Estimating parameters in a mixture of normal distributions dates back to the 19th century when Pearson originally considered data of crabs from the Bay of Naples. Since then, many real world applications of mixtures have led to various proposed methods for studying similar problems. Among them, maximum likelihood estimation (MLE) and the continuous empirical characteristic function (CECF) methods have drawn the most attention. However, the performance of these competing estimation methods has not been thoroughly studied in the literature and conclusions have not been consistent in published research. In this article, we review this classical problem with a focus on estimation bias. An extensive simulation study is conducted to compare the estimation bias between the MLE and CECF methods over a wide range of disparity values. We use the overlapping coefficient (OVL) to measure the amount of disparity, and provide a practical guideline for estimation quality in mixtures of normal distributions. Application to an ongoing multi-site Huntington disease study is illustrated for ascertaining cognitive biomarkers of disease progression. We also study joint modeling of longitudinal and time-to-event data and discuss pattern-mixture and selection models, but focus on shared parameter models, which utilize unobserved random effects in order to "join" a marginal longitudinal data model and marginal survival model in order to assess an internal time-dependent covariate's effect on time-to-event. The marginal models used in the analysis are the Cox Proportional Hazards model and the Linear Mixed model, and both of these models are covered in some detail before defining joints models and describing the estimation process. Joint modeling provides a modeling framework which accounts for correlation between the longitudinal data and the time-to-event data, while also accounting for measurement error in the longitudinal process, which previous methods failed to do. Since it has been shown that bias is incurred, and this bias is proportional to the amount of measurement error, utilizing a joint modeling approach is preferred. Our setting is also complicated by monotone degeneration of the internal covariate considered, and so a joint model which utilizes monotone B-Splines to recover the longitudinal trajectory and a Cox Proportional Hazards (CPH) model for the time-to-event data is proposed. The monotonicity constraints are satisfied via the Projected Newton Raphson Algorithm as described by Cheng et al., 2012, with the baseline hazard profiled out of the $Q$ function in each M-step of the Expectation Maximization (EM) algorithm used for optimizing the observed likelihood. This method is applied to assess Total Motor Score's (TMS) ability to predict Huntington Disease motor diagnosis in the Biological Predictors of Huntington's Disease study (PREDICT-HD) data.

Previous studies suggest that Medicaid-enrolled children have difficulties accessing dental care, which can lead to untreated dental disease, poor oral health, and compromised overall health status. While Medicaid-enrolled children with a chronic condition (CC) encounter additional barriers to dental care, most relevant studies on dental utilization fail to adopt risk adjustment methods. As such, the impact of CC status and CC severity on access to dental care for Medicaid-enrolled children is poorly understood. The main objectives of this dissertation were to: 1) compare dental utilization for Medicaid-enrolled children with and without a CC; 2) assess the relationship between CC severity and dental utilization; and 3) identify the other factors associated with dental utilization. The 3M Clinical Risk Grouping (CRG) Methods were applied to enrollee-level data from the Iowa Medicaid Program (2003-2008) to identify children with and without a CC and to classify children with a CC into a CC severity level. Three outcome measures were developed: 1) access to an annual dental visit; 2) use of dental services under general anesthesia (GA); and 3) time to the first dental visit after initial enrollment into the Medicaid program. We used multiple variable logistic regression models and survival analytic techniques to test our study hypotheses. Compared to Medicaid-enrolled children without a CC, those with a CC were more likely to have had an annual dental visit and earlier first dental visits. Having a CC was an important determinant of dental utilization under GA for older but not for younger Medicaid-enrolled children. In terms of CC severity, Medicaid-enrolled children with more severe CCs were less likely to have had an annual dental visit and more likely to have utilized dental services under GA. CC severity was not associated with the rate at which the first dental visit took place. Not residing in a dental Health Professional Shortage Area, previous use of dental care, and previous utilization of primary medical care were all positively associated with dental utilization. Identifying and understanding the determinants of access to dental care is an important first step in developing clinical interventions and policies aimed at improving access to dental care for all Medicaid-enrolled children. Future work should focus on identifying the socio-behavioral determinants of as well as the clinical outcomes associated with access to dental services for vulnerable children.

The disposition of cells whose mechanism of death is related to the age of the cell cannot be appropriately represented by pharmacodynamic (PD) models where the elimination rate is related to the number of cells. In cells with age-related death their disposition is determined by their lifespan. Thus in these cells PD models of cellular response must incorporate a lifespan component. Previous cellular lifespan PD models assumed that the lifespan of cells is predetermined and does not vary over time. However, in many instances these assumptions are inappropriate and thus extensions to the existing models are needed. An important application of these time variant PD models is determining the erythropoiesis rate, since the lifespan of reticulocytes and mature erythrocytes are known to change over time under specific conditions. The objectives us this work were to develop a general time variant lifespan-based PD model of cellular response and to use the model to determine the dynamic changes over time in both the erythrocyte lifespan and erythropoiesis rate under a variety of complex conditions. An initial time variant cellular lifespan model was formulated assuming no variability in lifespans and used to determine the dynamic changes in both the reticulocyte lifespan and erythropoiesis rate in sheep. Subsequently, the time variant model was extended to account for a distribution of cellular lifespans, which resulted in better capturing the physiology of sheep erythrocyte maturation. The model was then further extended to account for the effect of changes in the environment on cell lifespans and used to determine the effect of chemotherapy administration on sheep erythrocytes. In order to conduct studies on erythropoiesis in premature very low birth weight (VLBW) infants the ability to accurately measure erythrocytes and hemoglobin from clinically collected excess blood was validated. Then an in depth analysis of the relationship between erythropoietin, erythrocytes, and hemoglobin was conducted in a clinical study of premature VLBW infants that accounted for the dynamic hematological conditions experienced by these subjects. This analysis indicated that a nearly 4-fold increase in erythropoiesis could be achieved with only a modest increase in plasma erythropoietin concentrations.

L'objectif de cette thèse est d'explorer plusieurs approches pour l'étude des données censurées multivariées, à savoir l'estimation non paramétrique de la fonction de répartition jointe, la modélisation de dépendance par les modèles de copules et l'étude exploratoire par des méthodes de clustering. Le Chapitre 1 introduit le contexte général de cette thèse ainsi que ses contributions. Le Chapitre 2 est consacré à l'estimation de la distribution jointe des deux variables censurées dans le cadre d'un modèle de durée simplifié où la différence entre deux variables de censure est observée. Un nouvel estimateur non paramétrique de la fonction de répartition jointe y est introduit. La normalité asymptotique a été démontrée, pour les intégrales par rapport à la mesure définie par cet estimateur. Le Chapitre 3 est dédié à la problématique de l'estimation non paramétrique de la copule bivariée, à partir d'un échantillon de données censurées. La copule est d'abord estimée par une fonction discrète qui peut être interprétée comme une extension de la copule empirique en présence de censure, puis par ses versions lisses. Les propriétés asymptotiques et des applications de des estimateurs ont été considérées. Le Chapitre 4 présente une approche exploratoire pour l'étude de données censurées. Plus précisément, une configuration multivariée est considérée où une variable est une durée sujette à la censure, et toutes les autres variables sont observées. Sous ces conditions, une nouvelle méthode de quantification de la loi jointe est introduite. La méthode est étudiée théoriquement et appliquée à la construction d'un algorithme de clustering pour des observations censurées. / The main purpose of this thesis is to explore several approaches for studying multivariate censored data: nonparametric estimation of the joint distribution function, modeling dependence with copulas and k-clustering for the exploratory analysis. Chapter 1 presents the general framework and the contributions of this thesis. Chapter 2 deals with the estimation of the joint distribution function of two censored variables in a simplified survival model in which the difference between two censoring variables is observed. We provide a new nonparametric estimator of the joint distribution function and we establish the asymptotic normality of the integrals with respect to its associated measure. Chapter 3 is devoted to nonparametric copula estimation under bivariate censoring. We provide a discrete and two smooth copula estimators along with two estimators of its density. The discrete estimator can be seen as an extension of the empirical copula under censoring. Chapter 4 provides a new exploratory approach for censored data analysis. We consider a multivariate configuration with one variable subjected to censoring and the others completely observed. We extend the probabilistic k-quantization method in the case of random vector with one censored component. The definitions of the empirical distortion and of empirically optimal quantizer are generalized in presence of one-dimensional censoring. We study the asymptotic properties of the distortion of the empirically optimal quantizer and we provide a non-asymptotic exponential bound for the rate of convergence. Our results are then applied to construct a new two-step clustering algorithm for censored data.

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第22005号 / 医博第4519号 / 新制||医||1038(附属図書館) / 京都大学大学院医学研究科医学専攻 / (主査)教授 平井 豊博, 教授 松原 和夫, 教授 萩原 正敏 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM

This study examines the pattern of unemployment duration of African immigrants in Sweden as well as the effect of emigration origin, age, gender, level of education and family characteristics on the probability of getting a job upon arrival. The study is based on PLACE-database; the dataset is restricted to individuals born in Africa who immigrated to Sweden during the period of 1994-2008. Results from the Kaplan–Meier estimators and Proportional Hazard Models indicate that unemployment duration and the relative risk of getting a job upon arrival vary according to emigration origin and gender differences. In fact, immigrants from Somalia experience longer unemployment duration than Sub Saharan and North African immigrants. Additionally, African women are more likely to experience longer unemployment duration in comparison to men. Women from Sub Saharan Africa experience shorter unemployment duration in comparison to Somalis and North African ones. On the contrary, there are North African men who experience shorter unemployment duration than men from Sub- Saharan African and Somalia. The results also indicate that the relative risk of leaving unemployment upon arrival also differ by gender and region of emigration. In fact, men experience higher relative risk of leaving unemployment in comparison to women. In addition, the gender gap is found to be much more remarkable among the North African immigrants in comparison to Somalis and Sub Saharan ones. Furthermore, the possibility of leaving unemployment upon arrival decreases with age and childbearing, moreover holding university education increases the relative risk of leaving unemployment upon arrival.

This thesis first introduces the basic notions of univariate survival analysis. Then the survival analysis setting is extended to competing risk models, i.e. the cases considering several events of interest or several causes of one event. In the competing risk model, we discuss the problem of identification, which means that it is not possible to identify marginal distributions from observed competing risk data. Next, we present copula models, which are a suitable mathematical tool for modelling dependence structure between random variables. We explain their basic characteristics, present some useful copula families and the relationship of copula parameters with certain dependence (correlation) measures. Further, we show the utilization of copulas within competing risks models and how they can be helpful in the solution of identifiability problem. Finally, we apply the listed theoretical knowledge in a simulated example. Powered by TCPDF (www.tcpdf.org)

The thesis presents fundamental characteristics of survival analysis in the case of competing risks and their relationships. In the case without regression, basic nonparametric estimates and a logarithmic likelihood function for parameter estimates is given. The main focus is on Cox's proportional hazards model (PH), a model with accelerated time (AFT) and a flexible regression model (FG) are also mentioned. The identifiability of the associated survival function is solved using copulas. Basics of copula theory and the measurement of dependence by correlation coefficients (Pearson, Spearman and Kendal) are described in a separate chapter. A substantial part of the theory is practically used in a generated case without regression.

Venture capitalists enter into an investment with the intent of realising a substantial profit on theventure after a number of years; this realisation is usually labelled the exit. The disinvestment decisionis a critical issue in the venture capital industry, as the return of the investment is realised upon exit.There are two important dimensions to the disinvestment decision; how and when to exit.This thesis studies the role of Venture Capital (VC) syndication, and its’ effect on exit dynamics for VCfirms in Sweden. The aspects of syndication will be focused on firm characteristics of investing parties,were the ambition is to provide an analysis of these characteristics and their effect on exit route(Merger and Acquisitions, M&As, and Initial Public Offerings, IPOs) and exit timing. Our statisticalanalysis rely on survival analysis with Competing Risk Models (CRM), which is adequate to model timein one state, when exit is to a number of competing states. These models allow for a joint analysis ofexit type and exit timing, i.e. model durations that end with multiple exits. Specifically, we apply theWeibull distribution with Gamma Frailty.To conduct the study, we have used a self-collected data set of 300 investments derived from 20 VCfirms in Sweden. For each investment, the data includes information relating to a number ofexplanatory variables concerning selected characteristics of the portfolio company and investingparties. Our results reveal that the presence of one or more experienced VC firms in the syndicatewould prolong time to exit and increase the likelihood of exiting through an IPO. We provided evidencethat a larger syndicate size will increase the time to exit and increase the likelihood for exiting throughan IPO. We also provided empirical evidence that foreign investor involvement in a syndicate prolongstime to exit in comparison to investments with only domestic co-investors and should affect exit routeby increasing the probability of an IPO. Finally, we could infer that a match between location of at leastone VC firm in a syndicate and acquirer country will have an increasing effect on time-to-exit, whileincreasing the probability of an exit in that country.We hope that the findings of this thesis will provide scholars and venture capitalists with novel,valuable information on a syndicates’ effect on exit dynamics.

This empirical register study intends to estimate average causal effects of relapse treatment on the risk for acute myocardial infarction (AMI) among patients with Diffuse B-Cell Lymphoma (DLBCL) within the potential outcome framework. The report includes a brief introduction to causal inference and survival anal- ysis and mentions specific causal parameters of interest that will be estimated. A cohort of 2887 Swedish DLBCL patients between 2007 and 2014 were included in the study where 560 patients suffered a relapse. The relapse treatment is hypothesised to be cardiotoxic and induces an increased risk of heart diseases. The identifiability assumptions need to hold to estimate average causal effects and are assessed in this report. The patient cohort is weighted using inverse probability of treatment and censoring weights and potential marginal survival curves are estimated from marginal structural Cox models. The resulting point estimate indicates a protective causal effect of relapse treatment on AMI but estimated bootstrap confidence intervals suggest no significant effect on the 5% significance level.