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DOI: 10.1177/2167702612455742

2013 1: 16 originally published online 17 October 2012Clinical Psychological Science Jared W. Keeley, Chafen S. DeLao and Claire L. KirkThe Commutative Property in Comorbid Diagnosis: Does A + B = B + A?

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Clinical Psychological Science1(1) 16 29 The Author(s) 2013Reprints and permission:sagepub.com/journalsPermissions.navDOI: 10.1177/2167702612455742http://cpx.sagepub.com

Psychiatric disorders are among the most common disorders inthe United States, with approximately 50% of noninstitutional-ized people reporting at least one disorder during their lifetimesand 30% reporting at least one disorder occurring in the pastyear (Kessler et al., 1994). Psychiatric disorders, however, oftenoccur in bunches (Kessler, Chiu, Demler, & Walters, 2005).When two or more psychiatric disorders occur simultaneously,the coexisting disorders represent psychiatric comorbidity. Theterm comorbidity was introduced by Feinstein in 1970 and isdefined as any distinct additional clinical entity that has existedor that may occur during the clinical course of a patient who hasthe index disease under study (p. 456). Although comorbidityis not unique to psychiatric disorders, it has emerged as a ubiq-

uitous construct. Psychiatric comorbidity is commonplace bothin the community (Kessler, Chiu, et al., 2005) and in treatment-seeking populations (Evren, Barut, Saatcioglu, & Cakmak,2006), whereby half of the individuals meeting criteria for anysingle mental disorder will also meet criteria for two or moremental disorders (Kessler, Chiu, et al., 2005). When multipledisorders occur, said disorders may overlap simply by chance(e.g., an individual with clinical depression may also have acommon cold). Among psychiatric disorders, however, the ratesof comorbidity greatly exceed the expected rates predicted bychance alone (i.e., the product of the base rates of the two

disorders; Boyd et al., 1984; Kessler, Chiu, et al., 2005; Kessleret al., 1994).Although psychiatric comorbidity is a common phenome-

non, the current diagnostic system for psychopathology in theUnited States ( Diagnostic and Statistical Manual of Mental

Disorders , 4th edition, text revision [ DSM-IV-TR ]; AmericanPsychiatric Association [APA], 2000) does not explicitlyaddress the manner in which clinicians should conceptualizecomorbid cases. In fact, the word comorbidity is not evenmentioned in the DSM-IV-TR (APA, 2000), although the con-cept of diagnostic co-occurrence is addressed. In the Multiax-ial Assessment section, the DSM-IV-TR (APA, 2000) statesthat when an individual has one or more disorders on an axis,

the principal diagnosis or reason for the visit should be listedfirst under its respective axis and all subsequent diagnosesshould be listed beneath the principal diagnosis on theirrespective axes. The recording system of the DSM-IV-TR (APA, 2000) implicitly follows an additive model whereby thesymptoms of one disorder are added to the symptoms of the

Corresponding Author: Jared W. Keeley, P.O. Box 6161, Department of Psychology, Mississippi StateUniversity, Mississippi State, MS 39762E-mail: [email protected]

The Commutative Property in ComorbidDiagnosis: Does A + B = B + A?

Jared W. Keeley, Chafen S. DeLao, and Claire L. Kirk Mississippi State University

AbstractThe Diagnostic and Statistical Manual of Mental Disorders (4th edition, text revision) assumes an additive model for describingcomorbid symptomatology, including the commutativity of disorder descriptions across order of presentation (e.g., A +B = B + A). Given the high prevalence of individuals with comorbid conditions, it is important to investigate if cliniciansfollow an additive model when conceptualizing disorders. Three studies involving a total of 138 clinicians tested assumptionsof commutativity for conceptualizations of three disordersmajor depressive disorder (MDD), generalized anxietydisorder (GAD), and antisocial personality disorder (ASPD)by either fixed-choice or free-response descriptions of allpossible pairwise comparisons of the disorders. Clinicians demonstrated less-than-perfect commutativity for all disordercombinations, and this finding was replicated across two samples. In addition, MDD and ASPD tended to overshadow thepresence of GAD in combinations. These results challenge the additive assumptions of the current diagnostic system andmay suggest the order in which diagnoses are conceptualized influences the resulting symptomatology.

Keywordscomorbidity, Diagnostic and Statistical Manual of Mental Disorders (DSM), major depressive disorder, generalized anxietydisorder, antisocial personality disorder

Received 5/10/12; Revision accepted 6/25/12

Empirical Article


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Commutative Property 17

secondand possibly the third, fourth, and fifthto completethe clinical picture (e.g., Disorder A + Disorder B = DisorderAB). For example, the symptoms of an individual with majordepressive disorder (MDD) and generalized anxiety disorder(GAD) may include sad mood (from MDD), persistent worry(from GAD), and sleep disturbance (common to both).

Although the implicit additive model seems logical,research studying how humans combine concepts generallyhas found that people do not always follow additive strategies(Chater, Lyon, & Myers, 1990; Springer & Murphy, 1992;Wisniewski, 1996). One assumption of an additive model ofcombination is that symptom presentation is commutative. Inother words, a person with a principal diagnosis of MDD whosubsequently is diagnosed with GAD should look the same assomeone who has a principal diagnosis of GAD and is laterdiagnosed with MDD (i.e., MDD + GAD = GAD + MDD). Intheory, clinicians should provide an identical symptom profilewhen describing MDD + GAD and GAD + MDD because thedisorders are additive. Research, however, has shown that cli-nicians do not always follow an additive strategy (Keeley &Blashfield, 2010). The current study examines the assumptionthat comorbid disorder descriptions are commutative.

Clinicians conceptualizations of comorbid cases can beconsidered a special case of what cognitive psychologists termconceptual combination . A small but rich literature has exam-ined how humans combine concepts in natural language(Chater et al., 1990; Hampton, 1988; Osherson & Smith, 1981;Springer & Murphy, 1992). The focus of this work has been onnoun-noun combinations, like zebra pants or refrigeratordoor . Some combinations are relatively commonplace, likerefrigerator door , and usually are a means of specifying

languagea refrigerator door is a special kind of door. Othercombinations, like zebra pants , are more novel. Individualsmust undergo some sort of cognitive process when surmisingthe meaning of the new combination. For example, zebra

pants might be pants made out of a striped material or pantsmade specifically for a zebra.

There are two major theories that attempt to account forhow individuals combine concepts. The first, termed the com-

petition among relations in nominals (CARIN) model, pro- poses that a modifier and a head noun are joined through a particular relation (Gagne, 2002; Gagne & Shoben, 1997). Forexample, zebra pants could be pants made of zebra material the concepts are linked using the made of relation. In this

theory, each modifier and noun have particular types of rela-tions with which they are more commonly associated. Themeaning of a combination is chosen among possible relations

based on a probabilistic weighting of the available relations.The second, competing theory of conceptual combination

posits that there are two types of processes for combiningconcepts. The dual-process theory holds that although somecombinations are joined by relations, as in the CARINmodel, others involve a parallel property mapping process(Wisniewski, 1996, 1997; Wisniewski & Love, 1998). Anexample of property mapping would be taking the property

striped from zebra and applying it to a pair of pants in thecombination zebra pants . In this theory, property mapping isnot simply a different form of a relation (specifically, the iden-tity relation), as it is a mapping of alignable features of the twoconcepts involved and does seem to be an independent process(Estes, 2003).

It is interesting to note that the description of conceptualcombinations does not appear to be commutative (Hampton,1988, 1997; Storms, De Boeck, Van Mechelen, & Geeraerts,1993; Storms, De Boeck, Van Mechelen, & Ruts, 1996;Storms, Ruts, & Vandenbroucke, 1998). Reciprocal combina-tions do not have identical descriptions or properties. Forexample, exemplars of the combination sports that are also

games are not the same as exemplars of games that are also sports (Hampton, 1988). Classical set theory would predictthat members of a combination must be a subset of the two

parent concepts; that is, all sports that are games must also besports. Similarly, the overlap between the two concepts ofsports and games should lead to identical sets for the recipro-cal combinations. However, for this example and many others,

participants do not provide commutative descriptions of thecombined concepts (Hampton, 1997).

Conceptual combinations also demonstrate what has beentermed the dominance effect (Storms et al., 1993). Gener-ally speaking, one member of the combination tends to domi-nate the features of the combination. For example, thecombination of pet birds tends to have many more features of

birds than of pets (Storms et al., 1996). Again, the dominanceeffect would not be predicted by classical set theory. However,

both the CARIN and dual-process theories can accommodatedominance of a pair by weighting the influence of each mem-

ber, although the theories would account for the strength ofthat dominance by different means. The dominance effectmight be expressed in diagnostic concepts in a somewhatunconventional fashion, given how the effect has traditionally

been studied by cognitive psychologists. Typically, dominancehas interacted with order of presentation (i.e., pets that arealso birds tested against birds that are also pets ). Because thefeature lists of the concepts are unknown, this method allowsa relativistic comparison of the two lists to help determine ifone concept was dominated. With diagnostic concepts, thefeature list is more determined, due to the concepts definitionsin the diagnostic manual. Thus, it is possible to demonstratethe dominance of one concept over another in a single combi-

nation by determining which features belong to which parentconcept.

Keeley and Blashfield (2010) examined mental health cli-nicians conceptualizations of comorbid psychopathologyas an extension of conceptual combination in general. Theyfound that one property of combination, overextensions, was

present in clinicians descriptions of comorbid disorders,challenging an additive model of diagnostic comorbidity. Thecurrent study examines another property of combination, com-mutativity, given that the current diagnostic system does not

predict (or accommodate) meaningful symptom differences


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for reciprocal pairs of diagnoses (e.g., MDD + GAD vs. GAD+ MDD).

Rather, both the CARIN and dual-process models would predict some noncommutative pairings, depending on the roleand nature of the words in the combination. Clinicians might

judge the specific etiologies and symptoms of diagnostic cat-

egories (considered to be the features of the concept paral-lel to the features of zebra or pants ) to have differentialeffects in combination. Thus, two disorders that are phenom-enologically and etiologically similar should have more com-mutativity than disorders that are less compatible. Therefore,we selected two disorders (MDD and GAD) that share con-siderable symptom overlap to the degree some consider themto be different expressions of the same condition (Brown,Chorpita, & Barlow, 1998; Clark & Watson, 1991; Mineka,Watson, & Clark, 1998) and a third disorder that is phenom-enologically and etiologically dissimilar from both (antisocial

personality disorder [ASPD]; Krueger, Markon, Patrick, &Iacono, 2005). We predict that some degree of noncommuta-tivity will occur overall but that noncommutativity will begreater for combinations including ASPD. In addition, weexpect that the features of one disorder might overshadow thefeatures of another in combination, just as occurs with thedominance effect.

Study 1Study 1 was designed to examine if professionals follow thecommutative property when describing different reciprocalorders of comorbid mental disorders. Given the unstatedassumption that the classification system follows an additive

model, it is important to test if the model holds under workingconditions. This study utilized a relatively conservativemethod for describing disorders symptoms. Participants wereasked to describe disorders using a fixed list of predeterminedsymptoms in order to control for variability in response. Thismethod was chosen to ease the interpretability of results butmay have limited the scope and generalizability of the find-ings. Study 2 then addressed these limitations by altering themethod and replicating the results.

Method Participants. Participants were 35 members of the Associa-

tion for Behavioral and Cognitive Therapies (ABCT). Most par-ticipants were women ( n = 22, 62.86%; men n = 13, 37.14%)and specialized in working with adults ( n = 21, 60.00%, vs.working with children, n = 7, 20.00%, vs. other, n = 7, 20.00%).The mean age was 47.94 ( SD = 11.14) with a mean of 17.80(SD = 10.83) years of experience in the field. Most held aPh.D. ( n = 33, 94.3%; Psy.D., n = 1, 2.86%; other, n = 1,2.86%). The sample was geographically representative of allregions in the United States. Two participants who failed tofollow instructions were excluded from all analyses.

Materials. Participants noted the presence of the symptoms ofthree disorders: MDD, GAD, and ASPD. In an effort to reducethe time required to complete the task, only three stimuli wereused. These three disorders were chosen because they repre-sent two disorders that are conceptually and phenomenologi-cally very similar (MDD and GAD; Brown et al., 1998; Clark

& Watson, 1991; Mineka et al., 1998) and one disorder that isdissimilar to both (ASPD; Krueger et al., 2005).Stimuli were presented each on a separate page. At the top

of the first page, a heading read, Describe an individual with. . . where the ellipsis represented the name of one of the threedisorders used in the study. The next two pages asked partici-

pants what would change in their descriptions if one of theother two disorders in the study were added, such that theheading now read, What would change if the person with . . .also had . . . ? All possible combinations were presented andcounterbalanced across participants.

Under the heading on each page was a list of 120 descrip-tions. These descriptions were chosen to be representative ofthe entire domain of psychopathology and personality func-tioning. It was important to include symptoms beyond simplythe DSM criteria for each disorder in order to assure that par-ticipants were not producing results based only on the con-striction of their response options. The descriptions were takenfrom a major psychopathology assessment instrument (thePersonality Assessment Inventory [PAI], Morey, 1991) and thecurrently most investigated theory of personality functioning,the Big Five personality factors (Costa & Widiger, 1994). Ofthe 120 descriptors included, 60 came from the PAI and 60came from the Big Five factors. For the PAI, the 60 descrip-tions were taken from the 15 clinical and treatment scales,

excluding items on the validity and interpersonal scales. The60 items selected for inclusion were those from each scale thathad the highest loadings per scale in factor analytic studies(Morey, 1991). An equal number of items were selected fromeach scale, assuming that the items were not directly redun-dant. Items were rephrased to be one to three words in length(e.g., feeling worthless, fear of abandonment). The remain-ing 60 descriptors came from the Big Five personality factors.Each of the five factors has six facets. A representative descrip-tor for the extremes of each facet was included (2 extremes 6facets 5 factors = 60 items; e.g., accomplished vs. aim-less as the two poles of achievement striving). The 120descriptions were presented in alphabetical order.

Participants also completed a brief demographic question-naire assessing their sex, age, years of experience in the field,type of clients usually seen, degree, American Board of Pro-fessional Psychologist status, state of residency, and familiar-ity with a variety of assessment measures, including familiaritywith the five factor model and DSM systems.

Procedure. Six hundred members of ABCT were contactedthrough the mail with information about the study. Thoseexpressing interest were instructed to return a postcard with


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Commutative Property 19

their preferred mailing address. Sixty-eight potential participants returned postcards and received the materials (11.33%return rate); of those, 35 completed the study (51.47% returnrate).

Participants first completed the demographic question-naire, which was followed by an instruction sheet for the task.

Participants were instructed to create descriptions of three ini-tial disorders (by marking all descriptors that applied to the principal diagnosis) and note how those descriptions wouldchange (by either adding or subtracting symptoms) when the

principal diagnosis became comorbid with an additional diag-nosis. The instructions explicitly stated that participants shouldcomplete the task based on their own clinical experience ratherthan attempting to reproduce the DSM criteria. Each partici-

pant saw each of the three disorders singly (MDD, GAD, andASPD) as well as in all possible combinations (MDD + GAD,MDD + ASPD, GAD + MDD, GAD + ASPD, ASPD + MDD,and ASPD + GAD). The order in which the single disordersand their combinations were presented was counterbalancedacross participants. For the initial description of a single disor-der, participants were instructed to circle all descriptors fromthe list of 120 that they believed to be relevant for that disor-der. For a comorbid combination, participants were instructedto circle additional symptoms relative to the comorbid combi-nation and cross out symptoms that no longer applied as aresult of the secondary diagnosis. In that way, the methodol-ogy explicitly reflected participants intentional changes torule out possible chance omissions or commissions whendescribing comorbid pairs.

ResultsIntrarater agreement. The dependent variable of interest inthis study is the amount of agreement for a participant betweenreciprocal orders of disorder pairs (e.g., MDD + GAD andGAD + MDD). For ease of presentation, we refer to a disorder

pair with the convention MDD & GAD to represent theagreement between the reciprocal comorbid pairs. We calcu-lated agreement using Cohens (1960) kappa statistic. Kappais a metric commonly used in interrater agreement because itaccounts for chance levels of agreement. For this study, it isimportant to account for chance agreement because the natureof the disorder description task could inflate agreement artifi-cially. Of the list of 120 descriptors, often a large number

would not be selected as relevant to either pair. This high number of exclusions relative to descriptors included would inflateagreement but would be largely meaningless on a theoreticallevel. For example, a participant might exclude paranoid ide-ation from both reciprocal pairs of MDD & GAD because

paranoid ideation is not typically associated with MDD, GAD,or MAD & GAD, but that exclusion is not truly agreementon the commutativity of the disorder descriptions. Kappa isable to factor out the amount of agreement predicted by chance

based on the number of descriptions included versus thoseexcluded.

The description of the comorbid pair (e.g., MDD + GAD)was generated by taking the descriptors selected for the firstdisorder (MDD) and then adding the symptoms selected forthe second disorder (GAD) and removing symptoms specifi-cally excluded (those that the participant crossed out) from thesecond disorder. We were then able to calculate kappa by

examining the number of descriptors a participant included in both pairs (e.g., MDD + GAD and GAD + MDD), the numberincluded for one pair but not the other, and the numberexcluded from both. We calculated kappa for each of the threereciprocal disorder pairs (MDD & GAD, MDD & ASPD,GAD & ASPD) for each participant. Table 1 displays the meanand median kappa value for each disorder pair across all par-ticipants, as well as measures of variability.

The first thing to note about Table 1 is that participants var-ied widely in their agreement regarding the reciprocal pairs.Indeed, nearly the full range of variability (0.001.00) is pres-ent for two of the disorder pairs (MDD & ASPD and GAD &ASPD) and about half the range of variability for the other(MDD & GAD). Thus, some participants expressed near per-fect commutativity for a pair, whereas others displayed verylittle agreement. The standard deviations for each represent anaverage variability corresponding to 15% of the possible rangeof the scale. Clearly, clinicians approached the commutativityof these disorder pairs in different ways. However, it could bethat the majority of the sample conceptualized the pairs in aconsistent, commutative fashion. Thus, we also tested thecommutativity of the disorder pairs directly.

Test of commutativity. Perfect commutativity (i.e., MDD +GAD = GAD + MDD) would be represented by a kappa value

of 1.00. In that case, no descriptors would be given to onedisorder pair that were not also present in the other. Thus, wetested whether the mean kappa value for each disorder pairwas statistically equal to 1.00. We entered the kappa values forthe three disorder pairs into an overall multivariate analysis ofvariance (MANOVA). The overall model was significant,Wilkss (3, 30) = .031, p < .001, indicating differences

between or within variables. Custom hypothesis tests indi-cated that the mean value for each pair was significantly dif-ferent from 1.00, MDD & GAD F (1, 32) = 98.28, p < .001,2 = .75, 95% confidence interval (CI) for mean [.7094, .8085];

Table 1. Means, Medians, and Variability of Kappa Values for theDisorder Pairs in Study 1

Cohens Kappa MDD & GAD MDD & ASPD GAD & ASPD

Mean .7589 .6659 .6190Median .7620 .6666 .6320Standard deviation .1397 .1589 .1594Minimum .4234 .1215 .2652Maximum .9785 1.0000 .9409

Note: MDD = major depressive disorder; GAD = generalized anxietydisorder; ASPD = antisocial personalit y disorder.


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20 Keeley et al.

MDD & ASPD F (1, 32) = 145.87, p < .001, 2 = .82, 95% CIfor mean [.6096, .7223]; and GAD & ASPD F (1, 32) = 188.61,

p < .001, 2 = .85, 95% CI for mean [.5625, .6755]. Indeed, theconfidence intervals for these means do not approach 1.00.Rather, these means are spread well below the value of 1.00, asindicated by their relatively large effect sizes. Therefore, the

sample evidenced lower kappa values than perfect commuta-tivity for each disorder pair.Although the DSM-IV-TR (APA, 2000) would predict per-

fect commutativity (i.e., a kappa value of 1.00), perfection is ararely attained state. To allow for human error, we subse-quently compared the mean kappa value for each disorder pairto a reliability of .85. The comparison point was developed inlight of the Structured Clinical Interview for DSM Disorders(SCID; i.e., SCID-I and SCID-II) test-retest values for MDD,GAD, and ASPD. With a 7- to 10-day test-retest interval, theaverage kappa value for MDD was .73 and for GAD was .63(Zanarini & Frankenburg, 2001); with a 1- to 3-week test-retest interval, the average kappa value for MDD was .64 andfor GAD was .56 (Williams et al., 1992). With a 1- to 3-weektest-retest interval, the average kappa value for ASPD was .76(First et al., 1995). Because the test-retest interval in the previ-ously cited reliability tests was substantially greater than the30-min interval for the current study, we believed a kappavalue of .85 represented a fair adjustment. Custom hypothesistests indicated that the mean value for each pair was signifi-cantly different from .85, MDD & GAD F (1, 32) = 14.03,

p < .001, 2 = .305; MDD & ASPD F (1, 32) = 44.29, p

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