This thesis adopts a survival model to analyze China’s stock market. The data used are the capitalization-weighted stock market index (CSI 300) and the 300 stocks for creating the index. We define the recurrent events using the daily return of the selected stocks and the index. A shared frailty model which incorporates the random effects is then used for analyses since the survival times of individual stocks are correlated. Maximization of penalized likelihood is presented to estimate the parameters in the model. The covariates are selected using the Akaike information criterion (AIC) and the variance inflation factor (VIF) to avoid multicollinearity. The result of analyses show that the general capital, total amount of a stock traded in a day, turnover rate and price book ratio are significant in the shared frailty model for daily stock data.

Accurate prediction of mortality is an important component of forest growth and yield prediction systems, yet mortality remains one of the least understood components of the system. Whole-stand and individual-tree mortality models were developed for loblolly pine plantations throughout its geographic range in the United States. The model for predicting stand mortality were developed using stand characteristics and biophysical variables. The models were constructed using two modeling approaches. In the first approach, mortality functions for directly predicting tree number reduction were developed using algebraic difference equation method. In the second approach, a two-step modeling strategy was used where a model predicting the probability of tree death occurring over a period was developed in the first step and a function that estimates the reduction in tree number was developed in the second step. Individual-tree mortality models were developed using multilevel logistic regression and survival analysis techniques. Multilevel data structure inherent in permanent sample plots data i.e. measurement occasions nested within trees (e.g., repeated measurements) and trees nested within plots, is often ignored in modeling tree mortality in forestry applications. Multilevel mixed-effects logistic regression takes into account the full hierarchical structure of the data. Multilevel mixed-effects models gave better predictions than the fixed effects model; however, the model fits and predictions were further improved by taking into account the full hierarchical structure of the data. Semiparametric proportional hazards regression was also used to develop model for individual-tree mortality. Shared frailty model, mixed model extension of Cox proportional hazards model, was used to account for unobserved heterogeneity not explained by the observed covariates in the Cox model. / Ph. D.

Em análise de sobrevivência, usualmente o interesse esté em estudar o tempo até a ocorrência de um evento. Quando as observações estão sujeitas a mais de um tipo de evento (por exemplo, diferentes causas de óbito) e a ocorrência de um evento impede a ocorrência dos demais, tem-se uma estrutura de riscos competitivos. Em algumas situações, no entanto, o interesse está em estudar dois eventos, sendo que um deles (evento terminal) impede a ocorrência do outro (evento intermediário), mas não vice-versa. Essa estrutura é conhecida como riscos semicompetitivos e foi definida por Fine et al.(2001). Neste trabalho são consideradas duas abordagens para análise de dados com essa estrutura. Uma delas é baseada na construção da função de sobrevivência bivariada por meio de cópulas da família Arquimediana e estimadores para funções de sobrevivência são obtidos. A segunda abordagem é baseada em um processo de três estados, conhecido como processo doença-morte, que pode ser especificado pelas funções de intensidade de transição ou funções de risco. Neste caso, considera-se a inclusão de covariáveis e a possível dependência entre os dois tempos observados é incorporada por meio de uma fragilidade compartilhada. Estas metodologias são aplicadas a dois conjuntos de dados reais: um de 137 pacientes com leucemia, observados no máximo sete anos após transplante de medula óssea, e outro de 1253 pacientes com doença renal crônica submetidos a diálise, que foram observados entre os anos 2009-2011. / In survival analysis, usually the interest is to study the time until the occurrence of an event. When observations are subject to more than one type of event (e.g, different causes of death) and the occurrence of an event prevents the occurrence of the other, there is a competing risks structure. In some situations, nevertheless, the main interest is to study two events, one of which (terminal event) prevents the occurrence of the other (nonterminal event) but not vice versa. This structure is known as semicompeting risks, defined initially by Fine et al. (2001). In this work, we consider two approaches for analyzing data with this structure. One approach is based on the bivariate survival function through Archimedean copulas and estimators for the survival functions are obtained. The second approach is based on a process with three states, known as Illness-Death process, which can be specified by the transition intensity functions or risk functions. In this case, the inclusion of covariates and a possible dependence between the two times is taken into account by a shared frailty. These methodologies are applied to two data sets: the first one is a study with 137 patients with leukemia that received an allogeneic marrow transplant, with maximum follow up of 7 years; the second is a data set of 1253 patientswith chronic kidney disease on dialysis treatment, followed from 2009 until 2011.

Em análise de sobrevivência, usualmente o interesse esté em estudar o tempo até a ocorrência de um evento. Quando as observações estão sujeitas a mais de um tipo de evento (por exemplo, diferentes causas de óbito) e a ocorrência de um evento impede a ocorrência dos demais, tem-se uma estrutura de riscos competitivos. Em algumas situações, no entanto, o interesse está em estudar dois eventos, sendo que um deles (evento terminal) impede a ocorrência do outro (evento intermediário), mas não vice-versa. Essa estrutura é conhecida como riscos semicompetitivos e foi definida por Fine et al.(2001). Neste trabalho são consideradas duas abordagens para análise de dados com essa estrutura. Uma delas é baseada na construção da função de sobrevivência bivariada por meio de cópulas da família Arquimediana e estimadores para funções de sobrevivência são obtidos. A segunda abordagem é baseada em um processo de três estados, conhecido como processo doença-morte, que pode ser especificado pelas funções de intensidade de transição ou funções de risco. Neste caso, considera-se a inclusão de covariáveis e a possível dependência entre os dois tempos observados é incorporada por meio de uma fragilidade compartilhada. Estas metodologias são aplicadas a dois conjuntos de dados reais: um de 137 pacientes com leucemia, observados no máximo sete anos após transplante de medula óssea, e outro de 1253 pacientes com doença renal crônica submetidos a diálise, que foram observados entre os anos 2009-2011. / In survival analysis, usually the interest is to study the time until the occurrence of an event. When observations are subject to more than one type of event (e.g, different causes of death) and the occurrence of an event prevents the occurrence of the other, there is a competing risks structure. In some situations, nevertheless, the main interest is to study two events, one of which (terminal event) prevents the occurrence of the other (nonterminal event) but not vice versa. This structure is known as semicompeting risks, defined initially by Fine et al. (2001). In this work, we consider two approaches for analyzing data with this structure. One approach is based on the bivariate survival function through Archimedean copulas and estimators for the survival functions are obtained. The second approach is based on a process with three states, known as Illness-Death process, which can be specified by the transition intensity functions or risk functions. In this case, the inclusion of covariates and a possible dependence between the two times is taken into account by a shared frailty. These methodologies are applied to two data sets: the first one is a study with 137 patients with leukemia that received an allogeneic marrow transplant, with maximum follow up of 7 years; the second is a data set of 1253 patientswith chronic kidney disease on dialysis treatment, followed from 2009 until 2011.

La recherche sur le traitement des cancers a évolué durant les dernières années principalement dans une direction: la médecine personnalisée. Idéalement, le choix du traitement doit être basé sur les caractéristiques dupatient et de sa tumeur. Cet objectif nécessite des développements biostatistiques, pour pouvoir évaluer lesmodèles pronostiques, et in fine proposer le meilleur. Dans une première partie, nous considérons le problèmede l’évaluation d’un score pronostique dans le cadre de données multicentriques. Nous étendons deux mesuresde concordance aux données groupées analysées par un modèle à fragilité partagée. Les deux niveaux inter etintra-groupe sont étudiés, et l’impact du nombre et de la taille des groupes sur les performances des mesuresest analysé. Dans une deuxième partie, nous proposons d’améliorer la prédiction du risque de décès en tenantcompte des rechutes précédemment observées. Pour cela nous développons une prédiction issue d’un modèleconjoint pour un événement récurrent et un événement terminal. Les prédictions individuelles proposées sontdynamiques, dans le sens où le temps et la fenêtre de prédiction peuvent varier, afin de pouvoir mettre à jourla prédiction lors de la survenue de nouveaux événements. Les prédictions sont développées sur une série hospitalièrefrançaise, et une validation externe est faite sur des données de population générale issues de registres decancer anglais et néerlandais. Leurs performances sont comparées à celles d’une prédiction issue d’une approchelandmark. Dans une troisième partie, nous explorons l’utilisation de la prédiction proposée pour diminuer ladurée des essais cliniques. Les temps de décès non observés des derniers patients inclus sont imputés en utilisantl’information des patients ayant un suivi plus long. Nous comparons trois méthodes d’imputation : un tempsde survie moyen, un temps échantillonné dans une distribution paramétrique et un temps échantillonné dansune distribution non-paramétrique des temps de survie. Les méthodes sont comparées en termes d’estimationdes paramètres (coefficient et écart-type), de risque de première espèce et de puissance. / Research on cancer treatment has been evolving for last years in one main direction: personalised medicine. Thetreatment choice must be done according to the patients’ and tumours’ characteristics. This goal requires somebiostatistical developments, in order to assess prognostic models and eventually propose the best one. In a firstpart, we consider the problem of assessing a prognostic score when multicentre data are used. We extended twoconcordance measures to clustered data in the context of shared frailty model. Both the between-cluster andthe within-cluster levels are studied, and the impact of the cluster number and size on the performance of themeasures is investigated. In a second part, we propose to improve the prediction of the risk of death accountingfor the previous observed relapses. For that, we develop predictions from a joint model for a recurrent event anda terminal event. The proposed individual prediction is dynamic, both the time and the horizon of predictioncan evolve, so that the prediction can be updated at each new event time. The prediction is developed ona French hospital series, and externally validated on population-based data from English and Dutch cancerregistries. Its performances are compared to those of a landmarking approach. In a third part, we explore theuse of the proposed prediction to reduce the clinical trial duration. The non-observed death times of the lastincluded patients are imputed using the information of the patients with longer follow-up. We compared threemethods to impute the data: a survival mean time, a time sampled from the parametric distribution and atime sampled from a non-parametric distribution of the survival times. The comparison is made in terms ofparameters estimation (coefficient and standard-error), type-I error and power.

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). / A growing body of literature has documented the multiple and complex factors and pathways through which longevity and mortality in old age may be shaped. It appears indeed that surviving to a very old age is modulated by a familial component, whether it arises from environmental or genetic confounds. The scientific debate on longevity and its determinants has put considerable interest in studying the centenarians and the role of shared early life conditions have been addressed extensively in the literature, but those two elements have rarely been mixed together. The main objective of my research thesis is to discuss some of the key factors involved in aging and longevity with a focus on the role of family determinants and shared frailty. More specifically, it aims to (1) highlight the central importance of family on exceptional longevity by examining similarity in age at death among siblings and between spouses; (2) examine whether there is a persisting effect of maternal age and birth order on exceptional survival when both variables are considered and adjusted for season of birth; and (3) investigate whether early life factors, such as the socioeconomic background, shape the course of aging and longevity and whether this association is mediated by the socioeconomic status in adulthood. Our analysis rest upon family-based samples of siblings of centenarians and controls born in Québec at the end of the 19th and the beginning of the 20th century which compile information from the Canadian Census and Quebec vital statistics registers. The results, in the form of scientific articles, have shown that siblings of centenarians lived longer compared to members of their birth cohort suggesting the existence of a genetic component to longevity. However, there is also a survival benefit for spouses of centenarians compared to the general population which implies that longevity is also modulated by the shared environment in adulthood (1st article). Furthermore, the within-family analysis has shown that elements of the unshared early life environment, such as maternal age at reproduction, birth order and season of birth, not only have an independent impact on exceptional survival but also interact with one another to create vulnerabilities for later-life mortality (2nd article). Finally, the use of a longitudinal framework engaging both biodemographic and socioeconomic factors emphasize the contribution of early life conditions in longevity inequalities both directly and indirectly through adult profession. The influence of socioeconomic conditions in childhood were stronger for men of the general population compared to brothers of centenarians and early life origin showed almost no effect for women (3rd article).