Neuropsychology 2015, Vol. 29, No. 5, 683– 692

© 2015 American Psychological Association 0894-4105/15/$12.00 http://dx.doi.org/10.1037/neu0000153

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Greater Than the Sum of Its Parts: ␦ Improves Upon a Battery’s Diagnostic Performance Donald R. Royall

Teruyuki Matsuoka

University of Texas Health Science Center at San Antonio and the South Texas Veterans’ Health System, Audie L. Murphy Division GRECC, San Antonio, Texas

Kyoto Prefectural University of Medicine

Raymond F. Palmer

Yuka Kato

University of Texas, Health Science Center at San Antonio

Kyoto Prefectural University of Medicine

Shogo Taniguchi

Mayu Ogawa and Hiroshi Fujimoto

Reinan Hospital, Fukui, Japan

Kyoto Prefectural University of Medicine

Aiko Okamura

Keisuke Shibata

Yashio Hospital, Saitama, Japan

Kawagoe Hospital, Kyoto, Japan

Kaeko Nakamura

Shutaro Nakaaki

Kyoto Prefectural University of Medicine

Keio University

Hiroyuki Koumi

Masaru Mimura

Hanazono University

Keio University

Kenji Fukui and Jin Narumoto Kyoto Prefectural University of Medicine Objective: “␦”, a latent variable constructed from batteries that contain both cognitive and functional status measures, can accurately diagnose dementia relative to expert clinicians. The minimal assessment needed is unknown. Methods: We validated 2 ␦ homologs in a convenience sample of elderly Japanese persons with normal cognition (NC), mild cognitive impairment (MCI), and dementia (n ⫽ 176). The latent ␦ homolog “d” (for dementia) was constructed from Instrumental Activities of Daily Living (IADL) and Japanese translations

This article was published Online First February 9, 2015. Donald R. Royall, Departments of Psychiatry, Medicine, and Family and Community Medicine, University of Texas Health Science Center at San Antonio, and South Texas Veterans’ Health System, Audie L. Murphy Division GRECC, San Antonio, Texas; Teruyuki Matsuoka, Department of Psychiatry, Graduate School of Medical Science, Kyoto Prefectural University of Medicine; Raymond F. Palmer, Department of Family and Community Medicine, University of Texas Health Science Center at San Antonio; Yuka Kato, Department of Psychiatry, Graduate School of Medical Science, Kyoto Prefectural University of Medicine; Shogo Taniguchi, Reinan Hospital, Fukui, Japan; Mayu Ogawa and Hiroshi Fujimoto, Department of Psychiatry, Graduate School of Medical Science, Kyoto Prefectural University of Medicine; Aiko Okamura, Yashio Hospital, Saitama, Japan; Keisuke Shibata, Kawagoe Hospital, Kyoto, Japan; Kaeko Nakamura, Department of Psychiatry, Graduate School of Medical Science, Kyoto Prefectural University of Medicine; Shutaro Nakaaki, Department of Neuropsychiatry, Keio University School of Medicine; Hiroyuki Koumi, Department of Clinical Psychology, Faculty of Social Welfare, Hanazono University; Masaru Mimura, Department of Neuropsychiatry, Keio University School of Medicine; Kenji Fukui and Jin

Narumoto, Department of Psychiatry, Graduate School of Medical Science, Kyoto Prefectural University of Medicine. This research was supported by “Redesigning Communities for Aged Society” project (Research Institute of Science and Technology for Society, Japan Science and Technology Agency: RISTEX, JST). Dr. Royall is supported by the Julia and Van Buren Parr endowment for Alzheimer’srelated research. D. R. Royall holds copyrights to the EXIT25 and CLOX. DRR and RFP have disclosed ␦’s invention to the University of Texas Health Science Center at San Antonio (UTHSCSA), which has filed patent application 2012.039.US1.HSCS and provisional patents 61/ 603,226 and 61/671,858 relating to the latent variable ␦’s construction and biomarkers. D. R. Royall invented ␦, the CLOX, and EXIT25, designed the study, performed the analyses, and wrote the article. R. F. Palmer assisted in the analyses and with writing the article. J. Narumoto translated the J-EXIT25 and J-CLOX, collected data, and assisted with writing the article. All other authors collected the data, and assisted with editing the article. Correspondence concerning this article should be addressed to Donald R. Royall, Department of Psychiatry, UTHSCA, 7703 Floyd Curt Drive, San Antonio, TX 78299 –3900. E-mail: [email protected] 683

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of the Executive Clock-Drawing Task (CLOX), Frontal Assessment Battery (FAB), and Executive Interview (EXIT25). The latent delta homolog “d3” was constructed from a restricted set of d=s factor loadings. Results: d and d3 were highly intercorrelated (r ⫽ .97) and strongly related to both IADL and dementia severity, as rated blindly by the Clinical Dementia Rating Scale (CDR). d was more strongly related to IADL and CDR than any of its indicators. In multivariate regression, d explained more variance in CDR scores than all of its indicators combined. d=s areas under the receiver operating characteristic curve (AUC) were 0.95 for the discrimination between Alzheimer’s disease (AD) vs. NC, 0.84 for AD vs. MCI and 0.81 for NC vs. MCI. d3’s AUC’s were statistically indiscriminable. These AUC’s are higher than any of d=s indicators, as reported recently by Matsuoka et al. (2014), as well as the Mini-Mental State Examination (MMSE), which had been made available by Matsuoka et al. to the CDR raters. Conclusions: Latent variables can improve upon a battery’s diagnostic performance and offer the potential for accurate dementia case-finding after a minimal bedside assessment.

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Keywords: CLOX, dementia, executive function, EXIT25, instrumental activities of daily living

Dementia is a syndrome characterized by disabling cognitive impairment. Neither psychometric testing nor biomarkers have been found adequate to diagnose that syndrome in the absence of clinical examination. However, the resulting need for in-person assessment by expert clinicians limits dementia research and treatment to health care settings that disadvantage minorities, rural populations, those without caregivers, the uninsured, and underinsured. We have developed a novel method for the accurate psychometric diagnosis of dementia. Our approach uses theory-driven confirmatory factor analysis (CFA) in a structural equation model (SEM) framework to construct an error-free continuous measure of dementia severity (i.e., “␦” for dementia). Our approach is conceptually simple. While cognitive impairment is widely held to be the hallmark of dementia, three conditions are necessary to that diagnosis (Royall et al., 2007): 1.

there must be acquired cognitive impairment(s);

2.

there must be functional disability; and

3.

the disability must be related to the cognitive impairment(s) that are observed.

This implies that the essential feature(s) of dementing processes can be resolved to “the cognitive correlates of functional status.” Establishing the biomarkers of these correlates could open the way toward an empirical foundation for dementia’s prediction, diagnosis, evaluation, and treatment. Surprisingly, the association between many observed cognitive measures/domains and functional status is statistically “weak,” albeit significant (Royall et al., 2007). However, an empirical definition of the cognitive correlates of functional status is better approached by CFA in SEM. Some suggest that functional status is best linked to cognitive performance through “general intelligence” (Gottfredson, 1997). General intelligence is often operationalized by Spearman’s “g” factor (Spearman, 1904; Spearman & Wynn-Jones, 1951), that is, a latent variable representing the shared variance in the dominant factor extracted from a cognitive battery. We have explored whether g, that is, the shared variance across cognitive tasks, can be distinguished from “␦,” that is, the psychometric correlates of functional status. If so, then ␦ and not g may be most

relevant to dementia case-finding, and the biomarkers associated with ␦ may mediate dementing processes. ␦ can be constructed from any battery that contains both cognitive measures and one or more measures of Instrumental Activities of Daily Living (IADL). ␦’s design explicitly parses a battery’s shared variance (i.e., Spearman’s g) into orthogonal fractions (g= and ␦) of which only ␦ is related to functional status (i.e., ␦’s “target indicator”) (Royall & Palmer, 2012). Therefore, by our definition above, only ␦’s variance is both necessary and sufficient to dementia case finding. When constructing ␦, a battery of observed variables are fit to a linear measurement model as specified in Equation 1 (below). ␦ and g= are the latent dementia and cognitive constructs, respectively, and the εj’s are unobserved measurement errors. The ␭ js are regression coefficients that scale each indicator. Measurement errors are assumed uncorrelated and the latent variable means and variances were fixed to 0 and 1, respectively allowing all loadings to be freely estimated. Indicator variables are adjusted for covariates, usually age, gender, education, and ethnicity, resulting in latent variables adjusted for these variables. Y1 ⫽ ␦␭1

⫹g␭2

⫹ε1

Y2 ⫽ ␦␭3

⫹g␭4

⫹ε2

Y3 ⫽ ␦␭5

⫹g␭6

⫹ε3

···

···

···

Yn ⫽ ␦␭2n ⫺ 1

⫹g␭2n ⫹εn

YIADL ⫽ ␦␭(2n ⫹ 2) ⫺ 1

(1)

⫹εn ⫹ 1

␦ homologs have achieved areas under the receiver operating curve (AUC /ROC) of 0.92– 0.99 for the discrimination of wellcharacterized Alzheimer’s disease (AD) cases versus controls in four datasets to date, although each ␦ homolog accounts for a minority of the variance in observed cognitive performance. The latent variable g= (␦’s residual in Spearman’s g) and measurement “error” (including domain specific variance) account for the majority of variance, yet g= has an AUC of only 0.52– 0.66 (Gavett et al., in press; Royall & Palmer, in press; Royall, Palmer, O’Bryant, & the Texas Alzheimer’s Research and Care Consortium, 2012; Royall, Palmer, & the Texas Alzheimer’s Research and Care Consortium, 2013, 2014; Royall, Palmer, Vidoni, Honea, & Burns, 2012, 2013).

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LATENT VARIABLES FOR DEMENTIA CASE-FINDING

Because Spearman’s g contributes to every cognitive measure, ␦ might be derived from any existing dataset that also contains an IADL measure. We have constructed ␦ from a comprehensive battery of formal measures (Royall, Palmer, & O’Bryant, et al., 2012), from small batteries of formal measures (Royall, Palmer, et al., 2013), and from brief batteries of “bedside” measures (Royall, Palmer, et al., 2013). Regardless of the measures used to construct it, ␦ retains its strong association with dementia severity, as measured by clinical dementia rating (CDR) scale (Hughes et al., 1982) global scores or “sum of boxes” (CDR-SB), and large AUC for the discrimination between demented and nondemented persons. We have successfully modeled the rate of change in ␦ scores (“⌬␦”) over four waves of annual follow-up in the Texas Alzheimer’s Research and Care Consortium (TARCC). Baseline ␦ and ⌬␦ explain 74% of variance in Wave 4 CDR-SB, independent of g=, ⌬g=, baseline CDR-SB, and covariates (Palmer & Royall, 2013). In the National Alzheimer’s Coordinating Center (NACC)’s Unified Data set (UDS), ⌬␦ is strongly associated with prospective change in CDR-SB (r ⫽ ⫺0.94, p ⬍ .001) (Gavett et al., in press). The interindividual variability in ␦ scores among nondemented persons predicts their prospective rates of cognitive decline (Royall & Palmer, 2012). Therefore the future conversion risk of nondemented persons may also be amenable to modeling by this method. These observations have profound implications for dementia’s assessment: 1.

The majority of the information obtained by any psychometric battery will not relate to IADL, and therefore to dementia. This undermines the rationale for the “comprehensive” psychometric testing of dementia, since (a) ␦ can be extracted from briefer batteries at less expense and with less administrative and subject burden, (b) domain specific cognitive variance (i.e., “Memory,” “Executive Function,” etc.) is residual to Spearman’s g and therefore ␦ (by definition). This residual variance can be shown not to contribute to dementia status independently of ␦, and (c) norms-based dementia and MCI case definitions are based on observed cognitive performance and therefore biased by g=’s major (but irrelevant) contribution.

Until now, expert clinical consensus has been required to circumvent the limitations of psychometric testing. ␦ offers an empirical substitute for clinical consensus, as evidenced by its very strong ROC performance. This potentially frees valid dementia case finding from specialized centers and expert consensus. ␦ also potentially obviates the need for MCI’s categorical discrimination from “dementia” as the interindividual variability in ␦ scores conveys more detailed information about a subject’s dementia risk (i.e., r ⬎ .9 vs. future CDR scores) (Gavett et al., in press; Palmer & Royall, 2013). 2.

The latent variable ␦ can be constructed from almost any cognitive battery. We can construct ␦ homologs in existing datasets regardless of the measures they contain. We can construct ␦ from minimal batteries (possibly even item level data!) and yet achieve AUCs comparable to formal psychometrics.

3.

685

␦’s factor scores can be exported as a composite “␦ score.” The ␦ score then becomes a continuously varying, normally distributed dementia specific phenotype. It can be used to effectively rank order each individual in a cohort with respect to their relative position along a “dementia”-specific continuum. ROC analysis can then define optimal empirical boundaries for “normal cognition,” “MCI,” and “dementia.” Alternatively, the interindividual variability in dementia status can be modeled; that is, as predictors in biomarker studies.

We have examined ␦’s associations with regional gray matter density among n ⫽ 23 AD, n ⫽ 47 MCI cases, and n ⫽ 76 controls in the University of Kansas Brain Aging Project (BAP) (Royall et al., 2012). ␦’s AUC for the discrimination between AD and controls in this sample was 0.987, and AUC ⫽ 0.955 for the discrimination between MCI and AD. ␦ mapped to elements of the default mode network (DMN), which has recently been associated with AD (Buckner, Andrews-Hanna, & Schacter, 2008; Buckner et al., 2005, Greicius, Srivastava, Reiss, & Menon, 2004; Zhou & Seeley, 2014). ␦ scores correlated r ⫽ - 0.57 (p ⬍ .001) with DMN gray matter atrophy and survived adjustment for diagnosis, global atrophy, and atrophy in the motor or posterior cingulate-precuneus networks. The latent variable ␦’s exceptional ability to replicate clinicians’ dementia diagnoses may stem from its ability to detect pathology in this key network. The DMN’s hubs are specifically targeted by ␤-amyloid deposition (Buckner et al., 2009). Tauopathy in the same hubs is strongly and specifically associated with clinical dementia (Royall et al., 2002). The DMN has the interesting property of being “anticorrelated” with task-specific cortical activations (Uddin, Kelly, Biswal, Castellanos, & Milham, 2009). This means that activity in the DMN is reduced during cognitive testing. This suggests a fundamental limitation on the ability of observed cognitive measures to accurately diagnose dementia on their own; this key network cannot be easily interrogated by cognitive tasks! This also explains why ␦ accounts for such a small proportion of overall cognitive variance. One of ␦’s potential applications would be to construct it from a minimal cognitive assessment. The bare minimum required is currently unknown. Nevertheless, we have constructed one ␦ homolog (“dMA”) from as little as the Mini-Mental State Examination (Folstein, Folstein & McHugh, 1975) (MMSE) and CLOX: An Executive Clock-Drawing Task (CLOX) (Royall, Cordes, & Polk, 1998). dMA achieved an AUC of 0.96 for the diagnosis of AD versus all others, in well-characterized Mexican American (MA) TARCC participants (Royall, Palmer, & the Texas Alzheimer’s Research and Care Consortium, 2013). If ␦ retains its diagnostic accuracy when constructed from bedside measures, it would allow dementia to be diagnosed less expensively, since expert interpretation of formal psychometrics might not then be required. This would free valid dementia case finding from the clinic, and allow ␦’s determination in populationbased samples, either prospectively, or post hoc, in datasets that are currently limited by their lack of comprehensive psychometrics and/or expert consensus clinical diagnoses. A recent paper by Matsuoka et al. (2014) allows us to further explore this issue. They recently validated Japanese language

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translations of CLOX and the Executive Interview (EXIT25) (Royall, Mahurin, & Gray, 1992) in a small sample of elderly persons with AD and other dementias. These measures were compared with other bedside screening tests, including the Frontal Assessment Battery (FAB) (Dubois, Slachevsky, Litvan, & Pillon 2000) and the MMSE. Together, these explained 55% of the variance in IADL ratings. The MMSE, which was unblinded to the CDR rater, was the strongest IADL predictor. It achieved an AUC of 0.92 for the discrimination between dementia cases and NC. Matsuoka’s battery is sufficient for the post hoc construction of a new ␦ homolog (i.e., “d”). We hypothesize that d scores will explain more variance in IADL and the CDR than Matsuoka’s entire battery, and will outperform all of its individual measures as predictors of CDR-rated diagnostic status. We also intend to explore whether d=s psychometric properties can be retained by a minimal cognitive assessment that does not reference IADL performance (i.e., “d3”). Such a finding would facilitate ␦’s assessment in a wide range of clinical settings, and could extend its utility to the prediction of IADL and other clinical outcomes.

Method This study is a secondary analysis of data obtained by Matsuoka et al. (2014). They recently developed Japanese language versions of Executive Interview (J-EXIT25) and CLOX: An Executive Clock-Drawing Task (J-CLOX) and validated them in a convenience sample of elderly Japanese volunteers. Details of these measures translation and validation are available elsewhere.

Subjects The participants represented 201 consecutive older persons who visited the Center for Diagnosis of Dementia at Kyoto Prefectural University of Medicine (n ⫽ 172), Ayabe City Hospital (n ⫽ 8), or Fukuchiyama City Hospital (n ⫽ 2), or who lived in a nursing home (n ⫽ 19). Sixty-two men and 139 women (mean age ⫾SD, 78.4 ⫾ 6.4 years old; mean education ⫾SD, 11.4 ⫾ 3.0 years) participated in the study. A subset was chosen for this analysis. Inclusion criteria consisted of (a) subject’s age of 65 or above, (b) a CDR global score of less than 3, and (c) a MMSE score of 10 or above. All participants were comprehensively assessed by a geriatric psychiatrist. On the basis of that exam, the 176 selected subjects were diagnosed as NC (n ⫽ 45), MCI (n ⫽ 40), or “Dementia” (n ⫽ 91). The Ethics Committee of Kyoto Prefectural University of Medicine approved the study and informed consent was obtained from all subjects.

Clinical Assessments All subjects were evaluated using the CDR, J-CLOX, J-EXIT25, FAB (Dubois et al., 2000), IADL, and MMSE. The CDR was rated blind to the J-CLOX, J-EXIT25, and FAB. The CDR (Hughes et al., 1982) rates dementia severity across six domains—memory, orientation, judgment, community affairs, home and hobbies, and personal care. From these ratings, an algorithm derives global ratings of CDR ⫽ 0, “normal”; CDR 0.5,

“questionable dementia”; CDR ⫽ 1, “mild dementia”; CDR ⫽ 2, “moderate dementia”; or CDR ⫽ 3, “severe dementia” (excluded from these analyses). IADL (Lawton & Brody, 1969) were assessed using informant ratings. The ability to use the telephone, go shopping, use transportation, handle finances, and responsibility for medication adherence were rated in both genders. Additionally, housekeeping, food preparation, and laundry were rated only in women. The total IADL scale is 5 in men and 8 in women. The J-CLOX: An Executive Clock-Drawing Task (Royall, Cordes, & Polk, 1998) in Japanese translation (Matsuoka et al., 2014) is a brief executive control function measure based on a clock-drawing task and is divided into two parts. J-CLOX1 is an unprompted task that is sensitive to executive control. J-CLOX2 is a copied version that is less dependent on executive skills. CLOX1 is more “executive” than other comparable clock-drawing tasks (Royall et al., 1999). Each J-CLOX subtest is scored on a 15-point scale. Lower J-CLOX scores are impaired. Matsuoka et al. (2014) found CLOX1 to have an area under the receiver operating curve (AUC /ROC) of 0.82 for the discrimination between dementia cases and nondemented persons (MCI and NC) in their cohort. The CDR was rated blind to J-CLOX scores. The J-EXIT25 (Royall et al., 1992) in Japanese translation (Matsuoka et al., 2014) is composed of 25 items indicating frontal circuit pathology. Each item is rated on a 3-point response: 0 (intact performance), 1 (a specific partial error or equivocal response), and 2 (specific incorrect response or failure to perform). A total score ranges from 0 to 50, with a higher score indicating greater impairment. A score of 15/50 best discriminates normal elderly from all cause dementia (sensitivity ⫽ 93%, specificity ⫽ 83%, Receiver operating characteristic (ROC) ⫽ 0.93, n ⫽ 200) (Royall et al., 2001). Matsuoka et al. (2014) found the EXIT25 to have an AUC of 0.88 for the discrimination between dementia cases and nondemented persons. The CDR was rated blind to the J-EXIT25. The FAB (Dubois et al., 2000) consists of six items to explore the different aspects of frontal lobe function. A score in each item ranges from 0 to 3 and a total score of the FAB is 18, with a lower total score indicating more frontal lobe dysfunction. Matsuoka et al. (2014) found the FAB to have an AUC of 0.79 for the discrimination between dementia cases and nondemented persons. The CDR was rated blind to the FAB. The MMSE (Folstein, Folstein, & McHugh, 1975; Sugishita, 2012) is a well-known and widely used test for screening cognitive impairment. Scores range from 0 to 30. Scores less than 24 reflect cognitive impairment. MMSE scores were known to the CDR raters. Matsuoka et al. (2014) found the MMSE to have an AUC of 0.92 for the discrimination between dementia cases and nondemented persons.

Statistical Analyses Analysis Sequence This analysis was performed using analysis of moment structures (AMOS) software (Arbuckle, 2006). All analyses were conducted in an SEM framework. First we constructed two nested multivariate regression models. In these models, J-CLOX1, J-CLOX2, J-EXIT25, FAB, and

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LATENT VARIABLES FOR DEMENTIA CASE-FINDING

MMSE scores were treated as independent multivariate predictors of (a) IADL, and (b) CDR scores. The dependent variables were also adjusted for age, education, and gender (Figure 1). Next, we reorganized the same variables as a bifactor latent ␦ homolog (i.e., “d”), as previously described (Royall, Palmer, & the Texas Alzheimer’s Research and Care Consortium, 2013) (Figure 2). d was indicated by J-CLOX1, J-CLOX2, FAB, J-EXIT25, and IADL. d=s residual in Spearman’s g (i.e., “g’”) was indicated only by J-CLOX1, J-CLOX2, FAB, and J-EXIT25. All the observed indicators were again adjusted for age, education, and gender. The MMSE was omitted from this analysis because CDR raters were not blind to that measure. Covariances between the residuals were allowed to be estimated if they were significant and improved model fit. The latent variables d and g= are implicitly orthogonal. This was confirmed by intercorrelation. Covariate adjusted CDR scores were correlated with d. Finally, the latent variable d was output as two composite variables, d and d3. d was constructed from the factor loadings of d=s five indicator variables in Figure 2, including IADL and FAB. However, as a test of d=s “indifference to its indicators,” we removed IADL and the FAB (which is redundant with the EXIT25) from the model and used the remaining factor loadings to construct d3. Thus, the d3 composite is informed only by the EXIT25 and CLOX scores (nevertheless weighted by their multivariate associations with IADL and FAB scores). Since the d3 composite is informed by a briefer battery and does not invoke IADL, it could be estimated in patients without an intact patient/ informant dyad, and might also be used to estimate IADL from a simple bedside cognitive assessment. d and d3 were then validated as predictors of observed diagnostic class by ROC analyses (see below).

Figure 1. Nested multivariate regression models of cognitive measures as competing independent predictors of IADL and CDR scores. All observed indicators are adjusted for age, education and gender (pathways not shown for clarity).

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Figure 2. Latent variables d and g=. All observed indicators are adjusted for age, education and gender (pathways not shown for clarity).

Missing data. These models were all constructed in an SEM framework, using raw psychometric data. There was no missing data. Fit indices. Model fit was assessed using four common test statistics: chi-square, the ratio of the chi-square to the degrees of freedom in the model (CMIN/DF), the comparative fit index (CFI), and the root mean square error of approximation (RMSEA). Where two nested models were compared, Akaike’s information criterion (AIC) was added. A lower AIC statistic indicates better fit (Akaike, 1987). A nonsignificant chi-square signifies that the data are consistent with the model (Bollen & Long, 1993). However, in large samples, this metric is limited by its tendency to achieve statistical significance when all other fit indices (which are not sensitive to sample size) show that the model fits the data very well. A CMIN/DF ratio ⬍5.0 suggests an adequate fit to the data (Wheaton, Muthén, Alwin, & Summers, 1977).The CFI statistic compares the specified model with a null model (Bentler, 1990). CFI values range from 0 to 1.0. Values below 0.95 suggest model misspecification. Values approaching 1.0 indicate adequate to excellent fit. An RMSEA of 0.05 or less indicates a close fit to the data, with models below 0.05 considered “good” fit, and up to 0.08 as “acceptable“(Browne & Cudeck, 1993). All fit statistics should be simultaneously considered when assessing the adequacy of the models to the data. ROC curves. The diagnostic performance or accuracy of a test to discriminate diseased from normal cases can be evaluated using ROC curve analysis (Metz, 1978; Zweig & Campbell, 1993). Briefly, the true positive rate (sensitivity) is plotted as a function of the false positive rate (100-specificity) for different cut-off points of a parameter. Each point of the ROC

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curve represents a sensitivity/specificity pairing corresponding to a particular decision threshold. The area under the ROC curve (AUC) is a measure of how well a parameter can distinguish between two diagnostic groups (diseased/normal). For these analyses, “Dementia” was coded as CDR ⱖ1.0, “MCI” as CDR ⫽ 0.5, and NC as “CDR ⫽ 0.” The analysis was performed in Statistical Package for the Social Sciences (SPSS; PASW, 2009).

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Results As previously reported (Matsuoka et al., 2014), the mean J-CLOX1 score was 10.2 ⫾ 3.5, the mean J-CLOX2 score was 13.3 ⫾ 2.0, the mean J-EXIT25 score was 13.6 ⫾ 6.1, the mean FAB score was 12.8 ⫾ 2.8, and the mean MMSE score was 23.0 ⫾ 5.2. Table 1 shows the demographic and neuropsychological data for each diagnostic group. Figure 1 presents the two nested multivariate regression models of each cognitive measure as independent predictors of IADL and CDR score, respectively. Both the predictors and the outcomes were adjusted for age, education, and gender. The model had marginal fit [AIC ⫽ 145.21; RMSEA ⫽ 0.30; CFI ⫽ 0.983; ChiSQ ⫽ 17.21 (1), p ⬍ .001]. The dense intercorrelation among the residuals required to achieve this fit suggests the existence of one or more latent, but poorly modeled, factors loading broadly across the battery (i.e., Spearman’s g, or d and g=). The predictors (including covariates) explained 63% of the variance in IADL. The MMSE (partial r ⫽ .27, p ⬍ .001) and J-EXIT25 scores (r ⫽ ⫺0.19, p ⫽ .025) made significant independent contributions. The predictors explained 67% of the variance in CDR scores. The covariates explained 13% of that total. MMSE (partial r ⫽ ⫺0.53, p ⬍ .001) explained the most variance, but then it was available to the CDR raters at consensus, unlike the other cognitive measures. J-EXIT25 (r ⫽ .33, p ⬍ .001) and CLOX1 scores (r ⫽ ⫺0.13, p ⫽ .049) also made significant independent contributions. J-CLOX2 and the FAB were not independently associated with either outcome.

Table 1 Clinical Characteristics by Diagnostic Group (n ⫽ 176)

Gender, % female Age, years Education, year CDR J-EXIT25 J-CLOX1 J-CLOX2 MMSE FAB

NC (n ⫽ 45)

MCI (n ⫽ 40)

Dementia (n ⫽ 91)

75.6 75.8 ⫾ 6.0e 13.0 ⫾ 2.8e 0.0c,e 7.8 ⫾ 3.8c,e 12.8 ⫾ 2.1d,e 14.2 ⫾ 0.9e 27.8 ⫾ 2.1c,e 14.9 ⫾ 1.7c,e

72.5 78.6 ⫾ 6.7b 11.1 ⫾ 2.5b 0.5a,e 11.6 ⫾ 4.9a,e 10.8 ⫾ 2.9b,e 13.8 ⫾ 1.0f 24.8 ⫾ 2.9a,e 13.2 ⫾ 1.9a,e

67.0 80.5 ⫾ 5.8a 10.6 ⫾ 3.0a 1.2 ⫾ 0.4a,c 18.0 ⫾ 5.3a,c 8.3 ⫾ 3.5a,c 12.3 ⫾ 2.5d 18.9 ⫾ 4.3a,c 11.1 ⫾ 2.9a,c

Note. Except for gender, data are shown as the mean ⫾ standard deviation. CDR, clinical dementia rating; J-EXIT25, Japanese versions of Executive Interview; J-CLOX, Japanese version of Executive Clock Drawing Task; FAB, Frontal Assessment Battery; MMSE, Mini-Mental State Examination score; MCI, mild cognitive impairment; NC, normal control. a p ⱕ .001 versus NC. b p ⱕ .05 versus NC. c p ⱕ .001 versus MCI. d p ⱕ .05 versus MCI. e p ⱕ .001 versus dementia. f p ⱕ .05 versus dementia.

Figure 2 presents an alternative arrangement of the same observed variables. In this model, g= and d have been extracted from age, education and gender adjusted indicators. By definition, d only was allowed to be associated with IADL. The latent variables d and g= were correlated with CDR scores to facilitate the comparison of their associations with that outcome. This model had excellent and significantly improved fit relative to Figure 1 [AIC ⫽ 104.62; RMSEA ⫽ 0.000; CFI ⫽ 1.000; ChiSQ ⫽ 2.62 (3), p ⫽ .454]. This suggests that Model 2 provides a better representation of the data. d was significantly associated with each cognitive indicator (all p ⬍ .001). It was most strongly associated with J-EXIT25 scores (r ⫽ ⫺0.65) and least strongly with J-CLOX2 (r ⫽ .54). g= was significantly associated with J-CLOX2 (r ⫽ .36), J-EXIT25 (r ⫽ ⫺0.31) and FAB scores (r ⫽ .48) (all p ⱕ .001). J-CLOX1 showed a trend (r ⫽ .18, p ⫽ .053). d was significantly associated with covariate adjusted IADL scores (r ⫽ .51, p ⬍ .001). 67% of IADL variance was explained (i.e., more than the multivariate regression model, including MMSE and covariates). g= was not associated with IADL by definition. Only d was significantly associated with CDR (r ⫽ ⫺0.93, p ⬍ .001). d and d3 composite scores were output from this model as described above. The resulting composites were continuously varying normally distributed variables (i.e., d in Figure 3). They correlated strongly with each other (r ⫽ .97, p ⬍ .001), and with both IADL and CDR scores (Table 2).

ROC Analysis Table 3 presents ROC AUC for d and d3 scores as predictors of the diagnostic groups. d=s AUC was best for the relatively easy discrimination between dementia cases and NC (AUC ⫽ 0.95, CI ⫽ 0.91–0.98). However, it also performed well at more difficult discriminations, including dementia versus MCI (0.84, CI ⫽ 0.77–0.91), and MCI versus NC (AUC ⫽ 0.81, CI ⫽ 0.72–0.90). d3’s restricted battery performed almost as well, that is, Dementia cases and NC (AUC ⫽ 0.95, CI ⫽ 0.92–0.98), Dementia versus MCI (AUC ⫽ 0.84, CI ⫽ 0.77–0.92), and MCI versus NC (0.78, CI ⫽ 0.69 –0.88). d3’s discriminations were not statistically inferior to d=s for any diagnostic classification. Figure 3 presents d=s optimal thresholds for the discriminations between (a)Dementia versus MCI and (b) NC versus MCI. A d score of 0.85 best discriminated between Dementia versus MCI with 77.5% sensitivity and 83.5% specificity. A d score of 1.12 best discriminated between NC versus MCI with 73.3% sensitivity and 77.5% specificity.

Discussion We have confirmed the independent contributions of J-EXIT25 and MMSE scores to IADL, and the entire battery’s aggregate association with functional status [that is, R2 ⫽ 0.63 (with covariates) versus R2 ⫽ 0.565 in Matsuoka et al., 2014]. However, multivariate regression may not be their most efficient application. The latent variable d accounts for a minority of the variance in this cognitive battery. Nevertheless, d and d3 are both more strongly associated with IADL (r ⫽ .54) than are any of the measures that comprise them. In fact, both explain slightly more variance in IADL than does the entire battery,

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Table 3 ROC Analysis of d and d3 as Predictors of CDR Diagnostic Groups Discrimination

d AUC (CI)

d3 AUC (CI)

Dementia vs. NC Dementia vs. MCI MCI vs. NC

0.949 (0.914–0.984) 0.842 (0.770–0.914) 0.809 (0.717–0.901)

0.953 (0.922–0.983) 0.842 (0.768–0.916) 0.784 (0.686–0.882)

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Note. AUC ⫽ area under the curve; MCI ⫽ mild cognitive impairment; NC ⫽ normal controls.

Figure 3. Frequency distribution of d scores.

including the MMSE, which was omitted from d and d3’s construction. This confirms our Method’s ability to extract a battery’s IADL-related variance. d is also more strongly associated with CDR scores than is any of its indicators. Independent of d, g= has no significant association with CDR. The specific relevance of IADL to dementia severity has been demonstrated in our prior work (Royall, Palmer, O’Bryant, & the Texas Alzheimer’s Research and Care Consortium, 2012) and is confirmed here by d=s exceptionally strong association with CDR scores. These findings were expected because raw psychometric performance is composed of at least three compartments of variance, only one of which (␦) is relevant to IADL. Since a measure’s total score reflects g=’s contribution as well as measurement error, the association between observed psychometric performance and IADL is necessarily reduced relative to ␦’s. We have also found the composite d score to be an accurate predictor of categorical dementia status. d=s AUCs are higher than any of its individual indicators as reported by Matsuoka et al. (2014). Moreover, d=s diagnostic ability is not statistically compromised when it is calculated from a subset of its indicators (i.e., as d3). We believe this is because the factor weights of any subset of d=s indicators have already been adjusted for their multivariate associations with the omitted indicators. The significance of this is that ␦ homologs can thereby be exported into more easily acquired datasets, which would pose less

Table 2 Correlation Matrix

d3 IADL CDR

d

d3

IADL

0.97 0.74 ⫺0.74

0.62 ⫺0.73

⫺0.61

Note. CDR ⫽ Clinical Dementia Rating Scale (global); IADL ⫽ instrumental activities of daily living. All p ⬍ .001 by Spearman’s r.

burden to the subject, or achieve other agendas (e.g., low cost, availability in translation, informant free administration, telephone assessment, etc.). Moreover, the intended final battery’s indicators can be embedded within a much larger validation battery and might, therefore, be informed through their associations with more sophisticated, time consuming, or expensively acquired variables or target indicators. Finally, d3’s strong association with IADL demonstrates that a composite derived from a subset of a latent variable’s indicators can be used to estimate the latent variable’s target indicator. It is important to notice that we did not include the MMSE in d=s construction. That measure’s outcome was known to the CDR raters. This may explain the MMSE’s high individual AUC (⫽ 0.92) in Matsuoka et al. (2014). However, both d=s and d3’s AUC were stronger (both ⫽ 0.95), despite the fact none of their indicators were known to the CDR raters and that d3 was extracted from a subset of d=s indicators, which specifically did not include IADL. d also shows improved sensitivity to MCI (relative to the MMSE in Matsuoka et al., 2014) and can accurately distinguish that condition from AD cases, but less accurately from controls. d3 performs almost as well as d for all discriminations, especially considering its relative brevity. We may have had less success in distinguishing ␦ from Spearman’s g in this battery. In ancillary analyses of this cohort (data not shown) Spearman’s g correlated strongly with ␦ and had a comparable AUC for the discrimination between AD and controls. However, ␦’s creation attenuates g=’s associations with cognition relative to those of g, model fit improves, and ␦ explains more variance in IADL and CDR than g. The only way ␦ ⫽ g is if g= collapses as a factor after ␦’s creation. This is obviously not the case. g= is significantly loaded by its indicators. Thus, regardless of how ␦’s identity is adjudicated, ␦ ⫽ g. However, ␦ is operationalized here in a specific cognitive battery. The battery’s composition could conceivably affect ␦’s validity and psychometric performance, and ␦ might approach g as g= weakens as a factor in a specific battery. CLOX1, CLOX2, EXIT25, FAB, MMSE, and IADL might be criticized as “bedside measures” prone to some “‘nuisance variance” being shared among the tests. However, this is unlikely because (a) ␦’s diagnostic performance is no less strong in the current analysis than when constructed from more extensive formal psychometric batteries, as has been reported previously by us and others (notably Gavett et al., in press), and (b) Spearman himself demonstrated g’s validity with as little as a set of sensory discrimination tasks (Spearman, 1904), so the complexity of a measure and the quality of its indicators is not really an issue.

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Although our approach has achieved its goal of distilling a cognitive battery to its most salient aspect, “salience” is defined in relation to the model’s “target” indicator(s). ␦’s target indicator can be any measure IADL. However, we can alter the target and thereby extract the cognitive correlates of alternative clinical outcomes. We have previously constructed one such ␦ “ortholog” representing “the cognitive correlates of depressive symptoms,” and associated it as well with the DMN by voxel-based morphometry (Royall, Palmer, & the Texas Alzheimer’s Research and Care Consortium, 2013). This approach is consistent with the National Institute of Mental Health’s recent emphasis in dimensional conceptualizations of mental disorders, as operationalized in its Research Domain Criteria (RDoC). Other potential targets might be driving ability, decision-making capacity, financial and/or medication management. It is important to note that both ␦ and any alternative orthologs could be extracted from the same cognitive assessment, and simultaneously estimated in individuals after a single clinical interview. Moreover, our results also suggest that those other target indicators might be estimable from a restricted battery, limited to a subset of the validation battery’s cognitive measures. Thus, driving ability, decision-making capacity, and/or financial /medication management might be simultaneously predicted from a single brief telephone assessment, for example, and interpreted without expert review or adjudication. In this study, a d score of 0.85 was found to best discriminate between dementia versus MCI (AUC ⫽ 0.95: sensitivity ⫽ 0.78; specificity ⫽ 0.84). Remarkably, using a much larger battery of formal psychometrics, Gavett et al. (in press) found a ␦ score of 0.80 to most efficiently discriminate between those with and without dementia (including MCI) (AUC ⫽ 0.96: sensitivity ⫽ 0.97; specificity ⫽ 0.72). This suggests that ␦ scores are robust across samples and across psychometric batteries, and that d=s construction in this analysis from brief bedside measures in Japanese translation has not compromised its diagnostic accuracy relative to a battery of formal psychometrics interpreted by experts. ␦/d=s continuous distribution implies a dimensional aspect to dementia’s severity. Optimal d score thresholds precisely mark the boundaries that separate MCI from both controls and cases of dementia in the opinion of expert clinicians. This also suggests that individuals can be rank ordered within those boundaries with regard to their relative dementia status, regardless of their categorical clinical diagnoses. We have previously shown that the interindividual variability in the ␦ scores of nondemented persons predicts prospective rates of change in EXIT25 and CLOX2 scores (Royall & Palmer, 2012). This suggests that d and d3 may have prognostic implications for the dementia risks of even NC and MCI cases, despite their relatively poor categorical discrimination of those conditions. Our model may also help explain the difficult discrimination between NC and MCI. MCI is likely to be a heterogenous condition, composed of three subgroups with widely varying prognoses. ␦ ranks subjects along a continuous dimension of dementia severity. Thus, longitudinal change in ␦ is a very strong determinant of future CDR scores independently of baseline ␦. In contrast, g= is unrelated to functional status, and therefore to dementia, by definition. Thus, it ranks cases along a dimension of cognitive performance that is irrelevant to future dementia status. As a conse-

quence, g= and ⌬g= make trivial contributions to future CDR scores independently of baseline ␦ and ⌬␦ (Palmer & Royall, 2013; Gavett et al., in press). Since MCI is defined by cognitive impairment in the absence of dementia (i.e., a relatively high d score; see Figure 3), it should be comprised of at least three subgroups: cases with poor g=, cases with intermediate d scores, and cases with both. These are broadly recognizable as “amnestic,” “dysexecutive,” and “general” MCI. Only the latter two would be at near-term risk of conversion, and g’s contribution to the last category would be superfluous. Thus, our latent variables may also offer a means to more precisely quantify dementia status and conversion risk from minimal cognitive assessment. Finally, it should be possible to construct ␦ scores in a wide range of disorders based on objective measures of functional status and psychometric performance (Royall et al., 1993). This would allow the recognition of dementia outside of neurodegenerative disorders, for example, in schizophrenia (“dementia praecox”), mood disorders, head injury, and so forth. It would also allow the assessment of an intervention’s effectiveness against “the cognitive correlates of disability,” and/or adjustment for dementia severity when making comparisons across disorders. While our approach may have important theoretical implications for dementia’s psychometric assessment, d and d3 are but two unique ␦ score composites, derived from a single dataset, limited to a specific battery of indicators, and of undemonstrated validity and utility outside of this Japanese language dataset. It remains to be seen if ␦ score composites can be exported across samples, or across linguistic or cultural barriers. However, all ␦ homologs constructed to date have exhibited similar psychometric properties, regardless of their indicators or their sample frames, and we have demonstrated cross-ethnic equivalence with regard to one ␦ homolog’s mean and factor loadings for Mexican American versus Non-Hispanic White TARCC participants (Royall & Palmer, 2015). ␦’s use of caregiver-rated IADL measures further limits its construction to intact subject-informant dyads. However, d3’s validation potentially sidesteps that limitation, and may allow ␦ orthologs to predict their target indicators. Finally, ␦ has only been validated to date in convenience samples of well-characterized cases and controls. These samples are enriched for impaired cognition relative to unselected clinical samples or populations. The diagnostic accuracy of a measure is influenced by the target condition’s prior prevalence. It remains to be seen whether ␦ scores perform as well in unselected samples. In our opinion, a new conceptualization of dementia is emerging from these models. Dementia severity is most closely related to general intelligence and its subdomains rather than with domain specific cognitive faculties (i.e., “memory,” “executive functions,” and the like). This may shed new light on the biological substrates of dementia, since an association with general intelligence constrains the plausible biological mechanisms that might be invoked to explain our findings. The resulting composites rank order individuals along a continuous dimension of dementia severity. Diagnostic accuracy is improved relative to the battery that engendered the latent variable, and the ␦ composite need not include ␦’s target indicator. These findings suggest that it may be possible to build ␦ in one

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well-characterized reference cohort and export it to other samples or individuals. It may also be possible to predict ␦’s target indicator from as little as a convenient subset of its cognitive indicators.

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Received May 2, 2014 Revision received August 15, 2014 Accepted September 16, 2014 䡲

Greater than the sum of its parts: δ Improves upon a battery's diagnostic performance.

"δ", a latent variable constructed from batteries that contain both cognitive and functional status measures, can accurately diagnose dementia relativ...
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