Propensity score methods are increasingly being used to reduce the effect of measured confounders in observational research. In medicine, censored time-to-event data is common. Using Monte Carlo simulations, this thesis evaluates the performance of nearest neighbour matching (NNM) and inverse probability of treatment weighting (IPTW) in combination with Cox proportional hazards models for estimating marginal hazard ratios. Focus is on the performance for different sample sizes and censoring rates, aspects which have not been fully investigated in this context before. The results show that, in the absence of censoring, both methods can reduce bias substantially. IPTW consistently had better performance in terms of bias and MSE compared to NNM. For the smallest examined sample size with 60 subjects, the use of IPTW led to estimates with bias below 15 %. Since the data were generated using a conditional parametrisation, the estimation of univariate models violates the proportional hazards assumption. As a result, censoring the data led to an increase in bias.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

V této práci se zabýváme metodami pro regresní analýzu výskytu opako- vaných událostí, při které je třeba se vypořádat se závislostí čas· do události v rámci jednoho subjektu. V první části práce se zabýváme možným rozšířením Coxova modelu proporcionálního rizika, který se využívá při analýze cenzoro- vaných dat, pro analýzu výskytu opakovaných událostí. Hlavní část práce je věnována odhadu parametr· v marginálních modelech a jejich asymptotickým vlastnostem. Následně se zabýváme i odhadem parametr· v marginálních mo- delech pro mnohorozměrná cenzorovaná data. Vhodnost použití marginálních model· je zkoumána pomocí simulací. 1

Avec un taux d’incidence cumulée de 56 cas pour 100 000 habitants, la Guadeloupe est la deuxième région de France la plus touchée par le VIH. La plupart des publications sur le VIH/Sida en Guadeloupe sont essentiellement descriptives, issues de rapports d’activité. La base hospitalière, alimentant la Base de données Hospitalière française sur l’infection à VIH, n’a été que très peu exploitée pour la recherche. L’objectif de ce travail est d’évaluer les aspects fondamentaux de la prise en charge de l’infection VIH. Ainsi le dépistage tardif, le retard à la prise en charge spécialisée, l’interruption du suivi, les infections opportunistes et les décès sont étudiés ainsi que leurs facteurs prédictifs.Dans ce travail articulé autour de six publications, nous avons mis en évidence les points suivants : tout d’abord, le diagnostic très tardif (CD4<200/mm3) concernait 40,12 % des adultes infectés par le VIH suivis en Guadeloupe. Comparé à la France métropolitaine, ce taux est encore très élevé et souligne l’importance de poursuivre les efforts de dépistage. Pour pouvoir bénéficier d’une prise en charge précoce, le patient doit être dirigé dans un centre de traitement de l’infection par le VIH sans tarder. Or, le retard dans cette prise en charge spécialisée touchait 36 % des patients. L’analyse des éléments associés à ce retard a permis d’en identifier les facteurs de risque.Pour optimiser les résultats thérapeutiques, les patients nécessitent un suivi régulier. Ainsi, le système de santé devrait avoir comme objectif, entre autres, la rétention des patients dans le circuit de soins. Or, plus de 22 % des patients de cette cohorte étaient perdus de vue et jamais revus. Les patients plus jeunes, ceux au stade B de la classification CDC et ceux non traités par TTARV étaient plus à risque d’interruption de suivi, dès la première année suivant le diagnostic de l’infection VIH.Bien que la proportion des patients suivis sous ARV soit proche de 100 %, il en existe toujours développant un Sida. La comparaison avec la Guyane et la France métropolitaine montre que les trois premières affections classantes en Guadeloupe étaient la candidose oesophagienne, le syndrome de cachexie liée au VIH et la pneumocystose. Il existait des différences notables avec la métropole, mais aussi avec la Guyane. Ce taux élevé de syndrome de cachexie liée au VIH pose question. Derrière ce diagnostic, pourraient se cacher d’autres maladies opportunistes non diagnostiquées, mais également des différences de codage. Le recul de la mortalité avec le temps a entraîné une modification qualitative des causes de décès. Celles rapportées dans la littérature étaient les mêmes que celles observées dans notre étude. Contrairement à la métropole où le cancer représentait la première cause de mortalité, en Guadeloupe, les infections liées au Sida constituaient la première cause de décès.Ce travail de thèse s’est donc efforcé de dégager, pour l’une des régions de France les plus affectées par le VIH, quelques grands indicateurs à partir de la Base Hospitalière FHDH. Cette base ne comportait pas toujours toutes les informations souhaitées, mais le nombre substantiel d’observations donnait une puissance importante aux variables étudiées. Ces résultats, bien que confirmant souvent les connaissances empiriques des cliniciens, aura pu aider à mieux appréhender l’épidémie du VIH en Guadeloupe. / With an accumulated incidence rate of 56 cases per 100 000 inhabitants, Guadeloupe is the second French region most affected by HIV. Most of the publications on HIV/AIDS were essentially descriptive, stemming from annual reports. The Guadeloupean Hospital Database on HIV was scarcely exploited for research. The objective of this work was to estimate the fundamental aspects of HIV/AIDS in Guadeloupe. So late presentation for care, delay between HIV diagnosis and first specialised consultation, follow-up interruption, incidence of depression, opportunistic infections and deaths were studied as well as their predictive factors. We were able to highlight the following points: first, the very late HIV diagnosis (CD4< 200 / mm3) concerned 40, 12 % of HIV- infected adults followed in Guadeloupe. 36 % of patients had delays between HIV diagnosis and first specialised consultation. However, more than 22 % of patients were permanently lost to follow-up and never seen again. The first three classifying affections were oesophageal candidiasis, HIV-wasting syndrome and pneumocystosis. The causes of deaths reported in the literature were similar to those observed in our study. AIDS-related infections were the first cause of deaths.This thesis work thus tried to generate, in one of the most HIV-affected French regions, some indicators from the French Hospital Database on HIV. This database often did not contain all the desired informations, but the important number of observations allowed to have high power for the studied variables. These results, although often confirming the clinicians' empirical knowledge, may help understand some aspects of the HIV epidemic in Guadeloupe.

The worldwide population of patients with chronic kidney disease (CKD) is growing, with estimated prevalence at 12-15% of adults. Of particular concern are those with late stage CKD, defined as an estimated glomerular filtration rate (eGFR)of less than 30 ml/min/1.73m2, as they are susceptible to the highest risk of adverse outcomes such as progression to end stage kidney disease (ESKD), cardiovascular disease and all-cause mortality (1, 2). As such, late stage CKD patients are often managed in specialized clinics with set clinical targets, standardized education and multi-disciplinary care(3). A key clinical target for therapeutic intervention and prevention of the progression of CKD is blood pressure (BP) reduction(4). Yet, multiple relevant questions remain regarding the strength and nature of association of BP with clinical outcomes in late stage CKD. As the risks of hypotension-related complications are high in late stage CKD, it remains unclear whether strict BP control delays CKD progression in a real world clinic population(5). Furthermore, it is unclear how to appropriately specify the nature of the longitudinal association between BP and clinical outcomes of ESKD and mortality. The overall objective of this thesis is to examine the longitudinal association of BP and adverse clinical outcomes in a cohort of 1203 patients (mean eGFR 17.8 ml/min/1.73m2; mean of 6.7 BP measures per patient) with late stage CKD. In our first paper we examined the association of repeat measures of BP with CKD progression, defined as a decline in eGFR. When modeling eGFR using longitudinal linear regression, we found that its over-time trajectory was non-linear and that this trajectory was modified by BP; thus, we found a significant time-dependant association between BP and eGFR. When modeling time to eGFR decline ≥ 30% using Cox proportional hazards regression with categorized BP specified as a time-dependent exposure, BP was significantly associated with risk of eGFR decline; in particular, extremes of low and high systolic blood pressure (SBP) and high diastolic blood pressure (DBP) significantly increased the risk of eGFR decline. In our second paper, we examined different methods of modelling longitudinal BP and its association with time to mortality and ESKD. We found that elevations in SBP and DBP, in particular, when expressed as current (most recent visit), lag (previous visit), and cumulative exposure were significantly associated with increased risk of ESKD while low SBP (current, lag and cumulative exposure) was significantly associated with increased risk of mortality. Baseline BP measures were not statistically significantly associated with any outcomes. In patients with more moderate ranges of SBP (121-140) or DBP (60-85) at baseline, a subsequent rise to >160 or > 85 respectively, was associated with an increased risk of ESKD. Thus, longitudinal BP measures in late-stage CKD are significantly associated with adverse outcomes and convey important information beyond baseline BP measures.

Alzheimer's disease (AD), the most common form of dementia, is a chronic neurodegenerative disease. The HECT domain and ankyrin repeat containing E3 ubiquitin protein ligase 1 (HACE1) gene is expressed in human brain and may play a role in the pathogenesis of neurodegenerative disorders. Till now, no previous study has reported the association of the HACE1 gene with the risk and age at onset (AAO) of AD; while few studies have checked the proportional hazards assumption in the survival analysis of AAO of AD using Cox proportional hazards model. In this study, we examined the associations of 14 single nucleotide polymorphisms (SNPs) in the HACE1 gene with the risk and the AAO of AD using 791 AD patients and 782 controls. Multiple logistic regression model identified one SNP (rs9499937 with p = 1.8×10) to be associated with the risk of AD. For survival analysis of AAO, both classic Cox regression model and Bayesian survival analysis using the Cox proportional hazards model were applied to examine the association of each SNP with the AAO. The hazards ratio (HR) with its 95% confidence interval (CI) was estimated. Survival analysis using the classic Cox regression model showed that 4 SNPs were significantly associated with the AAO (top SNP rs9499937 with HR=1.33, 95%CI=1.13-1.57, p=5.0×10). Bayesian Cox regression model showed similar but a slightly stronger associations (top SNP rs9499937 with HR=1.34, 95%CI=1.11-1.55) compared with the classic Cox regression model. Using an independent family-based sample, one SNP rs9486018 was associated with the risk of AD (p=0.0323) and the T-T-G haplotype from rs9786015, rs9486018 and rs4079063 showed associations with both the risk and AAO of AD (p=2.27×10 and 0.0487, respectively). The findings of this study provide first evidence that several genetic variants in the HACE1 gene were associated with the risk and AAO of AD.

Indiana University-Purdue University Indianapolis (IUPUI) / Time-to-event outcomes are widely utilized in medical research. Assessing the cumulative effects of time-varying exposures on time-to-event outcomes poses challenges in statistical modeling. First, exposure status, intensity, or duration may vary over time. Second, exposure effects may be delayed over a latent period, a situation that is not considered in traditional survival models. Third, exposures that occur within a time window may cumulatively in uence an outcome. Fourth, such cumulative exposure effects may be non-linear over exposure latent period. Lastly, exposure-outcome dynamics may differ among groups defined by individuals' characteristics. These challenges have not been adequately addressed in current statistical models. The objective of this dissertation is to provide a novel approach to modeling group-specific dynamics between cumulative timevarying exposures and a time-to-event outcome. A framework of group-specific dynamic models is introduced utilizing functional time-dependent cumulative exposures within an etiologically relevant time window. Penalizedspline time-dependent Cox models are proposed to evaluate group-specific outcome-exposure dynamics through the associations of a time-to-event outcome with functional cumulative exposures and group-by-exposure interactions. Model parameter estimation is achieved by penalized partial likelihood. Hypothesis testing for comparison of group-specific exposure effects is performed by Wald type tests. These models are extended to group-specific non-linear exposure intensity-latency-outcome relationship and group-specific interaction effect from multiple exposures. Extensive simulation studies are conducted and demonstrate satisfactory model performances. The proposed methods are applied to the analyses of group-specific associations between antidepressant use and time to coronary artery disease in a depression-screening cohort using data extracted from electronic medical records.

L’intérêt principal de cette recherche porte sur la validation d’une méthode statistique en pharmaco-épidémiologie. Plus précisément, nous allons comparer les résultats d’une étude précédente réalisée avec un devis cas-témoins niché dans la cohorte utilisé pour tenir compte de l’exposition moyenne au traitement : – aux résultats obtenus dans un devis cohorte, en utilisant la variable exposition variant dans le temps, sans faire d’ajustement pour le temps passé depuis l’exposition ; – aux résultats obtenus en utilisant l’exposition cumulative pondérée par le passé récent ; – aux résultats obtenus selon la méthode bayésienne. Les covariables seront estimées par l’approche classique ainsi qu’en utilisant l’approche non paramétrique bayésienne. Pour la deuxième le moyennage bayésien des modèles sera utilisé pour modéliser l’incertitude face au choix des modèles. La technique utilisée dans l’approche bayésienne a été proposée en 1997 mais selon notre connaissance elle n’a pas été utilisée avec une variable dépendante du temps. Afin de modéliser l’effet cumulatif de l’exposition variant dans le temps, dans l’approche classique la fonction assignant les poids selon le passé récent sera estimée en utilisant des splines de régression. Afin de pouvoir comparer les résultats avec une étude précédemment réalisée, une cohorte de personnes ayant un diagnostique d’hypertension sera construite en utilisant les bases des données de la RAMQ et de Med-Echo. Le modèle de Cox incluant deux variables qui varient dans le temps sera utilisé. Les variables qui varient dans le temps considérées dans ce mémoire sont iv la variable dépendante (premier évènement cérébrovasculaire) et une des variables indépendantes, notamment l’exposition / The main interest of this research is the validation of a statistical method in pharmacoepidemiology. Specifically, we will compare the results of a previous study performed with a nested case-control which took into account the average exposure to treatment to : – results obtained in a cohort study, using the time-dependent exposure, with no adjustment for time since exposure ; – results obtained using the cumulative exposure weighted by the recent past ; – results obtained using the Bayesian model averaging. Covariates are estimated by the classical approach and by using a nonparametric Bayesian approach. In the later, the Bayesian model averaging will be used to model the uncertainty in the choice of models. To model the cumulative effect of exposure which varies over time, in the classical approach the function assigning weights according to recency will be estimated using regression splines. In order to compare the results with previous studies, a cohort of people diagnosed with hypertension will be constructed using the databases of the RAMQ and Med-Echo. The Cox model including two variables which vary in time will be used. The time-dependent variables considered in this paper are the dependent variable (first stroke event) and one of the independent variables, namely the exposure.

Este trabalho visa apresentar métodos de categorização de variáveis explicativas contínuas em Análise de Sobrevivência. Do ponto de vista clínico, agrupar pacientes em grupos de risco distintos é importante para agilizar tomadas de decisões; entretanto, perda de informação e outros problemas estatísticos podem ocorrer. Portanto, métodos para seleção de pontos de corte e correção dos possíveis problemas gerados pela categorização são criticamente avaliados. Para a aplicação e comparação dos métodos são utilizados dados do Instituto do Coração do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (InCor - FMUSP), em que a variável fração de ejeção é dicotomizada e tricotomizada. / This dissertation aims to present methods of categorization for continuous variables in Survival Analysis. From a clinical point of view, grouping patients into distinct risk groups is important for accelerating decision-making; however, loss of information and other statistical problems may occur. Therefore, methods for selecting cutpoints and correcting problems generated by categorization are critically evaluated. For the application and comparison of the methods, the dataset from Heart Institute - University of Sao Paulo Medical School (InCor FMUSP) is used, in which the variable ejection fraction is dichotomized and trichotomized.