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.

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.