P.Barberger-Gateau1, V.Bagdonavicius2, M.Nikulin1, O.Zdorova-Cheminade1,
1 IFR 99 Santé Publique, Université Victor Segalen Bordeaux 2, France ni[email protected]
2 Department of Mathematical Statistics, Vilnius University, Lithuania [email protected]
Summary. The paper considers the analysis of disablement process of the elderly using the general path model with noise. The impact of dementia and sex on degradation is analysed. These joint model for survival and longitudinal data is discussed.
Key words: aging, censored data , conjoint model , degradation process , dementia, disability , failure , elderly , noise , path model , Wulfsohn-Tsiatis model .
Aging of the French population, which included 21.3% persons aged 60 and over at the 1999 census, is the result of the decrease of the number of births and the increase of life expectancy. This phenomenon raises the problem of the management by the health care system and the society of age-related diseases and their consequences.
The World Health Organisation (WHO) proposed the International Classification of Impairment, Disability and Handicap to conceptualise the consequences of disease [WHO8O]. Disability is defined as the reduction of the capacity to accomplish daily activities, in a way normal for a given age and gender. These activities include basic Activities of Daily Living (ADL), such as bathing, dressing or eating, and more complex activities including household activities called Instrumental Activities of Daily Living (IADL). Activities performed outside, often referred to "mobility", correspond to an even higher level of difficulty. There is a hierarchical relationship between these three domains of disability. We showed that an indicator combining mobility disability, assessed by the Rosow scale [RB66], IADL disability assessed by the Lawton scale [LB69] and ADL disability assessed by five items of the Katz scale [KDCG70] was an almost perfect four grade Guttman scale
[B-GRLD00]. These four grades correspond to four degrees of increasing disability, from full functional independence to severe disability. Transitions observed over time between these disability grades may be progressions to a more severe grade (called increasing degradation) but also regressions to a less severe grade (called decreasing degradation) are possible. Transition to death may be observed from any disability grade. Thus the degradation process may be modelled by a five state model, including an absorbing state: death. Markov models have been used to estimate the transition intensities between these states, function of covariates [B-GVP01]. Other models may be used, which model the degradation process as a continuum from full independence to the most severe disability, including phases of recovery and different slopes of decline, function of the characteristics of the subject. Disability at older ages results from lifelong disabling diseases and living conditions, in addition to specific age-associated diseases such as dementia . Thus the degradation process will be modified by covariates, in particular socio-demographic factors. Age is a major factor to be taken into account since the risk of death strongly increases with age, but also because age is the main risk factor of age-associated diseases. In particular, oldest old persons, those aged 80 and over, often suffer from several pathologies in addition to the proper effect of physiological aging. Women have a longer life expectancy than men, and they experience living conditions and disease different from those of men. Dementia is a major disabling disease in the elderly. Thus all these factors are expected to impact the degradation process and the risk of death. The objective of this research was to describe the degradation process in elderly persons aged 65 and over function of their socio-demographic characteristics and the diagnosis of dementia, using the general path model of degradation with noise.
The data come from the PAQUID (Personnes Agées QUID) epidemiologi-cal study which aims to study cerebral aging and disability in elderly people. PAQUID is a prospective cohort study in which 3777 community dwellers aged 65 and over were included in 1988-89. The participants were randomly selected from electoral rolls of 75 parishes in Gironde and Dordogne, in southwestern France. The initial participation rate was 68% and the sample was representative in terms of age and sex of the local aged population. The participants were visited at home by a psychologist for the baseline interview, and then visited again one, three, five, eight, ten and thirteen years afterwards in the same manner. Disability was recorded at each follow-up with the following instruments: - Five activities from the Katz ADL scale [KDCG70]: bathing, dressing, toileting, transferring, and feeding. For each activity the subject was rated on a three grade scale : independent, needs partial help, dependent. We considered a subject as dependent for ADL if he was dependent for at least one of the five activities according to the threshold defined by Katz for each activity. - Five IADL from the Lawton scale [LB69] common to both sexes: using the telephone, means of transportation, shopping, responsibility for medication and budget management. Three activities were added when assessing women: meals preparation, housekeeping and doing the laundry. For each item a threshold for dependence was defined by Lawton and we considered that a subject was dependent for IADL if he was dependent for at least one in five (for men) or in eight (for women) of these activities. - Mobility was assessed on the Rosow and Breslau scale which includes three activities : doing heavy housework, climbing stairs, and walking between 500 m and 1 km. Subjects were considered as dependent if they were unable to perform at least one of these activities.
A four grade hierarchical disability indicator was built as follows [B-GRLD00] :
Grade 0: fully independent subject for the three domains of disability. Grade 1: subjects dependent only for the mobility scale, but independent for IADL and ADL.
Grade 2: subjects dependent for mobility and IADL but independent for ADL.
Grade 3: subjects dependent for each of the three domains. This indicator classified 99.3% of the subjects at baseline with a scalability coefficient of 0.98 [B-GRLD00]. In a second step a hierarchy was also identified within each of the three disability categories. The mobility disabled subjects (grade 1 disability) were divided into two subgroups : those dependent only for doing heavy housework and those also dependent for climbing stairs or walking. For IADL disability three groups of progressively increasing disability were identified : disability for shopping and/or using means of transportation, disability for managing medication and/or budget in addition to the previous category, and disability for using the telephone in addition to the two previous categories. For ADL disability three subgroups were identified : those dependent only for bathing and/or dressing, those also dependent for toileting and/or transferring, and those also dependent for feeding. Thus the number of disability items was reduced to eight levels of increasing disability. A score was built as follows.
Among the 3777 participants in the PAQUID cohort at baseline, 3642 had all the relevant disability variables recorded and at least one follow-up visit or deceased. This sample included 1530 men (42%) and 2112 women (58%). The distribution of the score in this sample is given in table 1. Older subjects had higher disability scores. In each age group women tended to have higher disability scores than men. Only 2864 subjects (1183 men and1681 women) with at least two measures of the score could be used for modelisation. In this sample 403 subjects (14.1%) had a diagnosis of dementia at any time of the follow-up. The sample included 929 subjects (32.4%) who had not achieved the "Cetrificat d'Etudes Primaires (CEP) corresponding to about seven years of schooling. These subjects were considered as "low educated", in opposition to the 1935 "high educated" who had at least reached this level.
Zdorova-Cheminade [Z-C03] studied by simulation the considered model as statistical degradation model of disablement in the elderly to verify that a hierarchical relationship exists between the concepts of Activities Daily Living, Instrumental Activities of Daily Living and mobility and to use this model to study the evolution of disability. The cumulative disability scale was used to describe the degradation process in time. In longitudinal analysis an additional level was considered to the disability index to take death into account. It is evident that this approach can be used in many other medical studies where a degradation is observed, especially in oncology.
Each of the 13 initial activities was given a rating between 0 and 1 :
• - 0 corresponds to the ability to perform the activity without help;
• - 1 corresponds to full dependency for this activity;
• - a step l/(m - l) was added for each intermediate level of ability, m being the number of degrees on each activity in its original version [RB66] - [KDCG70]. m varied between 3 and 5, function of the activity.
Each of the eight disability levels was then given a rating between 0 and
• - if the level corresponded to a single activity, the rating was that of the activity;
• - if the level was a combination of several activities, the rating was the mean of the ratings of each activity.
A score was built by summing up the eight ratings corresponding to each disability level. This score varies between 0 and 8. The score increases with increasing disability.
The time scale was age, starting at age 65 to model the process
2 Degradation model
Let us consider the degradation model with the noise:
Z(t)= g(t, A) U(t), t > 0, here A = (A1A2) is a random vector with the distribution function Fa, g is a continuously differentiable function, U(t), t > 0 is the noise. We suppose that
W is the standard Wiener process independent on A. The component g(t, A) explains the interior degradation process, different for each individual, the noise U explains the complementary influence on the obtained disability score by such factors as temporary disability, desease, low spirits, breaked leg, etc. Note that for any t > 0 the median of the the random variable U(t) is l. If a = 0 then we have the General Path Model [MEL98].
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