Explicit ruin formulas for models with dependence among risks

We show that a simple mixing idea allows one to establish a number of explicit formulas for ruin probabilities and related quantities in collective risk models with dependence among claim sizes and among claim inter-occurrence times. Examples include compound Poisson risk models with completely monotone marginal claim size distributions that are dependent according to Archimedean survival copulas as well as renewal risk models with dependent inter-occurrence times.

Aspectes metodològics i aplicacions de la modelització del temps de supervivència multivariant mitjançant models mixtes

Els estudis de supervivència s'interessen pel temps que passa des de l'inici de l'estudi (diagnòstic de la malaltia, inici del tractament,...) fins que es produeix l'esdeveniment d'interès (mort, curació, millora,...). No obstant això, moltes vegades aquest esdeveniment s'observa més d'una vegada en un mateix individu durant el període de seguiment (dades de supervivència multivariant). En aquest cas, és necessari utilitzar una metodologia diferent a la utilitzada en l'anàlisi de supervivència estàndard. El principal problema que l'estudi d'aquest tipus de dades comporta és que les observacions poden no ser independents. Fins ara, aquest problema s'ha solucionat de dues maneres diferents en funció de la variable dependent. Si aquesta variable segueix una distribució de la família exponencial s'utilitzen els models lineals generalitzats mixtes (GLMM); i si aquesta variable és el temps, variable amb una distribució de probabilitat no pertanyent a aquesta família, s'utilitza l'anàlisi de supervivència multivariant. El que es pretén en aquesta tesis és unificar aquests dos enfocs, és a dir, utilitzar una variable dependent que sigui el temps amb agrupacions d'individus o d'observacions, a partir d'un GLMM, amb la finalitat d'introduir nous mètodes pel tractament d'aquest tipus de dades.

Study on Robustness of Correlated Frailty Model

2000 Mathematics Subject Classifi cation: 62J12.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

Analyse des facteurs biodémographiques, sociéconomiques et familiaux de la longévité exceptionnelle

La recherche des facteurs de longévité gagne en intérêt dans le contexte actuel du vieillissement de la population. De la littérature portant sur la longévité et la mortalité aux grands âges, un constat émerge : bien que les déterminants associés à la survie humaine soient multiples, l'environnement familial aurait un rôle déterminant sur la mortalité et sur l'atteinte des âges avancés. Dès lors, l'objectif de cette thèse est d'évaluer les déterminants de la survie exceptionnelle et d'examiner le rôle des aspects familiaux, en début de vie et à l'âge adulte, dans les différentiels de durée de vie. Plus spécifiquement, elle vise à : (1) examiner la similarité des âges au décès entre frères, soeurs et conjoints afin d'apprécier l'ampleur de la composante familiale de la longévité; (2) explorer, d'un point de vue intrafamilial, les conséquences à long terme sur la survie des variables non partagées issues de la petite enfance tels l'âge maternel à la reproduction, le rang de naissance et la saison de naissance; et (3) s'interroger sur le rôle protecteur ou délétère de l’environnement et du milieu familial d'origine dans l’enfance sur l'atteinte des grands âges et dans quelle mesure le statut socioéconomique parvient à médiatiser la relation. Cette analyse s'appuie sur le jumelage des recensements canadiens et des actes de décès de l’état civil québécois et emploie des données québécoises du 20e siècle issues de deux échantillons distincts : un échantillon aléatoire représentatif de la population provenant du recensement canadien de 1901 ainsi qu’un échantillon de frères et soeurs de centenaires québécois appartenant à la même cohorte. Les résultats, présentés sous forme d'articles scientifiques, ont montré, en outre, que les frères et soeurs de centenaires vivent plus longtemps que les individus appartenant aux mêmes cohortes de naissance, reflétant la contribution d'une robustesse commune, mais également celle de l'environnement partagé durant la petite enfance. Ces analyses ont également témoigné d'un avantage de survie des conjoints des centenaires, soulignant l'importance d'un même environnement à l'âge adulte (1er article). De plus, nos travaux ont mis de l'avant la contribution aux inégalités de longévité des variables biodémographiques issues de l'environnement non partagé telles que l'âge maternel à la reproduction, le rang de naissance et la saison de naissance, qui agissent et interagissent entre elles pour créer des vulnérabilités et influer sur l'atteinte des âges exceptionnels (2e article). Enfin, une approche longitudinale a permis de souligner la contribution du milieu social d'origine sur la longévité, alors que les individus issus d’un milieu socioéconomique défavorisé pour l'époque (milieu urbain, père ouvrier) vivent moins longtemps que ceux ayant vécu dans un environnement socioéconomique favorable (milieu rural, fermier), résultat d'une potentielle accumulation des avantages liée à la reproduction du statut social ou d'une programmation précoce des trajectoires de santé. L’influence est toutefois moindre pour les femmes et pour les frères de centenaires et s'exprime, dans ce cas, en partie par l'effet de la profession à l'âge adulte (3e article).

Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates

Department of Statistics, Cochin University of Science and Technology

Modelagem em análise de sobrevivencia com eventos recorrentes aplicada a dados da área médica

Pós-graduação em Biometria - IBB

Survival analysis of longevity in siblings

Do siblings of centenarians tend to have longer life spans? To answer this question, life spans of 184 siblings for 42 centenarians have been evaluated. Two important questions have been addressed in analyzing the sibling data. First, a standard needs to be established, to which the life spans of 184 siblings are compared. In this report, an external reference population is constructed from the U.S. life tables. Its estimated mortality rates are treated as baseline hazards from which the relative mortality of the siblings are estimated. Second, the standard survival models which assume independent observations are invalid when correlation within family exists, underestimating the true variance. Methods that allow correlations are illustrated by three different methods. First, the cumulative relative excess mortality between siblings and their comparison group is calculated and used as an effective graphic tool, along with the Product Limit estimator of the survival function. The variance estimator of the cumulative relative excess mortality is adjusted for the potential within family correlation using Taylor linearization approach. Second, approaches that adjust for the inflated variance are examined. They are adjusted one-sample log-rank test using design effect originally proposed by Rao and Scott in the correlated binomial or Poisson distribution setting and the robust variance estimator derived from the log-likelihood function of a multiplicative model. Nether of these two approaches provide correlation estimate within families, but the comparison with the comparison with the standard remains valid under dependence. Last, using the frailty model concept, the multiplicative model, where the baseline hazards are known, is extended by adding a random frailty term that is based on the positive stable or the gamma distribution. Comparisons between the two frailty distributions are performed by simulation. Based on the results from various approaches, it is concluded that the siblings of centenarians had significant lower mortality rates as compared to their cohorts. The frailty models also indicate significant correlations between the life spans of the siblings. ^

A frailty modeling approach for parental effects in animal breeding

Survival models involving frailties are commonly applied in studies where correlated event time data arise due to natural or artificial clustering. In this paper we present an application of such models in the animal breeding field. Specifically, a mixed survival model with a multivariate correlated frailty term is proposed for the analysis of data from over 3611 Brazilian Nellore cattle. The primary aim is to evaluate parental genetic effects on the trait length in days that their progeny need to gain a commercially specified standard weight gain. This trait is not measured directly but can be estimated from growth data. Results point to the importance of genetic effects and suggest that these models constitute a valuable data analysis tool for beef cattle breeding.

Comparison of 2 frailty indexes for prediction of falls, disability, fractures, and death in older women.

BACKGROUND: Frailty, as defined by the index derived from the Cardiovascular Health Study (CHS index), predicts risk of adverse outcomes in older adults. Use of this index, however, is impractical in clinical practice. METHODS: We conducted a prospective cohort study in 6701 women 69 years or older to compare the predictive validity of a simple frailty index with the components of weight loss, inability to rise from a chair 5 times without using arms, and reduced energy level (Study of Osteoporotic Fractures [SOF index]) with that of the CHS index with the components of unintentional weight loss, poor grip strength, reduced energy level, slow walking speed, and low level of physical activity. Women were classified as robust, of intermediate status, or frail using each index. Falls were reported every 4 months for 1 year. Disability (> or =1 new impairment in performing instrumental activities of daily living) was ascertained at 4(1/2) years, and fractures and deaths were ascertained during 9 years of follow-up. Area under the curve (AUC) statistics from receiver operating characteristic curve analysis and -2 log likelihood statistics were compared for models containing the CHS index vs the SOF index. RESULTS: Increasing evidence of frailty as defined by either the CHS index or the SOF index was similarly associated with an increased risk of adverse outcomes. Frail women had a higher age-adjusted risk of recurrent falls (odds ratio, 2.4), disability (odds ratio, 2.2-2.8), nonspine fracture (hazard ratio, 1.4-1.5), hip fracture (hazard ratio, 1.7-1.8), and death (hazard ratio, 2.4-2.7) (P < .001 for all models). The AUC comparisons revealed no differences between models with the CHS index vs the SOF index in discriminating falls (AUC = 0.61 for both models; P = .66), disability (AUC = 0.64; P = .23), nonspine fracture (AUC = 0.55; P = .80), hip fracture (AUC = 0.63; P = .64), or death (AUC = 0.72; P = .10). Results were similar when -2 log likelihood statistics were compared. CONCLUSION: The simple SOF index predicts risk of falls, disability, fracture, and death as well as the more complex CHS index and may provide a useful definition of frailty to identify older women at risk of adverse health outcomes in clinical practice.

A comparison of frailty of primary neurons, embryonic, and aging mouse cortical layers.

Superficial layers I to III of the human cerebral cortex are more vulnerable toward Aβ peptides than deep layers V to VI in aging. Three models of layers were used to investigate this pattern of frailty. First, primary neurons from E14 and E17 embryonic murine cortices, corresponding respectively to future deep and superficial layers, were treated either with Aβ1-42, okadaic acid, or kainic acid. Second, whole E14 and E17 embryonic cortices, and third, in vitro separated deep and superficial layers of young and old C57BL/6J mice, were treated identically. We observed that E14 and E17 neurons in culture were prone to death after the Aβ and particularly the kainic acid treatment. This was also the case for the superficial layers of the aged cortex, but not for the embryonic, the young cortex, and the deep layers of the aged cortex. Thus, the aged superficial layers appeared to be preferentially vulnerable against Aβ and kainic acid. This pattern of vulnerability corresponds to enhanced accumulation of senile plaques in the superficial cortical layers with aging and Alzheimer's disease.

Official Positions for FRAX® clinical regarding falls and frailty: can falls and frailty be used in FRAX®? From Joint Official Positions Development Conference of the International Society for Clinical Densitometry and International Osteoporosis Foundation on FRAX®.

Risk factors for fracture can be purely skeletal, e.g., bone mass, microarchitecture or geometry, or a combination of bone and falls risk related factors such as age and functional status. The remit of this Task Force was to review the evidence and consider if falls should be incorporated into the FRAX® model or, alternatively, to provide guidance to assist clinicians in clinical decision-making for patients with a falls history. It is clear that falls are a risk factor for fracture. Fracture probability may be underestimated by FRAX® in individuals with a history of frequent falls. The substantial evidence that various interventions are effective in reducing falls risk was reviewed. Targeting falls risk reduction strategies towards frail older people at high risk for indoor falls is appropriate. This Task Force believes that further fracture reduction requires measures to reduce falls risk in addition to bone directed therapy. Clinicians should recognize that patients with frequent falls are at higher fracture risk than currently estimated by FRAX® and include this in decision-making. However, quantitative adjustment of the FRAX® estimated risk based on falls history is not currently possible. In the long term, incorporation of falls as a risk factor in the FRAX® model would be ideal.

Prevalence of frailty in middle-aged and older community-dwelling Europeans living in 10 countries.

BACKGROUND: Frailty is an indicator of health status in old age. Its frequency has been described mainly for North America; comparable data from other countries are lacking. Here we report on the prevalence of frailty in 10 European countries included in a population-based survey. METHODS: Cross-sectional analysis of 18,227 randomly selected community-dwelling individuals 50 years of age and older, enrolled in the Survey of Health, Aging and Retirement in Europe (SHARE) in 2004. Complete data for assessing a frailty phenotype (exhaustion, shrinking, weakness, slowness, and low physical activity) were available for 16,584 participants. Prevalences of frailty and prefrailty were estimated for individuals 50-64 years and 65 years of age and older from each country. The latter group was analyzed further after excluding disabled individuals. We estimated country effects in this subset using multivariate logistic regression models, controlling first for age, gender, and then demographics and education. RESULTS: The proportion of frailty (three to five criteria) or prefrailty (one to two criteria) was higher in southern than in northern Europe. International differences in the prevalences of frailty and prefrailty for 65 years and older group persisted after excluding the disabled. Demographic characteristics did not account for international differences; however, education was associated with frailty. Controlling for education, age and gender diminished the effects of residing in Italy and Spain. CONCLUSIONS: A higher prevalence of frailty in southern countries is consistent with previous findings of a north-south gradient for other health indicators in SHARE. Our data suggest that socioeconomic factors like education contribute to these differences in frailty and prefrailty.

Frailty, an Emerging Research and Clinical Paradigm: Issues and Controversies

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