Proceedings of the Annual Meeting of the American Statistical Association, August 5-9, 2001

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1 Proceedings of the Annual Meeting of the American Statistical Association, August 5-9, 1 SCREENING FOR DEMENTIA USING LONGITUDINAL MEASUREMENTS OF COGNITION Christopher H. Morrell, Mathematical Sciences Department, Loyola College in Maryland, 51 North Charles Street, Baltimore, MD Shan L. Sheng, Alan B. Zonderman, and Larry J. Brant, NIA, 56 Nathan Shock Drive, Baltimore, MD 22 Key Words: Classification, Linear Mixed-Effects Model, Prediction 1. INTRODUCTION The incidence rate of Alzheimer s disease increases exponentially with age (Brookmeyer, Gray, and Kawas, 199). The authors estimate that the number of Americans with Alzheimer s disease will nearly quadruple in the next 5 years. Consequently, as the population of the United States ages, this disease will impose an immense strain on the US health care system. Treatments that could postpone the onset of this disease would have a considerable impact. Thus it would be beneficial to be able to predict when a patient is at increased risk of Alzheimer s disease. The Benton Visual Retention Test (BVRT) (Benton, 197), a test of immediate recall of geometric figures, has been used as an indicator for dementia, for detecting brain injuries in children, and for other purposes. Subjects are required to reproduce geometric designs from memory after 1 seconds of study. On each test there are 1 separate designs with one or more figures, and the score is the total number of errors in reproduction. The test requires spatial conception, immediate recall, and visuomotor reproduction. Studies indicate that performance on tests of visual memory declines with age with even sharper declines after age 7 (Arenberg; 197, 197). In the United States, we have an aging population such that by it is predicted that an increasing number will be among the oldest old. This is expected to result in an even greater increase in the number of individuals being diagnosed with dementia. The aim of this study is to examine whether changes in performance (as measured by increases in error rates on the Benton Visual Retention Test) predict dementia, in particular, of the Alzheimer s type. We demonstrate a method of classification based on longitudinal trends in BVRT using a linear mixed-effects (LME) model. The procedure first fits a LME model to the data to describe the longitudinal trends in BVRT. This LME model contains terms that differentiate longitudinal changes between the normal and dementia groups. Then, based on an individual s longitudinal data, posterior probabilities are calculated for membership in the two groups sequentially after each BVRT measurement. The subject is classified as a dementia case once the calculated probability becomes larger than some cutoff value. Based on an individual s predicted starting level of BVRT and the predicted rate of change in BVRT, a cross-validation study of the current BVRT data set is performed in order to classify each individual into a pre-clinical diagnosis state of normal or dementia. 2. METHOD 2.1 THE DATA The data used for this study are from 199 participants from the Baltimore Longitudinal Study of Aging (BLSA) with at least 2 repeated Benton Visual Retention Test (BVRT) measurements, who had no evidence of dementia at first examination. There were 57 males and 22 females who were diagnosed with dementia during the study period. These dementia cases were matched (based on age and number of repeated measurements) with males and females, respectively, who showed no evidence of dementia throughout the follow-up period (see Table 1). Figure 1 plots the longitudinal BVRT for 5 normal and 5 Alzheimer s cases. The participants were selected by finding the mean BVRT over the repeated measurements and then selecting participants with the minimum, first quartile, median, third quartile, and maximum BVRT. BVRT values above the horizontal line in Figure 1 have been used to indicate individuals with abnormal cognition scores. 2.2 THE LINEAR MIXED-EFFECTS MODEL First the longitudinal data are modeled using a LME model. Using the notation in Laird and Ware (192), the model for the ith subject is i = 1,...,m where y i is the n i 1 vector of observations for subject i, X i is the design matrix of independent variables for subject i, $ is the p 1 vector of parameters for the fixed effects, Z i is the design matrix of predictor variables for the random effects, b i is the q 1 vector of random effects for subject i, e i is the error vector, and m represents the number of different subjects. It is assumed that b i ~ N (, D) where D is a q q variance-covariance matrix of the b i, e i ~ N (, F 2 I), and that b i and e i are independent.

2 Table 1. DESCRIPTION OF DEMENTIA DATA Normal Alzheimer s Normal Alzheimer s Number of participants at diagnosis Length of follow-up Number of BVRT measurements Interval between BVRT measurements Figure 1. OBSERVED BENTON VISUAL RETENTION TEST VALUES FOR 1 SYSTEMATICALLY SELECTED CASES 2 Alzheimer cases maximum BVRT Errors 2 median first quartile third quartile BVRT Errors minimum Normal cases third quartile first quartile minimum maximum Value for the reference line is based on the Benton Visual Retention Test Manual, 5th Edition,1992 median

3 The fixed effects, $, give the population average intercept and slopes. They model the systematic variation in the data that can be linked to explanatory variables that differ among the subjects and other explanatory variables that vary within the subjects. In contrast, the random effects, b i, account for the heterogeneity among the subjects by allowing the intercepts and slopes for each subject to differ from the overall average. Finally, the random errors, e i, account for the unexplained variation in the data. The variance components are estimated using either maximum likelihood (ML) or restricted maximum likelihood (REML) (Laird and Ware, 192; Lindstrom and Bates, 19). The estimators of the random effects, b i, are empirical Bayes estimators (Laird and Ware, 192), and the marginal covariance matrix of y i is F 2 V i where F 2 V i = F 2 I + Z i D Z it. The SPlus function, lme() is used to fit the LME models in this paper. 2. CLASSIFICATION We wish to classify a given participant as either normal or as having dementia of the Alzheimer s type based on repeated BVRT measurements taken preclinically. There are two stages in the classification procedure. The first stage is implemented by modeling the BVRT measurements and the clinical diagnosis for all the participants, except the kth individual who is being classified, using a LME model. The LME model contains an indicator variable to distinguish between the two diagnostic groups as well as interactions of the indicator variable and other explanatory variables to allow the two groups to have different patterns of change with age and over time. The mean of the two diagnostic groups is given by: : j = X kj $, where X k has the indicator variable for Alzheimer s set to and X k1 has the indicator variable set to 1. In the second stage, we calculate the posterior probability that subject k belongs to group j (j= 1 or 2) as: p kj = p j f kj (y k 2) / {p 1 f k1 (y k 2) + p 2 f k2 (y k 2)} where 2 represents the vector of all parameters replaced by their estimates when the kth subject is removed from the analysis, f kj = N(: j, V k ), and p j = the proportion of subjects in group j. Subject k is classified as having dementia if p kj is greater than a cutoff value. This procedure is applied sequentially, for k = 2,,..., n k or until the participant has been classified as having dementia. For the longitudinal BVRT data, the following LME model was fit: y ij = ($ + b i ) + ($ 1 + b i 1 ) time ij + ($ 2 + b i 2 ) time ij 2 + $ fage i + $ A i + $ 5 time ij A i + e ij where time ij is the jth follow-up time for the ith participant, fage i is the age at first visit for the ith participant, and A i = 1 () is the participant developed dementia of the Alzheimer s type (otherwise). For this model, : = $ + $ 1 time ij + $ 2 time ij 2 + $ fage i, and : 1 = ($ + $ ) + ($ 1 + $ 5 ) time ij + $ 2 time ij 2 + $ fage i represent the systematic component. The final mixedeffects model was selected by a backward elimination procedure as described in Morrell, Pearson and Brant (1997).. RESULTS Figures 2 and illustrate the application of this procedure to a female participant and a male participant. The figures show the ages of the predictions and the actual clinical diagnosis of Alzheimer s disease. Table 2 presents the results of the procedure for all the participants in the study. Two different values are used as the cutoff value for the posterior classification probabilities to illustrate the method. As the cutoff value decreases, the proportion correctly classified as Alzheimer s increases. However, the number of normal subjects incorrectly classified as having Alzheimer s also increases. The results in the table suggest that the measurements of the Benton Visual Retention Test are more useful in the diagnosis of Alzheimer s disease in females than males.. DISCUSSION Several recent studies support the belief that Alzheimer s disease is a chronic process that starts years before any clinical evidence of the disease and that subtle cognitive deficiencies can also be present years before a clinical diagnosis of the disease (Masur et al., 199; Petersen et al., 199; Jacobs et al., 1995). This study illustrates the usefulness of longitudinal measurements of visual cognitive memory scores as a basis for a classification method of preclinical Alzheimer s disease. The results indicate that such a classification method may perform better in women than in men with both higher percentages of diseased persons correctly classified (sensitivity) and higher percentages of non-diseased persons correctly classified (specificity) for women. Finally, these classification results suggest that there may be a window of opportunity for the early detection of Alzheimer s disease and hence the possibility of preventative treatment. REFERENCES American Psychological Association, Presidential Task Force on the Assessment of -Consistent Memory Decline and Dementia (199). Guidelines for the evaluation of dementia and age-related cognitive decline. Washington, DC: American Psychological Association.

4 Arenberg, D. (192). Changes with in Problem Solving. In Craik, F.I.M., and Trehub, S. (Editors), Aging and Cognitive Processes. New York: Plenum. Arenberg, D. (192). Estimates of Changes on the Benton Visual Retention Test, J. of Gerontology, 7, 7-9. Arenberg, D. (19). Memory and Learning Do Decline Late in Life. In Birren, J.E., Munnichs, J.M.A., and Marois, M. (Editors), Aging: A Challenge to Science and Society, Behavioral Sciences and Conclusions. Oxford: Oxford U.P. Benton, A.L. (19). Benton Visual Retention Test Stimulus Booklet. Fifth Edition. Psychological Corporation. Harcourt Brace & Company, San Antonio. Brookmeyer, R., Gray, S., and Kawas, C. (199) Projections of Alzheimer s Disease in the United States and the Public Health Impact of Delaying Disease Onset, American Journal Of Public Health,, Giambra, L.M., Arenberg, D., Zonderman, A.B., Kawas, C., and Costa, P.T. Jr. (1995). Adult Life Span Changes in Immediate Visual Memory and Verbal Intelligence, Psychology and Aging, 1, -19. Gilbert, J.G. (197). Thirty-five-year follow-up study of intellectual functioning, J. of Gerontology, 2, Jacobs, D.M., Sano, M., Dooneief, G., Marder, K., Bell, K.L., and Stern, Y. (1995) Neuropsychological Detection and Characterization of Preclinical Alzheimer s Disease, Neurology, 5, Laird, N.M. and Ware, J.H. (192), Random-Effects Models for Longitudinal Data, Biometrics,, Lindstrom, M. J. and Bates, D. M (19), Newton- Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data, Journal of the American Statistical Association,, Masur, D.M., Sliwinski, M., Lipton, R.B., Blau, A.D., and Crystal, H.A. (199) Neuropsychological Prediction of Dementia and the Absence of Dementia in Healthy Elderly Persons, Neurology,, 7-1. McCarty, S.M., Siegler, I.C., and Logue, P.E. (192). Cross-sectional and Longitudinal Patterns of Memory Scores, J. of Gerontology, 7, Morrell, C.H., Pearson, J.D., and Brant, L.J. (1997) Linear Transformations of Linear Mixed-Effects Models, The American Statistician, 51, -. Petersen, R.C., Smith, G.E., Ivnik, R.J., Kokmen, E., and Tangalos, E.G. (199) Memory Function in Very Early Alzheimer s Disease, Neurology,, Resnick, S.M., Trotman, K.M., Kawas, C., and Zonderman, A.B. (1995). -Associated Changes in Specific Errors on the Benton Visual Retention Test, J. of Gerontology: Psychological Sciences, 5B, Robinson-Whelen, S. (1992). Benton Visual Retention Test Performance among Normal and Demented Adults, Neuropsychology, 6, Shichita, K., Hatano, S., Ohashi, Y., Shibata, H., and Matuzaki, T. (196). Memory Changes in the Benton Visual Retention Test Between s 7 and 75, J. of Gerontology 1, 5-. Sivan, A. B. (1992). Benton Visual Retention Test Manual. Fifth Edition. Psychological Corporation. Harcourt Brace & Company, San Antonio. S-PLUS, Data Analysis Products Division, Seattle, WA.

5 Table 2. SUMMARY OF CLASSIFICATION RESULTS Actual Prediction (Cutoff Value =.5) Normal Alzheimer s Total Normal 6 (77%) Alzheimer s 7 (5%) 57 Normal 27 (%) 5 Alzheimer s 9 1 (59%) 22 Total (6%) Actual Prediction (Cutoff Value =.6) Normal Alzheimer s Total Normal 61 (69%) 27 Alzheimer s 27 (7%) 57 Normal 27 (%) 5 Alzheimer s 1 (6%) 22 Total (65%) Figure 2. TYPICAL FEMALE ALZHEIMER S CASE Figure. TYPICAL MALE ALZHEIMER S CASE Benton Visual Retention Test Errors 2 2 Diagnosed Predicted Benton Visual Retention Test Errors 2 2 Predicted Diagnosed (years) BVRTOT Probability (Normal) Probability (Alzheimer) (years) BVRTOT Probability (Normal) Probability (Alzheimer)