Indiana University-Purdue University Indianapolis (IUPUI) / Observational studies and clinical trials with time-to-event data frequently involve multiple event types, known as competing risks. The cumulative incidence function (CIF) is a particularly useful parameter as it explicitly quantifies clinical prognosis. Common issues in competing risks data analysis on the CIF include interval censoring, missing event types, and left truncation. Interval censoring occurs when the event time is not observed but is only known to lie between two observation times, such as clinic visits. Left truncation, also known as delayed entry, is the phenomenon where certain participants enter the study after the onset of disease under study. These individuals with an event prior to their potential study entry time are not included in the analysis and this can induce selection bias. In order to address unmet needs in appropriate methods and software for competing risks data analysis, this thesis focuses the following development of application and methods. First, we develop a convenient and exible tool, the R package intccr, that performs semiparametric regression analysis on the CIF for interval-censored competing risks data. Second, we adopt the augmented inverse probability weighting method to deal with both interval censoring and missing event types. We show that the resulting estimates are consistent and double robust. We illustrate this method using data from the East-African International Epidemiology Databases to Evaluate AIDS (IeDEA EA) where a significant portion of the event types is missing. Last, we develop an estimation method for semiparametric analysis on the CIF for competing risks data subject to both interval censoring and left truncation. This method is applied to the Indianapolis-Ibadan Dementia Project to identify prognostic factors of dementia in elder adults. Overall, the methods developed here are incorporated in the R package intccr. / 2021-05-06

Modelos de fração de cura compõem uma vasta subárea da análise de sobrevivência, apresentando grande aplicabilidade em estudos médicos. O uso deste tipo de modelo é adequado em situações tais que o pesquisador reconhece a existência de uma parcela da população não suscetível ao evento de interesse, consequentemente considerando a probabilidade de que o evento não ocorra. Embora a teoria encontre-se consolidada tratando-se de censuras à direita, a literatura de modelos de fração de cura carece de estudos que contemplem a estrutura de censura intervalar, incentivando os estudos apresentados neste trabalho. Três modelos semiparamétricos de fração de cura para este tipo de censura são aqui considerados para aplicações em conjuntos de dados reais e estudados por meio de simulações. O primeiro modelo, apresentado por Liu e Shen (2009), trata-se de um modelo de tempo de promoção com estimação baseada em uma variação do algoritmo EM e faz uso de técnicas de otimização convexa em seu processo de maximização. O modelo proposto por Lam et al. (2013) considera um modelo semiparamétrico de Cox, modelando a fração de cura da população através de um efeito aleatório com distribuição Poisson composta, utilizando métodos de aumento de dados em conjunto com estimadores de máxima verossimilhança. Em Xiang et al. (2011), um modelo de mistura padrão é proposto adotando um modelo logístico para explicar a incidência e fazendo uso da estrutura de riscos proporcionais para os efeitos sobre o tempo. Os dois últimos modelos mencionados possuem extensões para dados agrupados, utilizadas nas aplicações deste trabalho. Uma das principais motivações desta dissertação consiste em um estudo conduzido por pesquisadores da Fundação Pró-Sangue, em São Paulo - SP, cujo interesse reside em avaliar o tempo até a ocorrência de anemia em doadores de repetição por meio de avaliações periódicas do hematócrito, medido em cada visita ao hemocentro. A existência de uma parcela de doadores não suscetíveis à doença torna conveniente o uso dos modelos estudados. O segundo conjunto de dados analisado trata-se de um conjunto de observações periódicas de cervos de cauda branca equipados com rádiocolares. Tem-se como objetivo a avaliação do comportamento migratório dos animais no inverno para determinadas condições climáticas e geográficas, contemplando a possibilidade de os cervos não migrarem. Um estudo comparativo entre os modelos propostos é realizado por meio de simulações, a fim de avaliar a robustez ao assumir-se determinadas especificações de cenário e fração de cura. Até onde sabemos, nenhum trabalho comparando os diferentes mecanismos de cura na presença de censura intervalar foi realizado até o presente momento. / Cure rate models define an vast sub-area of the survival analysis, presenting great applicability in medical studies. The use of this type of model is suitable in situations such that the researcher recognizes the existence of an non-susceptible part of the population to the event of interest, considering then the probability that such a event does not occur. Although the theory finds itself consolidated when considering right censoring, the literature of cure rate models lacks of interval censoring studies, encouraging then the studies presented in this work. Three semiparametric cure rate models for this type of censoring are considered here for real data analysis and then studied by means of simulations. The first model, presented by Liu e Shen (2009), refers to a promotion time model with its estimation based on an EM algorithm variation and using convex optimization techniques for the maximization process. The model proposed by Lam et al. (2013) considers a Cox semiparametric model, modelling then the population cure fraction by an frailty distributed as an compound Poisson, used jointly with data augmentation methods and maximum likelihood estimators. In Xiang et al. (2011), an standard mixture cure rate model is proposed adopting an logistic model for explaining incidence and using proportional hazards structure for the effects over the time to event. The two last mentioned models have extensions for clustered data analysis and are used on the examples of applications of this work. One of the main motivations of this dissertation consists on a study conducted by researches of Fundação Pró-Sangue, in São Paulo - SP, whose interest resides on evaluating the time until anaemia, occurring to recurrent donors, detected through periodic evaluations of the hematocrit, measured on each visit to the blood center. The existence of a non-susceptible portion of donors turns the use of the cure rate models convenient. The second analysed dataset consists on an set of periodic observations of radio collar equipped white tail deers. The goal here is the evaluation of when these animals migrate in the winter for specic weather and geographic conditions, contemplating the possibility that deer could not migrate. A comparative study among the proposed models is realized using simulations, in order to assess the robustness when assuming determined specifications about scenario and cure fraction. As far as we know, no work has been done comparing different cure mechanisms in the presence of interval censoring data until the present moment.

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV.

Interval censoring arises frequently in life history data, as individuals are often only observed at a sequence of assessment times. This leads to a situation where we do not know when an event of interest occurs, only that it occurred somewhere between two assessment times. Here, the focus will be on methods of estimation for recurrent event data, current status data, and multistate data, subject to interval censoring. With recurrent event data, the focus is often on estimating the rate and mean functions. Nonparametric estimates are readily available, but are not smooth. Methods based on local likelihood and the assumption of a Poisson process are developed to obtain smooth estimates of the rate and mean functions without specifying a parametric form. Covariates and extra-Poisson variation are accommodated by using a pseudo-profile local likelihood. The methods are assessed by simulations and applied to a number of datasets, including data from a psoriatic arthritis clinic. Current status data is an extreme form of interval censoring that occurs when each individual is observed at only one assessment time. If current status data arise in clusters, this must be taken into account in order to obtain valid conclusions. Copulas offer a convenient framework for modelling the association separately from the margins. Estimating equations are developed for estimating marginal parameters as well as association parameters. Efficiency and robustness to the choice of copula are examined for first and second order estimating equations. The methods are applied to data from an orthopedic surgery study as well as data on joint damage in psoriatic arthritis. Multistate models can be used to characterize the progression of a disease as individuals move through different states. Considerable attention is given to a three-state model to characterize the development of a back condition known as spondylitis in psoriatic arthritis, along with the associated risk of mortality. Robust estimates of the state occupancy probabilities are derived based on a difference in distribution functions of the entry times. A five-state model which differentiates between left-side and right-side spondylitis is also considered, which allows us to characterize what effect spondylitis on one side of the body has on the development of spondylitis on the other side. Covariate effects are considered through multiplicative time homogeneous Markov models. The robust state occupancy probabilities are also applied to data on CMV infection in patients with HIV.

Modelos de fração de cura compõem uma vasta subárea da análise de sobrevivência, apresentando grande aplicabilidade em estudos médicos. O uso deste tipo de modelo é adequado em situações tais que o pesquisador reconhece a existência de uma parcela da população não suscetível ao evento de interesse, consequentemente considerando a probabilidade de que o evento não ocorra. Embora a teoria encontre-se consolidada tratando-se de censuras à direita, a literatura de modelos de fração de cura carece de estudos que contemplem a estrutura de censura intervalar, incentivando os estudos apresentados neste trabalho. Três modelos semiparamétricos de fração de cura para este tipo de censura são aqui considerados para aplicações em conjuntos de dados reais e estudados por meio de simulações. O primeiro modelo, apresentado por Liu e Shen (2009), trata-se de um modelo de tempo de promoção com estimação baseada em uma variação do algoritmo EM e faz uso de técnicas de otimização convexa em seu processo de maximização. O modelo proposto por Lam et al. (2013) considera um modelo semiparamétrico de Cox, modelando a fração de cura da população através de um efeito aleatório com distribuição Poisson composta, utilizando métodos de aumento de dados em conjunto com estimadores de máxima verossimilhança. Em Xiang et al. (2011), um modelo de mistura padrão é proposto adotando um modelo logístico para explicar a incidência e fazendo uso da estrutura de riscos proporcionais para os efeitos sobre o tempo. Os dois últimos modelos mencionados possuem extensões para dados agrupados, utilizadas nas aplicações deste trabalho. Uma das principais motivações desta dissertação consiste em um estudo conduzido por pesquisadores da Fundação Pró-Sangue, em São Paulo - SP, cujo interesse reside em avaliar o tempo até a ocorrência de anemia em doadores de repetição por meio de avaliações periódicas do hematócrito, medido em cada visita ao hemocentro. A existência de uma parcela de doadores não suscetíveis à doença torna conveniente o uso dos modelos estudados. O segundo conjunto de dados analisado trata-se de um conjunto de observações periódicas de cervos de cauda branca equipados com rádiocolares. Tem-se como objetivo a avaliação do comportamento migratório dos animais no inverno para determinadas condições climáticas e geográficas, contemplando a possibilidade de os cervos não migrarem. Um estudo comparativo entre os modelos propostos é realizado por meio de simulações, a fim de avaliar a robustez ao assumir-se determinadas especificações de cenário e fração de cura. Até onde sabemos, nenhum trabalho comparando os diferentes mecanismos de cura na presença de censura intervalar foi realizado até o presente momento. / Cure rate models define an vast sub-area of the survival analysis, presenting great applicability in medical studies. The use of this type of model is suitable in situations such that the researcher recognizes the existence of an non-susceptible part of the population to the event of interest, considering then the probability that such a event does not occur. Although the theory finds itself consolidated when considering right censoring, the literature of cure rate models lacks of interval censoring studies, encouraging then the studies presented in this work. Three semiparametric cure rate models for this type of censoring are considered here for real data analysis and then studied by means of simulations. The first model, presented by Liu e Shen (2009), refers to a promotion time model with its estimation based on an EM algorithm variation and using convex optimization techniques for the maximization process. The model proposed by Lam et al. (2013) considers a Cox semiparametric model, modelling then the population cure fraction by an frailty distributed as an compound Poisson, used jointly with data augmentation methods and maximum likelihood estimators. In Xiang et al. (2011), an standard mixture cure rate model is proposed adopting an logistic model for explaining incidence and using proportional hazards structure for the effects over the time to event. The two last mentioned models have extensions for clustered data analysis and are used on the examples of applications of this work. One of the main motivations of this dissertation consists on a study conducted by researches of Fundação Pró-Sangue, in São Paulo - SP, whose interest resides on evaluating the time until anaemia, occurring to recurrent donors, detected through periodic evaluations of the hematocrit, measured on each visit to the blood center. The existence of a non-susceptible portion of donors turns the use of the cure rate models convenient. The second analysed dataset consists on an set of periodic observations of radio collar equipped white tail deers. The goal here is the evaluation of when these animals migrate in the winter for specic weather and geographic conditions, contemplating the possibility that deer could not migrate. A comparative study among the proposed models is realized using simulations, in order to assess the robustness when assuming determined specifications about scenario and cure fraction. As far as we know, no work has been done comparing different cure mechanisms in the presence of interval censoring data until the present moment.

Les indicateurs épidémiologiques de la démence tels que l'espérance de vie sans démence pour un âge donné ou le risque absolu sont des quantités utiles en santé publique. L'observation de la démence en temps discret entraine une censure par intervalle du temps d'apparition de la pathologie. De plus, certains individus peuvent développer une démence et décéder entre deux visites de suivi. Un modèle illness-death pour données censurées par intervalle est une solution pour modéliser simultanément les risques de démence et de décès et pour éviter la sous-estimation de l'incidence de la démence.Ces indicateurs dépendent à la fois du risque de démence mais aussi du risque de décès, contrairement à l'intensité de transition de la démence. Les modèles de régression disponibles ne prennent pas en compte la censure par intervalle ou ne sont pas adaptés à ces indicateurs. L'objectif de ce travail est de quantifier l'effet de facteurs de risque sur ces indicateurs épidémiologiques par des modèles de régression. La première partie de cette thèse est consacrée à l'extension de l'approche par pseudo-valeurs aux données censurées par intervalle. Les pseudo-valeurs sont calculées à partir d'estimateurs paramétriques ou d'estimateurs du maximum de vraisemblance pénalisée. Elles sont utilisées comme variable d'intérêt dans des modèles linéaires généralisés ou des modèles additifs généralisés pour permettre un effet non-linéaire des variables explicatives quantitatives. La seconde partie de cette thèse porte sur le développement d'un modèle par linéarisation des indicateurs épidémiologiques. L'idée est de calculer l'indicateur conditionnellement aux variables explicatives à partir des intensités de transition d'un modèle illness-death avec censure par intervalle du temps d'apparition de la maladie. Ces deux approches sont appliquées aux données de la cohorte française PAQUID pour étudier par exemple l'effet d'un score psychométrique (le MMS) sur des indicateurs épidémiologiques de la démence. / Dementia epidemiological indicators as the life expectancy without dementia at a specific age or the absolute risk are quantities meaningful for public health. Dementia is observed on discrete-time in cohort studies which leads to interval censoring of the time-to-onset. Moreover, some subjects can develop dementia and die between two follow-up visits. Illness-death model for interval-censored data is a solution to model simultaneously dementia risk and death risk and to avoid under-estimation of dementia incidence. These indicators depend on both dementia and death risks as opposed to dementia transition intensity. Available regression models do not take into account interval censoring or are not suitable for these indicators. The aim of this work is to propose regression models to quantify impact of risk factors on these indicators. Firstly, the pseudo-values approach is extended to interval-censored data. Pseudo-values are computed by parametric estimators or by maximum penalized likelihood estimators. Then pseudo-values are used as outcome in a generalized linear models or in a generalized additive models in case of non-linear effect of quantitative covariates. Secondly, the effect of covariates are summarized by linearization of the maximum likelihood estimator. In this part, the idea is to compute indicators conditionally on the covariates values from transition intensities of an illness-death model. These two approaches are applied to the French cohort PAQUID to study effect of a psychometric test (the MMS) on these indicators for example.

Title: Moments Estimation under Type I Interval Censoring Author: Matej Ďurčík Department: Faculty of Probability and Mathematical Statistics Supervisor: RNDr. Arnošt Komárek Ph.D. Abstract: In this thesis we apply the uniform deconvolution model to the interval censoring problem. We restrict ourselves only on interval censoring case 1. We show how to apply uniform deconvolution model in estimating the probability distribution characteristics in the interval censoring case 1. Moreover we derive limit distributions of the estimators of mean and variance. Then we compare these estimators to the asymptotically efficient estimators based on the nonparametric maximum likelihood estimation by simulation studies under some certain distributions of the random variables. 1

Incomplete data often arise in the study of life history processes. Examples include missing responses, missing covariates, and unobservable latent processes in addition to right censoring. This thesis is on the development of statistical models and methods to address these problems as they arise in oncology and chronic disease. Methods of estimation and inference in parametric, weakly parametric and semiparametric settings are investigated. Studies of chronic diseases routinely sample individuals subject to conditions on an event time of interest. In epidemiology, for example, prevalent cohort studies aiming to evaluate risk factors for survival following onset of dementia require subjects to have survived to the point of screening. In clinical trials designed to assess the effect of experimental cancer treatments on survival, patients are required to survive from the time of cancer diagnosis to recruitment. Such conditions yield samples featuring left-truncated event time distributions. Incomplete covariate data often arise in such settings, but standard methods do not deal with the fact that the covariate distribution is also affected by left truncation. We develop a likelihood and algorithm for estimation for dealing with incomplete covariate data in such settings. An expectation-maximization algorithm deals with the left truncation by using the covariate distribution conditional on the selection criterion. An extension to deal with sub-group analyses in clinical trials is described for the case in which the stratification variable is incompletely observed. In studies of affective disorder, individuals are often observed to experience recurrent symptomatic exacerbations of symptoms warranting hospitalization. Interest lies in modeling the occurrence of such exacerbations over time and identifying associated risk factors to better understand the disease process. In some patients, recurrent exacerbations are temporally clustered following disease onset, but cease to occur after a period of time. We develop a dynamic mover-stayer model in which a canonical binary variable associated with each event indicates whether the underlying disease has resolved. An individual whose disease process has not resolved will experience events following a standard point process model governed by a latent intensity. If and when the disease process resolves, the complete data intensity becomes zero and no further events will arise. An expectation-maximization algorithm is developed for parametric and semiparametric model fitting based on a discrete time dynamic mover-stayer model and a latent intensity-based model of the underlying point process. The method is applied to a motivating dataset from a cohort of individuals with affective disorder experiencing recurrent hospitalization for their mental health disorder. Interval-censored recurrent event data arise when the event of interest is not readily observed but the cumulative event count can be recorded at periodic assessment times. Extensions on model fitting techniques for the dynamic mover-stayer model are discussed and incorporate interval censoring. The likelihood and algorithm for estimation are developed for piecewise constant baseline rate functions and are shown to yield estimators with small empirical bias in simulation studies. Data on the cumulative number of damaged joints in patients with psoriatic arthritis are analysed to provide an illustrative application.

In the presented thesis the aim is to apply methods of survival analysis to the data from the Labour Force Survey, which are interval-censored. With regard to this type of data, I use specific methods designed to handle them, especially Turnbull estimate, weighted log-rank test and the AFT model. Other objective of the work is the design and application of a methodology for creating a model of unemployment duration, depending on the available factors and its interpretation. Other aim is to evaluate evolution of the probability distribution of unemployment duration and last but not least aim is to create more accurate estimate of the tail using extreme value theory. The main benefits of the thesis can include the creation of a methodology for examining the data from the Labour Force Survey based on standard techniques of survival analysis. Since the data are internationally comparable, the methodology is applicable at the level of European Union countries and several others. Another benefit of this work is estimation of the parameters of the generalized Pareto distribution on interval-censored data and creation and comparison of the models of piecewise connected distribution functions with solution of the connection problem. Work brought empirical results, most important of which is the comparison of results from three different data approaches and specific relationship between selected factors and time to find a job or spell of unemployment.

Le traitement de la leucémie myéloïde chronique (LMC) par imatinib est un succès de thérapie ciblée en oncologie. Le principe de cette thérapie est de bloquer les processus biochimiques à l'origine du développement de la maladie, et de permettre à une majorité de patients de réduire leurs risques de progression mais aussi d'éviter des traitements lourds et risqués comme la greffe de cellules souches hématopoïétiques.Cependant, même si l'efficacité de l'imatinib à été prouvée dans un contexte clinique, il n'en demeure pas moins qu'une proportion non négligeable de patients n'obtient par de niveaux de réponse moléculaire jugés optimale. Le but de cette thèse est de tester l'hypothèse d'un lien entre des polymorphismes de gènes impliqués dans l'absorption des médicaments et de leurs métabolisme, et la réponse moléculaire dans la leucémie myéloïde chronique en phase chronique traitée par imatinib.Dans le but d'évaluer la réponse moléculaire des patients, des prélèvements sanguins sont réalisés tout les 3 mois afin de pratiquer le dosage d'un biomarqueur. Ce type particulier de suivi produit des données censurées par intervalles. Comme par ailleurs, les patients demeurent à risque de progression ou sont susceptible d'interrompre leurs traitements pour cause d'intolérance, il est possible que la réponse d'intérêt ne soit plus observable sous le traitement étudié. Les données ainsi produites sont censurées par intervalles dans un contexte de compétition (risques compétitifs).Afin de tenir compte de la nature particulière des données collectées, une méthode basée sur l'imputation multiple est proposée. L'idée est de transformer les données censurées par intervalles en de multiples jeux de données potentiellement censurées à droite et d'utiliser les méthodes disponibles pour l'analyser de ces données. Finalement les résultats sont assemblés en suivant les règles de l'imputation multiple. / Imatinib in the treatment of chronic myeloid leukemia is a success of targeted therapy in oncology. The aim of this therapy is to block the biochemical processes leading to disease development. This strategy results in a reduction of the risk of disease progression and allows patients to avoid extensive and hazardous treatments such as hematologic stem cell transplantation.However, even if imatinib efficacy has been demonstrated in a clinical setting, a significant part of patients do not achieve suitable levels of molecular response. The objective of this thesis, is to test the hypothesis of a correlation between polymorphisms of genes implied in drug absorption an metabolism and the molecular response in chronic myeloid leukemia in chronic phase treated by imatinib.In order to evaluate patients molecular response, blood biomarker assessments are performed every 3 months. This type of follow up produces interval censored data. As patients remain at risk of disease progression, or may interrupt their treatments due to poor tolerance, the response of interest may not be observable in a given setting. This situation produces interval censored competing risks data.To properly handle such data, we propose a multiple imputation based method.The main idea is to convert interval censored data into multiple sets of potentially right censored data that are then analysed using multiple imputation rules.