Rainer T. Schaub

The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

We here consider testing the hypothesis ofhomogeneity against the alternative of a two-component mixture of densities. The paper focuses on the asymptotic null distribution of 2 log λn, where λn is the likelihood ratio statistic. The main result, obtained by simulation, is that its limiting distribution appears pivotal (in the sense of constant percentiles over the unknown parameter), but model specific (differs if the model is changed from Poisson to normal, say), and is not at all well approximated by the conventional χ(2)2-distribution obtained by counting parameters. In Section 3, the binomial with sample size parameter 2 is considered. Via a simple geometric characterization the case for which the likelihood ratio is 1 can easily be identified and the corresponding probability is found. Closed form expressions for the likelihood ratio λn are possible and the asymptotic distribution of 2 log λn is shown to be the mixture giving equal weights to the one point distribution with all its mass equal to zero and the χ2-distribution with 1 degree of freedom. A similar result is reached in Section 4 for the Poisson with a small parameter value (θ≤0.1), although the geometric characterization is different. In Section 5 we consider the Poisson case in full generality. There is still a positive asymptotic probability that the likelihood ratio is 1. The upper precentiles of the null distribution of 2 log λn are found by simulation for various populations and shown to be nearly independent of the population parameter, and approximately equal to the (1–2α)100 percentiles of χ(1)2. In Sections 6 and 7, we close with a study of two continuous densities, theexponential and thenormal with known variance. In these models the asymptotic distribution of 2 log λn is pivotal. Selected (1−α) 100 percentiles are presented and shown to differ between the two models.

DHEA-S plasma levels and incidence of Alzheimer's disease

BACKGROUND Cross-sectional studies controlling for age and gender reported a relationship between Alzheimers disease and low dehydroepiandrosterone sulphate (DHEA-S) plasma levels. Prospective data with sufficient control for confounding factors are lacking. METHODS A nested case-control study examined baseline DHEA-S in participants of the Berlin Aging Study. Cases (n = 14) developed dementia of the Alzheimer type within 3 years. Control group A (n = 14) was matched for gender, age, multimorbidity, and immobility. Control group B (n = 13) was matched for gender and age and comprised participants free from multimorbidity, immobility, multimedication, need of help, incontinence, visual impairment, hearing impairment, and depression. RESULTS The mean plasma DHEA-S concentration of case subjects was 1.02 +/- 0.61 mumol/L. Both control groups had higher mean DEHA-S levels, in control group A, it was 1.89 +/- 1.24 mumol/L (p = .012) and in control group B 1.70 +/- 1.38 mumol/L (p = .093). CONCLUSIONS This population-based prospective study supports the role of DHEA-S as a risk factor for Alzheimers disease.

Carotid atherosclerosis, vascular risk profile and mortality in a population-based sample of functionally healthy elderly subjects: the Berlin ageing study.

Abstract. Hillen T, Nieczaj R, Münzberg H, Schaub R, Borchelt M, Steinhagen‐Thiessen E (Humboldt‐University Berlin, Berlin; Department of Public Health Medicine/King’s College London, London; and Klinikum der Hansestadt Stralsund, Stralsund, Germany). Carotid atherosclerosis, vascular risk profile and mortality in a population‐based sample of functionally healthy elderly subjects: the Berlin Ageing Study. J Intern Med 2000; 247: 679–688.

Self rating of health is associated with stressful life events, social support and residency in East and West Berlin shortly after the fall of the wall

STUDY OBJECTIVE To compare the health status and factors influencing the health of populations that had previously lived under different political systems. DESIGN Cross sectional health and social survey using postal interviews. The relation between self reported health and psychosocial factors (stressful life events, social support, education, health promoting life style and health endangering behaviour) was investigated. To determine East-West differences a logistic regression model including interaction terms was fitted. SETTING East and West Berlin shortly after reunification 1991. PARTICIPANTS Representative sample of 4430 Berlin residents aged 18 years and over (response rate 63%). RESULTS Of all respondents, 15.4% rated their health as unsatisfactory. Residents of East Berlin rated their health more frequently as unsatisfactory than residents of West Berlin (Orage adjusted= 1.29, 95%CI 1.08, 1.52), these differences occurred predominantly in the over 60 years age group. Logistic regression showed significant independent effects of stressful life events, social support, education, and health promoting life style on self rated health. The effects of education and health promoting life style were observed to be more pronounced in the western part of Berlin. Old age and female sex showed a stronger association with unsatisfactory health status in the eastern part of Berlin. CONCLUSIONS For subjects aged over 60 years there was evidence that living in the former East Berlin had an adverse effect on health compared with West Berlin. The impact of education and a health promoting lifestyle on self rated health seemed to be weaker in a former socialist society compared with that of a Western democracy. This study supports an “additive model“ rather than a “buffering model” in explaining the effects of psychosocial factors on health.

The multiaxial system of ICD-10 : Evaluation of a preliminary draft in a multicentric field trial

The multiaxial system (MAS) of ICD-10, chapter V (F) consists of three axes: axis I, clinical syndromes (psychiatric disorders including personality disorders and somatic diseases); axis II, disabilities; axis III, environmental/circumstantial and personal life-style/life management factors. Results of a multicentric field trial evaluating a preliminary draft of the MAS are presented. 45 raters in seven German centers made 488 ratings on 12 written case histories. With a mean kappa of 0.50 for 3-character diagnoses interrater reliability for axis I was moderate although lower than expected from previous field trials. On axis II the WHO Disability Diagnostic Scale (WHO-DDS) was compared to the Global Assessment of Functioning (GAF) used in DSM-III-R and DSM-IV. For both scales the intraclass correlation coefficient showed a moderate interrater reliability (WHO-DDS = 0.62; GAF = 0.65). On axis III the number of relevant psychosocial circumstances coded by the different raters varied greatly. Interrater reliability was very poor with kappa values ranging from 0.03 to 0.55 for the different categories and an overall kappa of 0.16.

Normal ageing, impaired cognitive functioning and senile dementia – a mixture distribution analysis

Dementia scores in the population of very old subjects (70 to > 95) do not demonstrate an obviously bimodal distribution. Heterogeneity analysis shows that the assumption of two distributions explains the data significantly better than a one-distribution model. The first distribution component can be regarded as representing the normal range of scores and the second the pathological range. An additional finding shows the normal range distribution shifting to the pathological range with increasing age.

Multiaxiales System des Kapitels V (F) der ICD-10 Erste Ergebnisse der multizentrischen Praktikabilitäts- und Reliabilitätsstudie*,**

ZusammenfassungMit der Einführung der operationalisierten psychiatrischen Diagnostik kam der multiaxiale Ansatz zu neuer Beachtung. Der Entwurf des multiaxialen Systems der ICD-10 umfaßt auf Achse I psychiatrische und somatische Diagnosen. Mit der Achse II (disability diagnostic scale, DDS) werden Beeinträchtigungen der psychosozialen Funktionsfähigkeit abgebildet, während auf der Achse III Belastungsfaktoren eingeschätzt werden. Als Teil der internationalen WHO-Anwendungsstudie wurden in 7 deutschsprachigen Zentren die Anwendbarkeit und Interraterreliabilität des Systems untersucht. Weiterhin wurde die Achse II mit der entsprechenden Achse des DSM-III-R (global assessment of functioning scale) verglichen. 45 deutschsprachige Kliniker beurteilten 12 englischsprachige, von der WHO bereitgestellte Fallgeschichten in insgesamt 488 diagnostischen Einschätzungen. Die Diagnosen der Achse I zeigten eine mittlere prozentuale Übereinstimmung von 65,6 % und einen ϰ-Wert von 0,50, der damit in einem mittleren Reliabilitätsbereich liegt. Für die Achse II wurde aufgrund der Skalenqualität als Maß der Interraterreliabilität der Intraclasskoeffizient berechnet, der für diese Achse (0,62) und auch für die GAF-Skala (0,65) in einem mittleren Bereich lag. Zwischen den Subskalen und der Globaleinschätzung der Achse II wurde eine hohe Korrelation gefunden. Auf der Achse III gab es nur eine geringe Übereinstimmung für die benannten Belastungsfaktoren, der ϰ-Wert lag hier im Mittel bei 0,16. In der Diskussion werden Anmerkungen für den Revisionsprozeß des multiaxialen Systems der ICD-10 gemacht.SummaryWith the introduction of operationalized diagnostic systems the multiaxial approach became a more important issue. The proposed multiaxial system of ICD-10 consists of three axes: on axis I psychiatric diagnoses are made according to the ICD-10 Clinical Guidelines or Diagnostic Criteria for Research. Axis II (Disability Diagnostic Scale, DDS) deals with impairment of psychosocial functioning. On axis III environmental/circumstantial and personal lifestyle management factors are rated. As part of the WHO international field trial, applicability and inter-rater reliability of the system were examined in seven German-speaking centers. In addition axis II was compared with the corresponding axis of DSM-III-R (Global Assessment of Functioning Scale). 45 German clinicians rated 12 case histories written in English (provided by WHO) with 488 ratings altogether. Diagnoses on axis I with an average percentage agreement of 65.6 % and a mean ϰ of 0.50 showed a moderate inter-rater reliability. For axis II the intraclass coefficient was 0.62, and that for the corresponding DSM-III axis was 0.65: both these axes thus also had a moderate inter-rater reliability. There was a close correlation between the subscales and the global assessment of axis II there was. Wide variation was found in the psychosocial circumstances on axis III, the mean ϰ value being 0.16. In the discussion proposals for the revision process for the multiaxial ICD-10 system are made.

Somatische Krankheiten als Kofaktoren bei Depression im Alter: Ergebnisse der Berliner Altersstudie (BASE)

Neben genetischen und psychosozialen Faktoren werden vor allem korperliche Erkrankimgen und Behinderungen als Risikofaktoren fur die Entstehung und Per-sistenz depressiver Storungen im Alter angesehen. So konnte gezeigt werden, das 1/3-2/3 der Menschen, die einen Schlaganfall erlitten, im darauffolgenden Jahr an Depressionen litten (8), und das diese Depressionen eine hohen Grad an Chroni-zitat aufwiesen (4,11). Andere korperliche Erkrankungen, die einen Zusammen-hang mit Depressionen zeigen, sind Malignome, Morbus Parkinson sowie diverse endokrine und metabolische Storungen, ohne das die vermittelnden Mechanis-men im einzelnen bekannt waren. Ein grundsatzliches Problem bei der Analyse derartiger Zusammenhange stellt das weitgehende Fehlen systematischer Studien an reprasentativen Stichproben dar, die ein breites geriatrisches Diagnosen-Spek-trum erfassen. Diese mussen aber vorausgesetzt werden, um den Einflus unter-schiedlicher Erkrankungen in einer oft multimorbiden Population zu kontrollie-ren. Von Interesse war daher fur uns, inwieweit sich unter Betrachtung des gesam-ten somatischen Diagnosen-Spektrums einzelne Erkrankungsgruppen als gehauft mit Depression im Alter assoziiert nachweisen lassen. Eine weitere Frage bestand darin, ob sich verschiedene Formen von Depression durch das assoziierte Krank-heitsspektrum unterscheiden lassen.