Indiana University-Purdue University Indianapolis (IUPUI) / Survival analysis often encounters the situations of correlated multiple events including the same type of event observed from siblings or multiple events experienced by the same individual. In this dissertation, we focus on the joint modeling of bivariate time to event data with the estimation of the association parameters and also in the situation of a semi-competing risk. This dissertation contains three related topics on bivariate time to event mod els. The first topic is on estimating the cross ratio which is an association parameter between bivariate survival functions. One advantage of using cross-ratio as a depen dence measure is that it has an attractive hazard ratio interpretation by comparing two groups of interest. We compare the parametric, a two-stage semiparametric and a nonparametric approaches in simulation studies to evaluate the estimation perfor mance among the three estimation approaches. The second part is on semiparametric models of univariate time to event with a semi-competing risk. The third part is on semiparametric models of bivariate time to event with semi-competing risks. A frailty-based model framework was used to accommodate potential correlations among the multiple event times. We propose two estimation approaches. The first approach is a two stage semiparametric method where cumulative baseline hazards were estimated by nonparametric methods first and used in the likelihood function. The second approach is a penalized partial likelihood approach. Simulation studies were conducted to compare the estimation accuracy between the proposed approaches. Data from an elderly cohort were used to examine factors associated with times to multiple diseases and considering death as a semi-competing risk.

In survival analysis or time-to-event analysis, one of the primary goals of analysis is to predict the occurrence of an event of interest for subjects within the study. Even though survival analysis methods were originally developed and used in medical re- search, those methods are also commonly used nowadays in other areas as well, such as in predicting the default of a loan and in estimating of the failure of a system. To include covariates in the analysis, the most widely used models are the propor- tional hazard model developed by Cox (1972) and the accelerated failure time model developed by Buckley and James (1979). The proportional hazard (PH) model as- sumes subjects from different groups have their hazard functions proportionally, while the accelerated failure time (AFT) model assumes the effect of covariates is to accel- erate or decelerate the occurrence of event of interest. In some survival analyses, not all subjects in the study will experience the event. Such a group of individuals is referred to `cured' group. To analyze a data set with a cured fraction, Boag (1948) and Berkson and Gage (1952) discussed a mixture cure model. Since then, the cure model and associated inferential methods have been widely stud- ied in the literature. It has also been recognized that subjects in the study are often correlated within clusters or groups; for example, patients in a hospital would have similar conditions and environment. For this reason, Vaupel et al. (1979) proposed a frailty model to model the correlation among subjects within clusters and conse- quently the presence of heterogeneity in the data set. Hougaard (1989), McGilchrist and Aisbett (1991), and Klein (1992) all subsequently developed parametric frailty models. Balakrishnan and Peng (2006) proposed a Generalized Gamma frailty model, which includes many common frailty models, and discussed model fitting and model selection based on it. To combine the key components and distinct features of the mixture cure model and the frailty model, a mixture cure frailty model is discussed here for modelling correlated survival data when not all the subjects under study would experience the occurrence of the event of interest. Longini and Halloran (1996) and Price and Manatunga (2001) developed several parametric survival models and employed the Likelihood Ratio Test (LRT) to perform a model discrimination among cure, frailty and mixture cure frailty models. In this thesis, we first describe the components of a mixture cure frailty model, wherein the flexibility of the frailty distributions and lifetime survival functions are discussed. Both proportional hazard and accelerated failure time models are considered for the distribution of lifetimes of susceptible (or non-cured) individuals. Correlated ran- dom effect is modelled by using a Generalized Gamma frailty term, and an EM-like algorithm is developed for the estimation of model parameters. Some Monte Carlo simulation studies and real-life data sets are used to illustrate the models as well as the associated inferential methods. / Thesis / Doctor of Philosophy (PhD)

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.

In clustered survival data, unobservable cluster effects may exert powerful influences on the outcomes and thus induce correlation among subjects within the same cluster. The ordinary partial likelihood approach does not account for this dependence. Frailty models, as an extension to Cox regression, incorporate multiplicative random effects, called frailties, into the hazard model and have become a very popular way to account for the dependence within clusters. We particularly study the two-level nested lognormal frailty model and propose an estimation approach based on the complete data likelihood with frailty terms integrated out. We adopt B-splines to model the baseline hazards and adaptive Gauss-Hermite quadrature to approximate the integrals efficiently. Furthermore, in finding the maximum likelihood estimators, instead of the Newton-Raphson iterative algorithm, Gauss-Seidel and BFGS methods are used to improve the stability and efficiency of the estimation procedure. We also study competing risks models with missing cause of failure in the context of Cox proportional hazards models. For competing risks data, there exists more than one cause of failure and each observed failure is exclusively linked to one cause. Conceptually, the causes are interpreted as competing risks before the failure is observed. Competing risks models are constructed based on the proportional hazards model specified for each cause of failure respectively, which can be estimated using partial likelihood approach. However, the ordinary partial likelihood is not applicable when the cause of failure could be missing for some reason. We propose a weighted partial likelihood approach based on complete-case data, where weights are computed as the inverse of selection probability and the selection probability is estimated by a logistic regression model. The asymptotic properties of the regression coefficient estimators are investigated by applying counting process and martingale theory. We further develop a double robust approach based on the full data to improve the efficiency as well as the robustness.

Recurrent data are widely encountered in many applications. This thesis work focuses on how the recurrent hospital admissions relate to the air pollutants. In particular, we consider the data for two major cities in Saskatchewan. The study period ranges from January 1, 2005 to December 30, 2011 and involves 20,284 patients aged 40 years and older. The hospital admission data is from the Canadian Institute for Health Information (CIHI). The air pollutants data is from the National Air Pollution Surveillance Program (NAPS) from Environment Canada. The data set has been approved by the Biomedical Research Ethics Board, University of Saskatchewan. The gaseous pollutants included in this study are carbon monoxide (CO), nitrogen dioxide (NO2), sulfur dioxide (SO2), ozone (O3), as well as particulate matter PM2:5 (tiny particles in the air that are 2:5 microns in width). In the data analysis, we applied three different existing models to all respiratory diseases and asthma, respectively. The three models are the Poisson process model (also called Andersen-Gill model), the Poisson process model with the number of previous events as a covariate and the Poisson process model with shared gamma distributed frailties (random effects). For all respiratory diseases, the Poisson process model with random effects provides the best t in comparison to the other two models. The model output suggests that the increased risk of hospital readmission is significantly associated with increased CO and O3. For asthma, the Poisson process model provides the best t in comparison to the other two models. We found that only CO and O3 have significant effects on recurrent hospital admissions due to asthma. We concluded this thesis with the discussion on the current and potential future work.

Indiana University-Purdue University Indianapolis (IUPUI) / Survival analysis has broad applications in diverse research areas. In this dissertation, we consider an innovative application of survival analysis approach to phase I dose-finding design and the modeling of multivariate survival data. In the first part of the dissertation, we apply time to event analysis in an innovative dose-finding design. To account for the unique feature of a new class of oncology drugs, T-cell engagers, we propose a phase I dose-finding method incorporating systematic intra-subject dose escalation. We utilize survival analysis approach to analyze intra-subject dose-escalation data and to identify the maximum tolerated dose. We evaluate the operating characteristics of the proposed design through simulation studies and compare it to existing methodologies. The second part of the dissertation focuses on multivariate survival data with semi-competing risks. Time-to-event data from the same subject are often correlated. In addition, semi-competing risks are sometimes present with correlated events when a terminal event can censor other non-terminal events but not vice versa. We use a semiparametric frailty model to account for the dependence between correlated survival events and semi-competing risks and adopt penalized partial likelihood (PPL) approach for parameter estimation. In addition, we investigate methods for variable selection in semi-parametric frailty models and propose a double penalized partial likelihood (DPPL) procedure for variable selection of fixed effects in frailty models. We consider two penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped absolute deviation (SCAD) penalty. The proposed methods are evaluated in simulation studies and illustrated using data from Indianapolis-Ibadan Dementia Project.

No description available.

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.

In this thesis we propose models based on a reparameterized Birnbaum-Saunder (BS) distribution introduced by Santos-Neto et al. (2012) and Santos-Neto et al. (2014), to analyze survival data. Initially we introduce the Birnbaum-Saunders frailty model where we analyze the cases (i) with (ii) without covariates. Survival models with frailty are used when further information is nonavailable to explain the occurrence time of a medical event. The random effect is the frailty, which is introduced on the baseline hazard rate to control the unobservable heterogeneity of the patients. We use the maximum likelihood method to estimate the model parameters. We evaluate the performance of the estimators under different percentage of censured observations by a Monte Carlo study. Furthermore, we introduce a Birnbaum-Saunders regression frailty model where the maximum likelihood estimation of the model parameters with censored data as well as influence diagnostics for the new regression model are investigated. In the following we propose a cure rate Birnbaum-Saunders frailty model. An important advantage of this proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for the model. In addition, we introduce a bivariate Birnbaum-Saunders distribution based on a parameterization of the Birnbaum-Saunders which has the mean as one of its parameters. We discuss the maximum likelihood estimation of the model parameters and show that these estimators can be obtained by solving non-linear equations. We then derive a regression model based on the proposed bivariate Birnbaum-Saunders distribution, which permits us to model data in their original scale. A simulation study is carried out to evaluate the performance of the maximum likelihood estimators. Finally, examples with real-data are performed to illustrate all the models proposed here. / Nesta tese propomos modelos baseados na distribuição Birnbaum-Saunders reparametrizada introduzida por Santos-Neto et al. (2012) e Santos-Neto et al. (2014), para análise dados de sobrevivência. Inicialmente propomos o modelo de fragilidade Birnbaum-Saunders sem e com covariáveis observáveis. O modelo de fragilidade é caracterizado pela utilização de um efeito aleatório, ou seja, de uma variável aleatória não observável, que representa as informações que não podem ou não foram observadas tais como fatores ambientais ou genéticos, como também, informações que, por algum motivo, não foram consideradas no planejamento do estudo. O efeito aleatório (a fragilidade) é introduzido na função de risco de base para controlar a heterogeneidade não observável. Usamos o método de máxima verossimilhança para estimar os parâmetros do modelo. Avaliamos o desempenho dos estimadores sob diferentes percentuais de censura via estudo de simulações de Monte Carlo. Considerando variáveis regressoras, derivamos medidas de diagnóstico de influência. Os métodos de diagnóstico têm sido ferramentas importantes na análise de regressão para detectar anomalias, tais como quebra das pressuposições nos erros, presença de outliers e observações influentes. Em seguida propomos o modelo de fração de cura com fragilidade Birnbaum-Saunders. Os modelos para dados de sobrevivência com proporção de curados (também conhecidos como modelos de taxa de cura ou modelos de sobrevivência com longa duração) têm sido amplamente estudados. Uma vantagem importante do modelo proposto é a possibilidade de considerar conjuntamente a heterogeneidade entre os pacientes por suas fragilidades e a presença de uma fração curada. As estimativas dos parâmetros do modelo foram obtidas via máxima verossimilhança, medidas de influência e diagnóstico foram desenvolvidas para o modelo proposto. Por fim, avaliamos a distribuição bivariada Birnbaum-Saunders baseada na média, como também introduzimos um modelo de regressão para o modelo proposto. Utilizamos os métodos de máxima verossimilhança e método dos momentos modificados, para estimar os parâmetros do modelo. Avaliamos o desempenho dos estimadores via estudo de simulações de Monte Carlo. Aplicações a conjuntos de dados reais ilustram as potencialidades dos modelos abordados.

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.