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We demonstrate the use of Grade-of-membership (GoM) (Manton et al. 1994) for sibpair linkage analysis: GoM was used to map the IDDM11 locus to the region of chromosome 14q24.3 identified by Field et al. (1996). Haplotype groups were constructed from sib pair information on the number of shared alleles. The sample consisted of 578 sibling pairs found in 246 multiplex IDDM families. Both siblings were diabetic in 53% of the pairs (AA). Pair members could share 0, 1 or 2 alleles IBS at each of eight linked marker loci spanning IDDM11. Three model-based groups best represented the data on allele sharing: the groups corresponded to 'No', 'One' and 'Two' shared haplotypes for the region. Group 'Two' was larger (37% vs. 25%, p < 0.0001) and more homogeneous (p < 0.0001) than expected by chance consistent with the IDDM11 locus being a determinant of diabetes in multiplex families. Genetic linkage of IDDM to the region was demonstrated by a 19% increase in the proportion of AA pairs over the haplotype groups: 'No', 42%; 'One', 49%; 'Two', 61%, p = 0.0005, representing a 43% relative increase.

Density profiles of Alzheimer's disease (AD) regional brain pathology were constructed for 249 subjects in the Huddinge Brain Bank. Counts per square millimeter for neurofibrillary tangles (NFT), diffuse plaques (DP), and neuritic plaques (NP) in 38 areas were investigated using a pattern recognition technique called GoM. The seven distributional profiles of AD neuropathology emulated and expanded upon Braak staging illustrating induction (Groups 1-3) and clinical progression (Groups 4-7). Normal aging represented limited AD changes, few NFT in the entorhinal cortex and hippocampal CA1 (Group 1). The threshold for possible AD was NFT in the subiculum (Group 2), found with DP in the neocortex. Temporal medial NFT was the threshold for probable AD (Group 4). The 'oldest-old', often demented without brain atrophy, had extensive entorhinal/CA1 NFT and cortical DP, but few cortical NFT or NP (Group 5). A second subtype 'disconnection' (Group 6) lacked AD pathology for a specific set of subcortical and cortical areas. Accumulation of NFT in first-affected areas continued through end-stage disease (Group 7), with apparent rapid transition of DP to NP in the cortex during clinical progression. The evolution of AD is a highly ordered sequential process. Pattern recognition approaches such as GoM may be useful in better defining the process.

Objective: To describe the types and costs of care received for 10 years after the identification of an older person with suspected Alzheimer's disease (AD) by using data from 3254 patients with suspected AD who participated in the National Long Term Care Survey (NLTCS)., Methods: By using a Markov model derived using grade of membership techniques, the following were determined: survival probabilities at 10 years; years of survival during the 10 years; years in institutions; years with two or more impairments in basic activities of daily living; hours of paid and informal care while the older person lived in the community; and costs of paid community, institutional, and medical care., Results: Greater degrees of cognitive impairment present when AD was identified were associated with reduced predicted probability of surviving 10 years, increased predicted number of years spent in institutions, increased hours of care required while affected individuals remained in the community, and increased costs of paid community, institutional, and medical care. Substantial differences between men and women were seen: severity-adjusted 10-year costs were almost two times higher for women with AD than for men ($75,000 compared with $44,000); according to sensitivity analysis, average 10-year costs might be as high as $109,000 for women and $67,000 for men., Conclusions: AD imposes a substantial burden on older persons. Interventions that slow the progression of the disease may therefore affect community survival as well as healthcare costs.

This study employed grade of membership (GoM) analysis in a clinical setting to determine if the DSM-III-R personality disorder (PD) diagnostic criteria cluster into recognizable disorders resembling the official axis II nosology. The GoM model, based on fuzzy-set theoretic concepts, explicitly examines medical diagnostic systems by quantitatively identifying and characterizing subpatterns of illness within a broad class. A semistructured assessment of 110 outpatients was performed for 12 PDs and their 112 diagnostic criteria. GoM analysis was performed using internal variables of the 112 PD criteria rated as present or absent. Demographic variables, axis I and II diagnosis (structured clinical Interview for DSM [SCID]), and treatment response (Global Adjustment Scale [GAS]) information were used as external validators. Four pure types (PT) provided the most satisfactory solution to the data. PT-I is characterized by marked maladaptive personality pathology, which is manipulative, egocentric, impulsive, and alloplastic. PT-II consists primarily of exaggerated socially anxious and detached traits. PT-III is sociably dependent and autoplastic. PT-IV is essentially asymptomatic. GoM provides a more parsimonious handling of the PD criteria than provided by classifying according to DSM categories. The analysis fails to confirm the natural occurrence of any single specific axis II PD or cluster.

Objective: To determine the prevalence and 3-year incidence of dementia in Blacks and Whites age 65 and older in a five-county Piedmont area of North Carolina., Design: Stratified random sample of members of the Duke Established Populations for Epidemiologic Studies of the Elderly (EPESE) (baseline n = 4,136; 55% Black; weighted n = 28,000). Prevalence study members were differentially selected on the basis of score on the Short Portable Mental Status Questionnaire at the second in-person Duke EPESE wave. Incidence study members included all persons with obvious cognitive decline over a 3-year period, and a 10% sample of the remainder., Measurements: Self- and informant report on health history, functional status, and memory. Consortium to Establish a Registry for Alzheimer's Disease (CERAD) Neuropsychology Battery administered to all subjects, and CERAD Clinical Battery to those with impaired memory. Clinical consensus to determine presence and type of dementia., Results: Prevalence of dementia for persons > or =68 years old was 0.070 (95% confidence interval = 0.021-0.119) for Blacks and 0.072 (0.022-0.122) for Whites. Rates for Black men (0.078, 0.001-0.155) exceeded those for Black women (0.066, 0.003-0.129), but gender rates for Whites were reversed (men: 0.044, 0.000-0.103), (women: 0.087, 0.015-0.160). Neither race nor gender differences were significant. Prevalence of dementia increased through age 84 and tapered off thereafter. Three-year incidence of dementia was 0.058 (0.026-0.090) for Blacks and 0.062 (0.027-0.097) for Whites. Neither race nor gender differences were significant. Incidence increased through age 84, but moderated thereafter for all but Black men. The proportional representation of different types of dementia varied little by race., Conclusion: Prevalence, 3-year incidence, and types of dementia are comparable in Black and White elderly in the Piedmont area of North Carolina.

We are three dimensional egocentric beings existing within a specific space/time continuum and dimensionality which we assume wrongly is the same for all times and places throughout the entire universe. Physicists name Omnipoint the origin of the universe at Dimension zero, which exploded as a Big Bang of energy proceeding at enormous speed along one dimension which eventually curled up into matter: particles, atoms, molecules and Galaxies which exist in two dimensional space. Finally from matter spread throughout the cosmos evolved life generating eventually the DNA molecules which control the construction of brains complex enough to construct our three dimensional Body Representation from which is extrapolated what we perceive as a 3-D universe. The whole interconnected structures which conjure up our three dimensionality are as fragile as Humpty Dumpty, capable of breaking apart with terrifying effects for the individual patient during a psychotic panic, revealing our three dimensionality to be but "maya", an illusion, which we psychiatrists work at putting back together.

Our 3-D Body Representation constructed during development by our Central Nervous System under the direction of our DNA, consists of a holographic representation arising from sensory input in the cerebellum and projected extraneurally in the brain ventricular fluid which has the chemical structure of liquid crystal. The structure of 3-D holographic Body Representation is then extrapolated by such cognitive instruments as boundarization, geometrization and gestalt organization upon the external environment which is perceived consequently as three dimensional. When the Body Representation collapses as in psychotic panic states. patients become terrified as they suddenly lose the perception of themselves and the world around them as three dimensional, solid in a reliably solid environment but feel suddenly that they are no longer a person but a disorganized blob. In our clinical practice we found serendipitously that the structure of three dimensionality can be restored even without medication by techniques involving stimulation of the body sensory system in the presence of a benevolent psychotherapist. Implications for Virtual Reality will be discussed.

We examined the use of proxies in samples of persons aged 65 years and over from the 1982 and 1984 National Long-Term Care Surveys (NLTCS). The NLTCS are designed to describe the Medicare-enrolled elderly population, their health and functioning, hospital, home health, and institutional use. The NLTCS, being longitudinal, allows trends in functional and health status to be examined as well as the changing character of community-based and institutional services used by chronically disabled persons aged 65 years and older. In analyses of proxy responses there was little evidence of differences in accuracy between self- and proxy reports in persons with different health and functional characteristics. The amount and type of proxy reporting did depend on the health and functional characteristics of the sample person. The cognitively impaired, and the frail elderly, had high levels of proxy use as well as small differences in the accuracy of reporting service use and program enrollment. The results are consistent with methodological studies of proxy reporting in health surveys of other populations.

Models of gender differences in human mortality and aging depend on assumptions about temporal rates of physiological change. Simple models like the Gompertz fail to describe the mortality of either males or females at late ages. This suggests a need for biologically more detailed models to represent the age dependency of human mortality as well as gender differences in that age dependence. By modeling the sex-specific interaction of time-varying covariates with multiple dimensions of mortality selection, one can more accurately describe the age dependence of mortality and more complex physiological aging patterns. The multivariate model of aging changes is used to describe gender differences using data from (a) a longitudinal study of physiological changes and mortality and (b) a nationally representative longitudinal survey of changes in function and mortality.

Background: Elderly residents of nursing homes often have multiple comorbidities and functional limitations. The status of 4,525 residents of complex and standard care units in 177 nursing homes where the nursing home was determined to provide adequate care, and from 14 specialized Alzheimer's units, was evaluated on 111 measures of medical condition, functional status, psychological well-being and cognitive performance in a demonstration study assessing quality of care in six states. Detailed measurements were also made of the types and amounts of services used (in minutes per day) by the residents., Methods: Given the number of health measures, and the possibility of assessment error, a multivariate analytic procedure called Grade of Membership (GoM) was used. This procedure identified profiles of health and functioning measures to identify the characteristics of clinically distinct groups of nursing home residents., Results: The analysis identified 11 profiles of health and functioning characteristics which described the 111 resident measurements. The 11 profiles predicted differentials in nursing home length of stay, and service use by various classes of caregivers. The GoM profiles described the data better than several other classification procedures applied to the same data., Conclusions: In nursing homes, elderly and oldest-old residents often have multiple comorbidities and disabilities. A multivariate procedure was able to identify the fundamental dimensions describing residents' variation on a number of health measures. These profiles predicted differences in service use so they had predictive validity. Thus, multivariate procedures may help identify clinically distinct groups in studies where complex measures are made.

A model of human health history and aging, based on a multivariate stochastic process with both continuous diffusion and discrete jump components, is presented. Discrete changes generate non-Gaussian diffusion with time varying continuous state distributions. An approach to calculating transition rates in dynamically heterogeneous populations, which generalizes the conditional averaging of hazard rates done in "fixed frailty" population models, is presented to describe health processes with multiple jumps. Conditional semi-invariants are used to approximate the conditional p.d.f. of the unobserved health history components. This is useful in analyzing the age dependence of mortality and health changes at advanced age (e.g., 95+) where homeostatic controls weaken, and physiological dynamics and survival manifest nonlinear behavior.

Grade of Membership (GoM) analysis, a multivariate classification technique based on fuzzy-set mathematics, was applied to the demographic, history, and mental-state data on 53 dementia praecox cases and 134 manic-depressive insanity cases admitted to Kraepelin's University Psychiatric Clinic in Munich in 1908. The original data recorded by Kraepelin and his collaborators on special Zählkarten (counting cards) were rated and coded in terms of the Present State Examination (PSE) Syndrome Check List. The statistical analysis resulted in a high degree of replication of Kraepelin's clinical entities. However, the dichotomy of dementia praecox and manic-depressive insanity was not fully supported. The catatonic syndrome tended to occupy an intermediate position between the two major psychoses. The possibility is discussed that catatonia in Kraepelin's time shared certain clinical features with the later diagnostic groupings of schizoaffective disorder, cycloid psychoses, and other "atypical" forms of psychotic illnesses.

In this article, analyses are made of home health and skilled nursing facility (SNF) use for the period 1982-90 using Medicare records linked to data on community and institutional residents from the National Long-Term Care Surveys (NLTCSs) of 1982, 1984, and 1989. The combined survey and administrative data analyses are performed to ascertain how the chronic health and functional characteristics of community and institutional residents using Medicare-reimbursed services changed during the period. During this period, changes had been made in the Medicare system that affected the use of services for persons with specific health and functional problems.

Models of mortality and aging depend on assumptions about physiological change even if they are not made explicit. Standard models, like the Gompertz, often fail to describe mortality at extreme ages, suggesting a need for biologically more detailed and flexible models. One solution is to model the interaction of time-varying covariates with mortality to better describe the age dependence of mortality, test hypotheses about the relation of physiological change and mortality, and use longitudinal data to generalize assumptions about physiological change. This model is applied to (a) a 34-year follow-up of risk factors and mortality and (b) a 9.5-year follow-up of function and mortality from longitudinal surveys of the U.S. elderly population.

1. Classification methods in sensory systems in general, and gustation in particular, tend to place each of the relevant objects, such as stimuli or neurons, into one class each. Some of these methods are based on the responsiveness of neurons to various stimuli; in these, each group must contain a variety of nonidentical members because of the individuality of each neuron or stimulus. 2. The "fuzzy" set method is appropriate for more accurate classification in such heterogeneous populations. In this method each member is given graded membership in several sets rather than membership in only one set. In the present paper we subjected previously published data on the responses of individual taste neurons to a variety of stimuli to fuzzy set analysis. 3. We found that the amounts of response of 46 neurons in the solitary nucleus of the rat to NaCl, HCl, sucrose, quinine HCl, and KCl could accurately be accounted for by giving each a grade of membership in three sets; the same held in the parabrachial nucleus of the rat for the responses of 41 neurons to the first four of these stimuli. The response was calculated as the sum of the products of the stimulus times neuron ratings in each set. 4. Temporal patterns of response have often been related, but with only moderate success, to the identity of the stimulus or neuron. These patterns could be accurately accounted for with the present method. Each of the products of designated parts of the stimulus ratings times the neuron ratings gave the basis for accurate description of the temporal course of the response of each neuron to each stimulus. 5. This method appears to account for the varieties of amount and temporal pattern of response of taste neurons with a simple mathematical process of few parameters. This suggests that within the known complexities of receptor mechanisms and mechanisms of neural processing, the neural message is reduced to a rather simple form. 6. The fuzzy set approach, which is based on disclosing underlying sets rather than placement of heterogeneous members into one of several essentialistic groups, may be useful in disclosure of the underlying mechanisms producing the neural responses in taste.

The Grade of Membership (GoM) model is a classification procedure which allows a person to be a member of more than one diagnostic class. It simultaneously quantifies the degrees of membership in classes while generating the discrete symptom profiles or 'pure types' describing classes. The model was applied to the symptomatology, history, and follow-up of 1065 cases in the WHO International Pilot Study of Schizophrenia. The model produced an eight diagnostic class or 'pure type' solution, of which five were related to the diagnostic concepts of schizophrenia and paranoid disorder, two types were affective disorders, and one asymptomatic type. A subtype of paranoid schizophreniform disorder found primarily in developing countries was identified. There was a strong association between pure types and the original clinical and computer generated (CATEGO) diagnoses. A GoM based psychiatric classification might more clearly identify core disease processes than conventional classification models by filtering the confounding effects of individual heterogeneity from pure type definitions.

Objective: The case mix-adjusted pattern of use of health care services, especially posthospital care, is compared before and after the introduction of Medicare's Prospective Payment System (PPS)., Data Sources: The 1982 and 1984 National Long Term Care Surveys (NLTCS) linked to Medicare administrative records 1982-1986 provide health and health service use data for 12-month periods before and after the introduction of PPS., Study Design: Case-mix differences between pre- and post-periods are controlled by using the Grade of Membership model to identify health groups from the NLTCS data. Differences in timing (e.g., hospital length of stay) were controlled using life table models estimated for each health group, that is, service use patterns pre- and post-PPS are compared within groups., Principal Findings: Hospital LOS and admission rates declined post-PPS. Changes in the timing and location of death occurred but, overall, mortality did not increase. Changes in post-acute care service use by elderly, chronically disabled Medicare beneficiaries were observed: home health service use increased overall and among the unmarried disabled population., Conclusions: PPS did not adversely affect quality of care as reflected in mortality or in hospital readmissions. Moreover, the differential use of post-acute care, and changes in hospital LOS by health group, indicate that the system responded, specific to marital status and age, to the severity of needs of chronically disabled persons.

Choline supplementation has been used with moderate success in subgroups of adult patients with neuropsychiatric and medical problems. The dietary fish oils have also been used in adults with hypercholesterolemia. We report on two young children with multiple neurodevelopmental delays, one who responded to choline and eicosapentaenoic acid, and the other to choline alone. A brief discussion about choline's metabolic pathways and benefits is included.

Grade of membership analysis (GoM) may have particular relevance for genetic epidemiology. The method can flexibly relate genetic markers, clinical features, and environmental exposures to possible subtypes of disease termed pure types even when population allele frequencies and penetrance functions are not known. Hence, GoM may complement existing strategies that sometimes fail in the presence of heterogeneity or when case definition is not well established. To illustrate the method, individuals in the Seattle data set were evaluated with respect to affection status, age at onset, pedigree, sex, and genetic markers on chromosomes 19 and 21. Seven pure types were found which we have designated as: Early Onset, Late Onset, Probable, and Unaffected 1 to Unaffected 4.

Neuroleptic-induced catatonia is reported in an adolescent patient who responded successfully to lorazepam. The authors propose five discrete stages toward the progression of neuroleptic malignant syndrome, each with a separate treatment.

Often environmental hazards are assessed by examining the spatial variation of disease-specific mortality or morbidity rates. These rates, when estimated for small local populations, can have a high degree of random variation or uncertainty associated with them. If those rate estimates are used to prioritize environmental clean-up actions or to allocate resources, then those decisions may be influenced by this high degree of uncertainty. Unfortunately, the effect of this uncertainty is not to add "random noise" into the decision-making process, but to systematically bias action toward the smallest populations where uncertainty is greatest and where extreme high and low rate deviations are most likely to be manifest by chance. We present a statistical procedure for adjusting rate estimates for differences in variability due to differentials in local area population sizes. Such adjustments produce rate estimates for areas that have better properties than the unadjusted rates for use in making statistically based decisions about the entire set of areas. Examples are provided for county variation in bladder, stomach, and lung cancer mortality rates for U.S. white males for the period 1970 to 1979.

The Grade of Membership (GOM) model is a general multivariate procedure for analyzing high dimensional discrete response data. It does this by estimating, using maximum likelihood principles, two types of parameters. One describes the probability that a person who is exactly like one of the K analytically defined types has a particular response on a given variable. The second describes each individual's degree of membership in each of the K types. This "partial" membership score reflects the logic of the fuzzy partitions (rather than of discrete groups) that are employed in the analyses. By modifying the probability structure of the basic model we show how the procedure can be applied to a number of different types of data and analytic problems. The utility of the different GOM models for different types of aging research is discussed.

Cancer is often reported as contributing to the risk of noncancer causes of death. The age variation of these reports was studied using U.S. data on all causes of death listed on death certificates for 1968 to 1986. The occurrence of cancer as a nonunderlying cause of death increased with age and was higher for treatable and slowly growing tumor types. These patterns persisted even if the cancer manifested changes in occurrence. Nonunderlying occurrences were highest in the 85 to 94 age group and were correlated with cancer survival. This suggests increased importance of cancer as a cause of death and a comorbid condition among oldest-old persons. The high rate of occurrence as an associated cause of death suggests that if life expectancy increases due to declines in circulatory and other chronic disease mortality, cancer could become the preeminent cause of death in the United States.

In describing high dimensional discrete response data, mathematical and statistical issues arise that require multivariate procedures that are not based on normal distributions, that is, the mathematical representation of high dimensional discrete response data (Event Spaces) requires a representation in lower dimensional parameter spaces consistent with the discrete properties of the Event Space. Mapping discrete responses to latent discrete classes has the limitation of not representing real individual variation within the categories. The use of a fuzzy partition model is proposed which describes individuals in terms of partial membership in multiple latent categories which represents bounded discrete event spaces with significant third and higher order moments. We discuss statistical issues arising in identifying both the deterministic and the stochastic variation of data when applications involve systematic variation due to observed and unobserved variables. We present an empirical Bayes-maximum likelihood estimation scheme for the application of the fuzzy partition models.

Analyzing multivariate clinical data to identify subclasses of patients being treated for a specific disease may improve patient management and increase understanding of the behavior of disease under clinical conditions. In some cases, patients have been classified on prognostic characteristics using standard risk assessment procedures (e.g., Cox' regression). This requires long term follow-up, differentiates patients only on attributes relevant to survival, and assumes that patients are sampled from a common population. Other approaches involve the use of clustering algorithms to classify patients into categories based on multiple clinical attributes. We illustrate the use of a multivariate statistical procedure to directly characterize patients on multiple clinical characteristics. The procedure is designed to analyze discrete response data with parameters representing individual differences within groups. Its use is illustrated for patients with Stage I melanoma in determining how age is related to treatment response in different patient groups.

Many diseases have both genetic and environmental determinants. Some require both, and the disease phenotype then appears only when a vulnerable genotype is expressed after interaction with environmental factors. The detection of such environmental factors has received little prior consideration in diseases with genetic causes. In particular, case-control studies of such diseases may compare exposures among cases, who have the susceptible genotype, and controls who mostly lack it. The authors explored the likely results of such studies, using the example of Alzheimer's disease as an illness where environmental factors may interact with a necessary susceptible genotype to accelerate disease expression. They found that case-control studies of environmental factors in complex genetic diseases will usually produce an odds ratio that differs little from the relative risk among susceptible individuals. In rare situations, however, the discrepancy may be gross. The statistical power of such studies also agrees well with familiar published estimates, suggesting that little power is lost even though the controls are mostly not susceptible. Power may be increased, however, in studies of common illnesses with genetic determinants when the case-control method is applied among discordant monozygotic twins.

Aimed to document the psychological sequelae of a disaster in the adult (17-68 years) population of the Caribbean island of Puerto Rico, by surveying 912 persons (including 375 previously interviewed) with a Spanish version of the Diagnostic Interview Schedule. A rigorous methodology, which included both retrospective and prospective designs, was used, enabled by the occurrence of a catastrophic disaster only a year after a comprehensive survey was completed. Framed in a stress theoretical perspective, disaster effects for new depressive, somatic, and posttraumatic stress symptoms were identified, even after adjusting for demographic and methodologic factors. All the effects, however, were relatively small, suggesting that most disaster victims were rather resilient to the development of new psychological symptoms. Comparison of results with previous findings and its implications for both disaster and stress research are discussed, as well as the role of community psychologists in disaster action.

The functional and health characteristics of nursing home residents in New York State using a multivariate classification procedure are examined in this article. This analysis suggested that these characteristics could be explained in terms of six dimensions. The association of these six dimensions with two existing sets of nursing home case-mix groups was analyzed in order to determine how groups based only on the health and functional characteristics of residents related to groups based primarily on measures of current service use. A number of resident characteristics were not described well by case-mix measures based only on service use, suggesting the need to modify such groups using additional sources of input.

The results of a comparison of two typologies of sibling relationships in old age are reported. Both analyses rely on the same data collected in individual interviews with adults over the age of 65. The first typology was constructed using constant comparative analysis; the second relied on the grade of membership (GOM) technique. This is the first time GOM has been used to create a taxonomy of human relationships based on psychosocial variables. The two typologies are compared in terms of number of types generated, the characteristics of each type, factors influencing typological construction, and the utility of empirical results. Implications for additional use of the GOM technique to study late-life sibling relations are discussed.

Isolated cold stress testing (ICST) has been used to assess cold stress performance or digital thermoregulation, but statistical analysis of the results has been limited to visual comparisons of data. In this prospective study, 11 patients who underwent complete digital replantation were followed serially with ICST at 6 weeks, 3 months, 6 months, 1 year, and 2 years postoperatively, and the results were analyzed quantitatively. For that analysis, we devised a mathematical method that provided a cooling and a warming coefficient to fit the data. Differences in these cooling and warming coefficients were then regressed against time after replantation, patient age, number of digits replanted, hand dominance, and clinical evidence of sensory recovery. There was a significant correlation between response to isolated cold stress testing (thermoregulation) and degree of sensory recovery (p less than or equal to 0.02). This method for quantitative analysis of isolated cold stress testing data allows objective evaluation of digital blood flow patterns based on temperature, thereby providing a reliable and objective assessment of the recovery of thermoregulation in the replanted human digit.

Statistical methods designed specifically for the analysis of chronic disease incidence and progression in longitudinal studies are presented. These method model the risk of acute phases of chronic disease separately from the temporal change in risk variables. This could be accomplished because, under a specific biological model of the disease mechanism, the problems of estimating the risk of an acute event and of predicting the change in risk variables are independent. Specifically, a quadratic equation relating risk variable values to chronic disease risk and a system of linear equations predicting future risk variable values from present values may beestimated separately. Taken together, they utilize the full information available in a longitudinal study on the temporal dimension of chronic disease progression. In addition, the model is found to possess a number of attractive statistical and theoretical properties. These methods are applied to longitudinal data from the Framingham Study on coronary heart disease (CHD) in males. A quadratic function relating the risk of a CHD event to selected risk variables (age, and the natural logarithms of serum cholesterol, uric acid, diastolic blood pressure and pulse pressure) was estimated from measurements made at four points equally spaced in time (two years) with a further morbidity follow-up at a fifth point. The risk function was found to predict CHD risk accurately. It showed that, apart from the linear effects of the risk variables, cohort effects, quadratic effects and interaction effects were important predictors of CHD risk. The linear regression equations used to predict future risk variable values showed that there was an intricate network of cross-temporal associations. Study of the two types of equations jointly show that putative risk variables could affect the risk of CHD incidence both directly, by being associated with higher levels of risk, and indirectly, by causing other risk variable values to change with time. The results led us to identify several different roles that risk variables might play in CHD incidence.

The logistic multiple regression model is often used in the analysis of the relation between chronic disease risk and selected risk factors in longitudinal data. Unfortunately, the logistic function has certain properties that make it inappropriate as a mode of risk analysis for longitudinal studies. The consequences of applying the logistic function to longitudinal data is that the numerical values of logistic regression coefficients cannot be meaningfully compared between studies of different durations. Sample calculations are presented to illustrate the magnitude of the problem for a range of relative study lengths and levels of risk. Two solutions are offered for the problem. First, a series of approximations are derived which permit such comparisons if the studies are not greatly dissimilar in length. Second, if comparisons of the risk coefficients are to be made across studies of greatly dissimilar duration, it is necessary to model risk via an appropriate statistical model. Criteria for assessing the appropriateness of risk functions for the analysis of longitudinal data are proposed and alternatives evaluated.

A mixed categorical-continuous variable model is proposed for the analysis of mortality rates. This model differs from other available models, such as weighted least squares and loglinear models, in that the within-cell populations are assumed to be heterogeneous in their levels of mortality risk. Heterogeneity implies that, in addition to the sampling variance considered in other available models, there will be a second component of variance due solely to within-cell heterogeneity. Maximum likelihood procedures are presented for the estimation of the model parameters. These procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function. This assumption is shown to be equivalent to assuming a mixture of Poisson processes with the differential risk levels among individuals within each cell being governed by a two-parameter gamma distribution. The model is applied to data on lung cancer mortality for 1970-1975 for the 100 counties of North Carolina. The analysis shows that, though a gradient in lung cancer mortality rates exist in space, the gradient is restricted to specific demographic categories identified by race, age and sex.

A computer program initially written by the Milwaukee Blood Bank has been modified to use a new algorithm for the assignment of HLA specificities to antisera. The assignment is based on the reactions of cells with known specificities. Specificities which are present only on cells which do not react are first ruled out. This step is followed by one or more steps in which the 'least reactive' specificities are ruled out. The rationale for the algorithm is discussed and an example is presented.

A new multivariate analytical technique for the analysis of medical classification, Grade of Membership analysis, is utilized to examine somatization disorder in a community population. The authors examine whether somatic symptoms will cluster into a clinical syndrome resembling somatization disorder, as defined by the Diagnostic and Statistical Manual of Mental Disorders (DSM-III), if no prior assumptions are made about the inter-relationship of somatic symptoms or their clustering into clinical syndromes. Using respondents in the US National Institute of Mental Health Epidemiologic Catchment Area project of the Piedmont Region of North Carolina, Grade of Membership analysis was applied to all respondents reporting 3 or more somatic symptoms from the somatization disorder section of the Diagnostic Interview Schedule. Seven 'pure' types, roughly analogous to clusters in cluster analysis emerged from the analysis. One 'pure' type in the analysis is nearly identical to DSM-III somatization disorder and is associated with demographic characteristics found among patients with DSM-III somatization disorder. The results indicate that symptoms associated with somatization disorder cluster in a highly predictable fashion and represent a strong validation of the natural occurrence of an entity resembling somatization disorder.

An analysis of sex differentials in the dynamics of coronary heart disease (CHD) in the Framingham study is conducted using a methodology designed process which aids in the interpretation of the longitudinal results. This methodology permits the analysis of risk variable changes over time to be conducted independently of the analysis of the relation of risk variable values to CHD risk. The independent analyses afford a complete utilisation of information from longitudinal studies of chronic disease risk and produce insights into the dynamics of chronic disease development not available by other analytic strategies. The results of this analysis are compared with results obtained from a similarly structured multiple logistic analysis--a comparison which illustrates some of the technical and conceptual deficiencies of the often employed multiple logistic analysis when applied to longitudinal data.

The World Health Organization, in collaboration with the Indonesian Institute of Health Research and Development, conducted a survey of disability in 14 of 24 Indonesian provinces. This survey was designed to assess the validity of the disablement process as described in WHO's (1980) classification of impairments, disabilities, and handicaps. We analyzed these data with a multivariate procedure which simultaneously identifies subgroups in the surveyed population and the typical attributes of those subgroups. The purpose of the analysis was to (a) determine the association of basic patterns of physical and psychological impairments with disabilities (limitations of the ability to perform certain functions) and handicaps (limitations in the ability to fulfill social roles); (b) assess how those disabilities and handicaps were expressed in urban and rural contexts in a developing country, and (c) determine how the relation of impairments with disabilities and handicaps varied with age.

The spatial variation of site-specific cancer mortality rates at the county or state economic area level can provide a) insights into possible etiologic factors and b) the basis for more detailed epidemiologic studies. One difficulty with such studies, especially for rare cancer types, is that unstable local area rate estimates, resulting from small population sizes, can obscure the underlying spatial pattern of disease risk. This paper presents a methodology for producing more stable rate estimates by statistically weighting the local area rate estimate toward the experience at the national level. The methodology is illustrated by the analysis of the spatial variation of two cancer types, bladder and lung, for U.S. white males over the three decades 1950-79.

One likely consequence of the aging of the U.S. population is the growth of the number of persons in nursing homes. As the numbers of persons in nursing homes increase so will the amount of resources required to keep them in those homes. This will make it increasingly important to understand the dynamics of nursing home utilization so that we can more effectively plan the allocation of resources. Unfortunately, we lack direct information on the dynamics of nursing home utilization both because of the expense of implementing longitudinal studies to gather such information and because the available data on current residents are inappropriate to study the dynamics of utilization because of several types of bias. Demographic methods are presented that can be applied to survey data to remove sample biases from the data and permit study of the dynamics of the utilization of facilities for the total U.S. nursing home population and for various of its components.

A number of theoretical models of aging and human mortality have been proposed. Only a few of these theoretical models, however, have been translated into statistical procedures and applied to data. In this paper we outline a theoretical model of human aging and mortality and compare it with models developed by Sacher and Trucco and Forbes and Brown. The ways in which this new model can be viewed as a generalization of these other formulations are discussed as are ways in which this model can be translated into a statistical model for empirical application.

Free formaldehyde may be released from wood products and foam insulation where urea-formaldehyde resins have been used. From January, 1978 to November, 1979, 100 structures were investigated by the Wisconsin Division of Health after receiving complaints of health problems from occupants. Air samples were collected in midget impingers and analyzed for formaldehyde content by the chromotropic acid procedure. Health information was obtained from the occupants via questionnaires. Mean formaldehyde concentration observed ranged from below the limit of detection to 3.68 ppm. Eye irritation, burning eyes, runny nose, dry or sore throat, headache, and cough were the primary symptoms which were reported by the occupants. Statistically significant associations were seen between formaldehyde levels and age of home/building materials. Observations presented suggest nonoccupational, indoor environmental exposure to formaldehyde is significant and may reach levels which exceed occupational exposure standards.

Grade of Membership (GOM) analysis, a multivariate technique for studying disease, was used to explore depressive typology and relationships between depression and anxiety. One hundred and ninety patients with RDC diagnoses of major or minor depression were assessed by the Hamilton and SCL-90 symptom rating scales, the Newcastle diagnostic indices for endogenous depression and for anxiety and depression. Demographic, family and treatment response information were used as external validators. Five pure types provided the most satisfactory solution to these data. One group corresponded to classical melancholia, occurring in older, stable, in-patients, who lacked panic-phobic symptoms. All patients with agoraphobia fell into two distinct in-patient and out-patient groups, which differed from each other in several ways. In one group, a link was found between panic attacks, agitated melancholia and familial pure depression. The second group was less symptomatic and had more atypical vegetative symptoms. Two more groups comprised mildly symptomatic, hypochondriacal, depression, and a highly neurotic, obsessive, anxious, non-phobic depression, which was commonly related to a physical stressor.