Multi-State-Markov (MSM) models can be used to characterize the behaviour of categorical outcomes measured repeatedly over time. Kalbfleisch and Lawless (1985) and Gentleman et al. (1994) examine the MSM model under the assumption of time-homogeneous transition intensities. In the context of non-homogeneous intensities, current methods use piecewise constant approximations which are less than ideal. We propose a local likelihood method, based on Tibshirani and Hastie (1987) and Loader (1996), to estimate the transition intensities as continuous functions of time. In particular the local EM algorithm suggested by Betensky et al. (1999) is employed to estimate the in-homogeneous intensities in the presence of missing data. A simulation comparing the piecewise constant method with the local EM method is examined using two different sets of underlying intensities. In addition, model assessment tools such as bandwidth selection, grid size selection, and bootstrapped percentile intervals are examined. Lastly, the method is applied to an HIV data set to examine the intensities with regard to depression scores. Although computationally intensive, it appears that this method is viable for estimating non-homogeneous intensities and outperforms existing methods.

Multi-State-Markov (MSM) models can be used to characterize the behaviour of categorical outcomes measured repeatedly over time. Kalbfleisch and Lawless (1985) and Gentleman et al. (1994) examine the MSM model under the assumption of time-homogeneous transition intensities. In the context of non-homogeneous intensities, current methods use piecewise constant approximations which are less than ideal. We propose a local likelihood method, based on Tibshirani and Hastie (1987) and Loader (1996), to estimate the transition intensities as continuous functions of time. In particular the local EM algorithm suggested by Betensky et al. (1999) is employed to estimate the in-homogeneous intensities in the presence of missing data. A simulation comparing the piecewise constant method with the local EM method is examined using two different sets of underlying intensities. In addition, model assessment tools such as bandwidth selection, grid size selection, and bootstrapped percentile intervals are examined. Lastly, the method is applied to an HIV data set to examine the intensities with regard to depression scores. Although computationally intensive, it appears that this method is viable for estimating non-homogeneous intensities and outperforms existing methods.

Modelos multi-estados têm sido utilizados para descrever o comportamento de unidades amostrais cuja principal resposta é o tempo necessário para a ocorrência de seqüências de eventos. Consideramos um modelo multi-estados markoviano, não homogêneo, que incorpora covariáveis cujos efeitos podem variar ao longo do tempo (efeitos dinâmicos), o que permite a generalização dos modelos usualmente empregados. Resultados assintóticos mostram que procedimentos de estimação baseados no método histograma crivo convergem para um processo gaussiano. A metodologia proposta mostra-se adequada na modelagem de dados reais para comparação de desenvolvimento de recém-nascidos pré-termo com os a termo. Estudos com dados gerados artificialmente confirmam os resultados teóricos obtidos. / Multi-state models have been used to describe the behavior of sample units where the principal response is the time needed for the occurrence of a sequence of events. We consider a non-homogeneous Markovian multi-state model that incorporates covariates with time-dependent coefficient (dynamic effects), generalizing models usually employed. The asymptotic results show that the estimators based on the method of histogram sieves converge to a Gaussian process. The proposed methodology revels adequated for modeling data related to the comparison of developement of preterm infants with term infants. The studies with artificially generated data confirm the asymptotic results.

Modelos multi-estados têm sido utilizados para descrever o comportamento de unidades amostrais cuja principal resposta é o tempo necessário para a ocorrência de seqüências de eventos. Consideramos um modelo multi-estados markoviano, não homogêneo, que incorpora covariáveis cujos efeitos podem variar ao longo do tempo (efeitos dinâmicos), o que permite a generalização dos modelos usualmente empregados. Resultados assintóticos mostram que procedimentos de estimação baseados no método histograma crivo convergem para um processo gaussiano. A metodologia proposta mostra-se adequada na modelagem de dados reais para comparação de desenvolvimento de recém-nascidos pré-termo com os a termo. Estudos com dados gerados artificialmente confirmam os resultados teóricos obtidos. / Multi-state models have been used to describe the behavior of sample units where the principal response is the time needed for the occurrence of a sequence of events. We consider a non-homogeneous Markovian multi-state model that incorporates covariates with time-dependent coefficient (dynamic effects), generalizing models usually employed. The asymptotic results show that the estimators based on the method of histogram sieves converge to a Gaussian process. The proposed methodology revels adequated for modeling data related to the comparison of developement of preterm infants with term infants. The studies with artificially generated data confirm the asymptotic results.

In practice, data are frequently incomplete in one way or another. It can be a significant challenge to make valid inferences about the parameters of interest in this situation. In this thesis, three problems involving such data are addressed. The first two problems involve interval-censored life history data with mismeasured covariates. Data of this type are incomplete in two ways. First, the exact event times are unknown due to censoring. Second, the true covariate is missing for most, if not all, individuals. This work focuses primarily on the impact of covariate measurement error in progressive multi-state models with data arising from panel (i.e., interval-censored) observation. These types of problems arise frequently in clinical settings (e.g. when disease progression is of interest and patient information is collected during irregularly spaced clinic visits). Two and three state models are considered in this thesis. This work is motivated by a research program on psoriatic arthritis (PsA) where the effects of error-prone covariates on rates of disease progression are of interest and patient information is collected at clinic visits (Gladman et al. 1995; Bond et al. 2006). Information regarding the error distributions were available based on results from a separate study conducted to evaluate the reliability of clinical measurements that are used in PsA treatment and follow-up (Gladman et al. 2004). The asymptotic bias of covariate effects obtained ignoring error in covariates is investigated and shown to be substantial in some settings. In a series of simulation studies, the performance of corrected likelihood methods and methods based on a simulation-extrapolation (SIMEX) algorithm (Cook \& Stefanski 1994) were investigated to address covariate measurement error. The methods implemented were shown to result in much smaller empirical biases and empirical coverage probabilities which were closer to the nominal levels. The third problem considered involves an extreme case of interval censoring known as current status data. Current status data arise when individuals are observed only at a single point in time and it is then determined whether they have experienced the event of interest. To complicate matters, in the problem considered here, an unknown proportion of the population will never experience the event of interest. Again, this type of data is incomplete in two ways. One assessment is made on each individual to determine whether or not an event has occurred. Therefore, the exact event times are unknown for those who will eventually experience the event. In addition, whether or not the individuals will ever experience the event is unknown for those who have not experienced the event by the assessment time. This problem was motivated by a series of orthopedic trials looking at the effect of blood thinners in hip and knee replacement surgeries. These blood thinners can cause a negative serological response in some patients. This response was the outcome of interest and the only available information regarding it was the seroconversion time under current status observation. In this thesis, latent class models with parametric, nonparametric and piecewise constant forms of the seroconversion time distribution are described. They account for the fact that only a proportion of the population will experience the event of interest. Estimators based on an EM algorithm were evaluated via simulation and the orthopedic surgery data were analyzed based on this methodology.

In practice, data are frequently incomplete in one way or another. It can be a significant challenge to make valid inferences about the parameters of interest in this situation. In this thesis, three problems involving such data are addressed. The first two problems involve interval-censored life history data with mismeasured covariates. Data of this type are incomplete in two ways. First, the exact event times are unknown due to censoring. Second, the true covariate is missing for most, if not all, individuals. This work focuses primarily on the impact of covariate measurement error in progressive multi-state models with data arising from panel (i.e., interval-censored) observation. These types of problems arise frequently in clinical settings (e.g. when disease progression is of interest and patient information is collected during irregularly spaced clinic visits). Two and three state models are considered in this thesis. This work is motivated by a research program on psoriatic arthritis (PsA) where the effects of error-prone covariates on rates of disease progression are of interest and patient information is collected at clinic visits (Gladman et al. 1995; Bond et al. 2006). Information regarding the error distributions were available based on results from a separate study conducted to evaluate the reliability of clinical measurements that are used in PsA treatment and follow-up (Gladman et al. 2004). The asymptotic bias of covariate effects obtained ignoring error in covariates is investigated and shown to be substantial in some settings. In a series of simulation studies, the performance of corrected likelihood methods and methods based on a simulation-extrapolation (SIMEX) algorithm (Cook \& Stefanski 1994) were investigated to address covariate measurement error. The methods implemented were shown to result in much smaller empirical biases and empirical coverage probabilities which were closer to the nominal levels. The third problem considered involves an extreme case of interval censoring known as current status data. Current status data arise when individuals are observed only at a single point in time and it is then determined whether they have experienced the event of interest. To complicate matters, in the problem considered here, an unknown proportion of the population will never experience the event of interest. Again, this type of data is incomplete in two ways. One assessment is made on each individual to determine whether or not an event has occurred. Therefore, the exact event times are unknown for those who will eventually experience the event. In addition, whether or not the individuals will ever experience the event is unknown for those who have not experienced the event by the assessment time. This problem was motivated by a series of orthopedic trials looking at the effect of blood thinners in hip and knee replacement surgeries. These blood thinners can cause a negative serological response in some patients. This response was the outcome of interest and the only available information regarding it was the seroconversion time under current status observation. In this thesis, latent class models with parametric, nonparametric and piecewise constant forms of the seroconversion time distribution are described. They account for the fact that only a proportion of the population will experience the event of interest. Estimators based on an EM algorithm were evaluated via simulation and the orthopedic surgery data were analyzed based on this methodology.

Multi-state models are useful for modelling progression of a disease, where states represent the health status of a subject under study. In practice, patients may be observed when necessity strikes thus implying that the disease and observation processes are not independent. Often, clinical visits are postponed or advanced by the clinician or patient themselves based on the health status of the patient. In such situations, there is a potential for the frequency and timing of the examinations to be dependent on the latent transition times, and the observation process may be informative. We consider the case where the exact times of transitions between health states of the patient are not observed and so the disease process is interval censored. We model the disease and observation processes jointly to ensure valid inference. The transition intensities are modelled assuming proportional hazards and we link the two processes via random effects. Using a Bayesian framework we apply our joint model to the analysis of a large study examining cancer trajectories of palliative care patients. / Graduate

L'incidence de l'infection par le VIH, définie comme le nombre de sujets nouvellement infectés par le VIH au cours du temps, est le seul indicateur permettant réellement d'appréhender la dynamique de l'épidémie du VIH/SIDA. Sa connaissance permet de prévoir les conséquences démographiques de l'épidémie et les besoins futurs de prise en charge, mais également d'évaluer l'efficacité des programmes de prévention. Jusqu'à très récemment, l'idée de base pour estimer l'incidence de l'infection par le VIH a été d'utiliser la méthode de rétro-calcul à partir des données de l'incidence du SIDA et de la connaissance de la distribution de la durée d'incubation du SIDA. L'avènement, à partir de 1996, de nouvelles combinaisons thérapeutiques très efficaces contre le VIH a contribué à modifier la durée d'incubation du SIDA et, par conséquent, à augmenter la difficulté d'utilisation de la méthode de rétro-calcul sous sa forme classique. Plus récemment, l'idée d'intégrer des informations sur les dates de diagnostic VIH a permis d'améliorer la précision des estimations. La plupart des pays occidentaux ont mis en place depuis quelques années un système de surveillance de l'infection à VIH. En France, la notification obligatoire des nouveaux diagnostics d'infection VIH, couplée à la surveillance virologique permettant de distinguer les contaminations récentes des plus anciennes a été mise en place en mars 2003. L'objectif de ce travail de thèse est de développer de nouvelles méthodes d'estimation de l'incidence de l'infection par le VIH capables de combiner les données de surveillance des diagnostics VIH et SIDA et d'utiliser les marqueurs sérologiques recueillis dans la surveillance virologique dans le but de mieux saisir l'évolution de l'épidémie dans les périodes les plus récentes. / The knowledge of the dynamics of the HIV/AIDS epidemic is crucial for planning current and future health care needs. The HIV incidence, i.e. the number of new HIV infections over time, determines the trajectory and the extent of the epidemic but is difficult to measure. The backcalculation method has been widely developed and used to estimate the past pattern of HIV infections and to project future incidence of AIDS from information on the incubation period distribution and AIDS incidence data. In recent years the incubation period from HIV infection to AIDS has changed dramatically due to increased use of antiretroviral therapy, which lengthens the time from HIV infection to the development of AIDS. Therefore, it has become more difficult to use AIDS diagnosis as the basis for back-calculation. More recently, the idea of integrating information on the dates of HIV diagnosis has improved the precision of estimates. In recent years, most western countries have set up a system for monitoring HIV infection. In France, the mandatory reporting of newly diagnosed HIV infection, coupled with virological surveillance to distinguish recent infections from older, was introduced in March 2003. The goal of this PhD thesis is to develop new methods for estimating the HIV incidence able to combine data from monitoring HIV and AIDS diagnoses and use of serologic markers collected in the virological surveillance in order to better understand the evolution of the epidemic in the most recent periods.

Infectious diseases are increasingly being recognised as significant threatening processes in conservation biology. Developing strategies to effectively manage infectious diseases in wildlife is, therefore, of the utmost importance to the maintenance of global biodiversity. The effective management of infectious diseases relies on understanding the ecology of the host, the epidemiological characteristics of the pathogen and the impacts of the pathogen on the host population. However, for most wildlife-disease systems this information remains poorly understood. This is particularly true for endangered species threatened by novel infectious agents as opportunities to observe and assess disease impacts and host-pathogen dynamics in the wild are limited. The Tasmanian devil (Sarcophilus harrisii), the world’s largest carnivorous marsupial, is threatened with extinction as a result of an epidemic of an emerging disease, a fatal infectious cancer known as Devil Facial Tumour Disease (DFTD). In this thesis I capitalised on a unique dataset from a population of Tasmanian devils where disease arrived part-way through an intensive longitudinal study, and utilised existing genetic samples collected prior to DFTD outbreak, to determine the impact of DFTD on the demography, population dynamics, genetic diversity and population genetic structure of wild Tasmanian devils. I then used this knowledge of the impacts of DFTD impacts in an unmanaged population to evaluate the effectiveness of a disease management trial involving the selective culling of infected individuals. I employed mark-recapture models to investigate the impact of DFTD on age-specific and sex-specific apparent survival rates, to examine the pattern of variation in infection rates (force of infection), and to investigate the impact of DFTD on population growth rate. I investigated demography, life-history traits and morphometric parameters of infected and uninfected individuals to determine the impacts of DFTD on age-structure and sex-structure, female fecundity and individual growth rates. I used this information to assess the population’s ability to respond to low population densities and to compensate for the detrimental impacts of DFTD. To determine the genetic consequences of disease-induced population decline I used microsatellite DNA to compare genetic diversity, population genetic structure and dispersal patterns in three Tasmanian devil populations prior to and following DFTD outbreaks. Capture-mark-recapture analyses revealed that the arrival of DFTD triggered an immediate decline in apparent survival rates of devils, the rate of which was predicted well by the increase in disease prevalence in the population over time. Transition rates of healthy individuals to the diseased class (the force of infection) increased in relation to disease prevalence, while the arrival of DFTD coincided with a marked and ongoing decline in the population growth rate. There was a significant change to the age structure following the arrival of DFTD. This shift to a younger population was caused by the loss of older individuals as a direct consequence of DFTD-driven declines in adult survival rates. Evidence of reproductive compensation in response to these disease impacts was observed via a reduction in the age of sexual maturity of females over time. However, widespread precocial breeding in devils was precluded by physiological and ecological constraints that limited the ability of one year olds to breed. Using temporally-replicated spatial genetic data, I found evidence of increased inbreeding following DFTD arrival and greater population genetic differentiation in post-disease populations. These changes appeared to be driven by a combination of selection and altered dispersal patterns of females in DFTD-affected populations. Comparison of demographic and epidemiological parameters indicative of disease progression and impact between the managed and unmanaged populations revealed that selective culling of infected individuals neither slowed the rate of disease progression nor reduced the population level impacts of this debilitating disease; with culling mortality simply compensating for disease mortality. This thesis provides one of the few direct empirical evaluations of the impact of an emerging wildlife disease epidemic on a wild population. This thesis revealed that infectious diseases can result in major demographic and genetic changes in host populations over relatively few generations and short time-scales. Results showing dramatic and ongoing population declines and very limited population compensation in DFTD-affected populations indicate that DFTD poses a significant extinction risk for wild devil populations. Hence, this study confirms that host-specific pathogens can pose a significant extinction risk for wild species, even in the absence of alternate reservoir hosts, a finding critical to our understanding of host-pathogen dynamics. My thesis also highlights the potential negative interplay between disease susceptibility and host genetic variability, which is of utmost importance to the management of novel wildlife epizootics and the conservation of threatened wildlife in general. The thorough understanding of the ecology and impacts of DFTD in the wild obtained in this study has provided a solid base from which to both rigorously assess the outcome of management strategies and also formulate recommendations for the management of this disease in the wild. The lack of evidence for successful control of the DFTD epidemic in a wild population during the first phase of a selective culling experimental adaptive management approach, points to the need to implement a multi-faceted disease management program when attempting to control a novel infectious disease in the wild. By drawing on the lessons learnt in this case study I show that it is possible to establish a set of general guidelines for the future management of infectious diseases in threatened wildlife.

A travers l'exemple du lièvre d'Europe (Lepus europaeus), l'objectif de cette thèse est de contribuer à une meilleure compréhension des mécanismes régissant les variations d'abondance observées dans les populations animales. Dans ce cadre la dispersion est pressentie comme l'une des principales sources de variation. Après avoir rappelé les principales notions théoriques nécessaires à l'appréhension de ce travail et décrit brièvement l'intérêt du modèle d'étude, nous abordons la problématique sous deux angles différents mais néanmoins complémentaires. Le 1èr est dédié à l'identification des facteurs promouvant les départs et favorisant l'installation des dispersants. L'âge, le sexe et la densité de congénères apparaissent comme les principales variables influentes. Le 2nd angle a pour objectif d'identifier les variables pouvant moduler le succès de la dispersion. Bien qu'induisant des départs supplémentaires, la chasse apparait comme facteur déterminant dans l'échec de la dispersion en augmentant les risques de mortalité pendant le transit. Aussi, la densité dans le site de départ est proposée comme variable diminuant la qualité phénotypique des dispersants. L'ensemble de ces résultats souligne l'importance des conditions environnementales rencontrées au moment du départ, pendant le transit et à l'installation dans la réussite de la dispersion. L'action combinée de la chasse et de la densité sur la dispersion est proposée comme mécanisme probable à l'origine des fluctuations d'abondance observées sur le court terme chez le lièvre d'Europe / Through the example of the European hare (Lepus europaeus), the aim of this work is to contribute to a better understanding of the mechanisms underlying the fluctuation of abundances in animal populations. In this context, dispersal may be seen as the main source of variation. After reminding the theoretical concepts needed to understand this work and briefly describing the interest of the model, we address the topic in two different but complementary approaches. The 1st one is dedicated to the identification of the factors that promote departures and favor settlement of dispersers. Age, sex and density appear to be the main explanatory variables. The 2nd approach is designed to identify the factors that modulate the success of dispersal. Although inducing supplementary emigrants, hunting appears as an important factor decreasing the success of dispersal by increasing the mortality risk during transience. In addition, density in the original site is proposed as one potential factor decreasing the phenotypic quality of dispersers. Overall, these results emphasize the importance of the environmental conditions encountered at the time of departure, during transience and settlement in the dispersal success. The combined action of hunting and density on dispersal is proposed as one potential cause for the short term fluctuations of abundances in the European hare