whic bot member werdiagnose a readin disable werdouble-entere fo al regressio analyses i analogou t th computatio o proband-wis concordancrates whic bot affecte membero concordan pair ar include aproband (DeFrie & Gillis 1991)Standar erro estimate an test osignificanc provide b conventionacompute regressio program weradjuste accordinglyResultConcordanceCross-Concordance T tes th hypothesi tha matdeficit displaye b individual witreadin disabilitie ar du a leas ipar t geneti factor tha als influenc readin performance w conducte bot concordanc an regressio analyses I Tabl 1 M an Dproba

nd an co-twin ar classifieaccordin t thei readin an matstatus pair concordan fo Rbein double-entered A indicate bth number tabulate i column 1 an 2 68 (154/226 o th M cotwin an 40 (56/139 o th Dco-twin o R proband wer alsreadin disabled Th differenc betwee th M an D concordancrate i significan ( = 4.46 p .001)strongl suggestin a geneti etiologfo readin disabilityO mor relevanc t th presenstud wer th M an D crossconcordanc rate betwee probanreadin an co-twi mat status Ashow i column 3 an 4 o Tabl 149 th M co-twin an thD co-twin o R proband wermat disabled Thes M an Dcross-concordanc rate ar als significantl differen ( = 2.71 p .01)suggestin tha geneti influence contribut t th observe comorbiditbetwee readin an mathematic performanc deficitsMultipleof Data Tabl 2 summarize th M an Dproban an co-twi readin performanc (READ scor means standardize agains th mea o 45 controtwins M an D proban REAscore ar highl simila an ar ove2. standar deviation belo th contro twi mean However ther i a differentia regressio o th M anD co-twi REA scores Wherea Mco-twin regres onl 0.2 standardeviatio units D co-twin regres0.9 standar deviatio unit towarth unselecte populatio mean Ashow i Tabl 3 whe proban anco-twi transforme REA scorewer fitte t th univariat basi regressio mode (Equatio 1) Bh = 0.5 ± 0.10 suggestin thaapproximatel th probanici i readin i du t geneti influences Th differenc betwee thtransforme co-twi mea (0.92 anh* a estimat o measuro th exten t whic th probandefici i readin i du t environmenta influence share b twipairs is 0.4 ± 0.40 Thusapproximatel 40 o th probanreadin defici ca b attribute tenvironmenta influence share bmember o twi pairsTabl 4 present th mea compositmathematic score (MATH fo thM an D proband wit R anthei co-twins A wa th cas witTABL 1 Frequenc o Readin Disabilit (RD an Mat Disabilit (MDi Co-twin o R ProbandR ProbIdenticaFraternainR Non-R15 75 8Co-twiM114Non-M119TABL 2 Mea Readin Performanc (READ ScoreIdenticaFraternaStandardize agains controlsWpair1411Proban Co-twi-2.7 ± 0.8 -2.5 ± 1.0-2.6 ± 0.8 -1.7 ± 1.3Transforme REAProban1.0 ± 0.31.0 ± 0.3scoresCo-twi0.90.6± 0.3± 0.5a i standar deviatio unit fro th mea o a sampl o 45 contro twins scor iexpresse a a deviatio fro th REA mea o th unselecte populatio an the divide b thdifferenc betwee th proban an contro mea REA scores 10JOURNA O LEARNIN DISABILITIEth REA scores ther wa differentiaregressio o th M an D co-twiMAT scores Wherea M co-twinso average di no regres towar thunselecte populatio mean th Dco-twin regresse 0.3 standar deviatio unitsTh result o fittin proban REAscore an co-twi MAT score t thbivariat regressio mode (Equatio 2ar show i Tabl 5 Th B\ estimato 0.1 ± 0.0 (p = .06 i a measuro averag MZ-D cross-variabl twiresemblance tha is th exten twhic proban REA score ar relatet co-twi MAT score i M an Dtwi pairs o average Th Bmat o 0.2 ± 0.0 (p = .015 providea direc estimat o bivariat heritability a measur o th exten t whicth proban defici i readin i dut geneti factor tha als influenccomposit MAT scores Furthermoreth rati o B th observe covarianc (0.47 betwee transformeREA an MAT score (estimatefro th regressio o MAT o REAi th proban sample indicate thproportio o th phenotypi relationshi betwee readin an mattha ca b attribute t geneti influences magnitud o thi rati (i.e.0.26/0.4 = 0.55 suggest tha abouhal o th observe covarianc betwee readin an mat deficit i dut geneti influences I additionbecaus th expecte transforme Mco-twi mea fo MAT withi th Rsampl equal bivariat hi + bivariatci (se Appendix) subtractin bivariatB th M co-twi transformeMAT mea provide a direc estimat o bivariat ci, a measur o thexten t whic th proban rea

dindefici i du t environmenta factortha influenc composit MAT scorean ar share b member o twipairs th presen study bivariatc 0.5 - 0.2 = 0.25 suggestintha proban readin deficit ar alssubstantiall du t share environmenta factor tha influenc MATperformance Thus bot geneti anshare environmenta factor appea tcontribut t comorbi readin anmat performanc deficitsDiscussioA majo objectiv o th ColoradReadin Projec (DeFries Olson Pennington & Smith 1991 wa t assesth geneti an environmenta etiologie o readin disability Subsequenfundin b th Nationa Institut oChil Healt an Huma Developmen ha provide th LD coinvestigator th opportunit t asses thgeneti an environmenta etiologieo bot readin an mathematic disabilities a wel a thei covariatiowit measure o readin an languag processes ADHD an executiv functions Althoug previou studie hav indicate tha childre witlearnin disabilitie ofte experienccomorbi readin an mathematicdeficits th natur o thi observecomorbidit i no wel understoo(Fletche & Loveland 1986 Kosc 1974McLeo 1982) Th presen stud employe behaviora genetianalyse o readin an mat performanc dat collecte fro twi pairi whic a leas on membe o thpai evidence a readin problem iorde t asses th exten t whic thobserve comorbidit betwee readinan mathematic deficit i du tcommo geneti an environmentainfluencesBase o previou findings i wahypothesize tha mat deficit displaye b individual wit readindisabilitie ar du a leas i par tgeneti factor tha als influenc thesindividuals readin performance Onapproac w employe t tes thihypothesi wa t compar M anD cross-concordanc rate betweeproban readin statu an co-twimat status I th presen study 49o th M co-twin an 32 o th Dco-twin wer foun t b mat disabled Th differenc betwee thcross-concordanc rat o M twin(wh share al o thei gene wit aR proband an tha o D twin(wh shared o average onl 50 othei segregatin gene wit a proband wa significant Thus comorbireadin an mat deficit ar apparTABL 3 Fi o Basi Mode t Proban an Co-twi Transforme REA ScoreCoefficienBEstimat ± SE 0.6 ± 0.00.5 ± 0.1t p8.8 .005.2 .00aQne-tailedTABL 4 Mea Mathematic Performanc (MATH ScoreIdenticaFraternaStandardize agains controlsNpair1411Proban Co-twi-1.4 ± 0.8 -1.4 ± 0.8-1.3 ± 0.8 -1.0 ± 1.0Transforme MAT scoresProban Co-twi0.5 ± 0.3 0.5 ± 0.30.5 ± 0.3 0.3 ± 0.3a i standar deviatio unit fro th mea o a sampl o 45 contro twins standardizescor i divide b th differenc betwee th proban an contro mea REA scores VOLUM 28 NUMBE 2 FEBRUAR 19910TABL 5 Fi o Bivariat Mode t Proban REA Score an Co-twi MAT ScoreCoefficien Estimat ± SE t pBi 0.1 ± 0.0 1.5 .0B bivariat heritabilit 0.2 ± 0.0 2.9 .00entl du a leas i par t genetiinfluencesDeFrie an Fulke (1985,1988 suggeste tha whe proband ar selectebecaus o extremel hig o lo performanc o a continuou measuremultipl regressio analysi providea mor flexibl an statisticall powerfu metho o testin fo geneti etiology Applyin thi methodolog t a composit measur o readin collectefro M an D proband an cotwins o 0.5 ± 0.1wa obtained suggestin tha approximatel th grou readin deficidisplaye b proband i du t genetiinfluences I th presen study a bivariat extensio o thi basi multipl regressio mode wa use t asses th etiolog o comorbi readinan mat deficits Subject fo thianalysi include 14 M an 11same-se D twi pair i whic aleas on membe o th pai ha a readin disability Whe th bivariatregressio mode wa fitte t proban readin score an co-twi matscores th resultin estimat o bivariat h* suggeste tha approximatel26 th proban readin deficii du t geneti factor tha als influence mat performance A correspondin estimat o bivariat d, (0.25wa als obtained Thes result sugges tha geneti an share environmenta

influence contribut almosequall t th observe covariancbetwee readin an mat scorei twi pair exhibitin readin disabilitiesOn limitatio o th presen studi th smal numbe o measure omathematica abilit tha wer administered Becaus bot th WISC-Arithmeti an PIA Mathematic subtest primaril involv wor problemsi perhap i no surprisin tha a sampl o twin wit readin problemwoul als manifes problem o thestests smal subsampl o th LDtwi pair an 3 DZ wer alsadministere th Wid Rang Achievemen Test-Revise (WRAT-R Jasta & Wilkinson 1984) a paper-and-pencimeasur o mathematica ability Wheathes dat wer subjecte t regressioanalysis th resultin estimat o bivariat ki (0.35 wa surprisingl simila t tha fo th WISC- an PIAcomposit measure Th estimat obivariat - 0.3 = 0.06 walower however suggestin tha whemat abilit i assesse usin a paperand-penci measure comorbi readinan mat deficit ma b du primaril t geneti factors Becaus th sampl siz fo thi analysi wa small thihypothesi wil b teste agai whea large numbe o twi pair i thLD projec hav bee administereth WRAT-RA secon limitatio o th presenstud concern th smal numbe otwi pair wit specifi mat disabilit i th LDC Becaus th primarobjectiv o th Colorad Readinec wa t stud readin disabilitytwi pair wer selecte wit regar tthei readin status Mor recentlyLD staf member hav identifietwin o th basi o eithe readin omat deficits However th overwhelmin majorit o twin teste tdat ar pair i whic a leas onmembe ha evidence difficult ireadin o i bot readin an mathThus presen sampl i no adequat fo regressio analysi o specifimat deficits Becaus dat fro a sampl o twin wit mat disabilitiewil facilitat uniqu analyse o subtyp validit (e.g. childre wit specifi mat deficit vs thos wit comorbi readin problems Fletcher1985 & Loveland 1986Rourke 1985 1993 Rourk & Finlayson 1978 Rourk & Strang 1983 Siege & Linder 1984) w wil undertaksuc analyse wit a large sampl ochildre wit mat disabilit i thnea futureThes finding addres a importanissu concernin th observe comorbidit betwee readin an mathematic deficit withi population witlearnin problems namely whethecomorbi readin an mat deficitar independen disorder o whethether i som share etiology Resultobtaine fro a compariso o M anD cross-concordanc rate an a bivariat extensio o th basi multiplregressio analysi (DeFrie & Fulker1985 bot sugges tha th matdeficit o proband wit readin problem ar due i part t geneti factortha als influenc readin performance I addition ther i evidenct sugges tha comorbidit betweereadin an mat disabilitie i alsdu t environmenta influence shareb member o twi pairs Thes tentativ conclusion wil b teste morrigorousl durin th nex severayear whe th sampl o twin i thColorad Learnin Disabilitie Researc Cente wit mat disabilitiebecome substantiall largerABOU TH AUTHORJacquelyn Gillis Light, PhD, isresearch at the Institute forsearch,is supported by a grant from the National Institute of Mental Health. John DeFries, PhD, psychol­ogy and forGenetics, University ofis the Learning Disabilities Research Center and serves as a consulting editor the 10JOURNA O LEARNIN DISABILITIEAddress: forioral ofCOAUTHORS NOTE1. work was supported in part by pro­gram project and center grants from NICHD (HD-11681 and HD-27802) to John CDeFries. This report was prepared while Jacauelyn Light wasNICHD No. HD-07289. 2. contributionsbers many Colorado school districts and of families who participated in thisare gratefully also thank Judith twoers comments ansion of this article. REFERENCEAckerman P T. Anhalt J M. & Dykman R A (1986) Arithmeti automatizatio failur i childre wit attentioan readin disorders Association ansequela222-232Anderson J C Williams S. McGee R.& Silva P A (1987)

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