Indiana University-Purdue University Indianapolis (IUPUI) / Joint models for longitudinal and time-to-event data has been introduced to study the association between repeatedly measured exposures and the risk of an event. The use of joint models allows a survival outcome to depend on some characteristic functions from the longitudinal measures. Current estimation methods include a two-stage approach, Bayesian and maximum likelihood estimation (MLEs) methods. The twostage method is computationally straightforward but often yields biased estimates. Bayesian and MLE methods rely on the joint likelihood of longitudinal and survival outcomes and can be computationally intensive. In this work, we propose a joint generalized estimating equation framework using an inverse intensity weighting approach for parameter estimation from joint models. The proposed method can be used to longitudinal outcomes from the exponential family of distributions and is computationally e cient. The performance of the proposed method is evaluated in simulation studies. The proposed method is used in an aging cohort to determine the relationship between longitudinal biomarkers and the risk of coronary artery disease.

Joint modeling of a single event time response with a longitudinal covariate dates back to the 1990s. The three basic types of joint modeling formulations are selection models, pattern mixture models and shared parameter models. The shared parameter models are most widely used. One type of a shared parameter model (Joint Model I) utilizes unobserved random effects to jointly model a longitudinal sub-model and a survival sub-model to assess the impact of an internal time-dependent covariate on the time-to-event response. Motivated by the Muscular Dystrophy Surveillance, Tracking and Research Network (MD STARnet), we constructed a new model (Joint Model II), to jointly analyze correlated bivariate time-to-event responses associated with an internal time-dependent covariate in the Frequentist paradigm. This model exhibits two distinctive features: 1) a correlation between bivariate time-to-event responses and 2) a time-dependent internal covariate in both survival models. Developing a model that sufficiently accommodates both characteristics poses a challenge. To address this challenge, in addition to the random variables that account for the association between the time-to-event responses and the internal time-dependent covariate, a Gamma frailty random variable was used to account for the correlation between the two event time outcomes. To estimate the model parameters, we adopted the Expectation-Maximization (EM) algorithm. We built a complete joint likelihood function with respect to both latent variables and observed responses. The Gauss-Hermite quadrature method was employed to approximate the two-dimensional integrals in the E-step of the EM algorithm, and the maximum profile likelihood type of estimation method was implemented in the M-step. The bootstrap method was then applied to estimate the standard errors of the estimated model parameters. Simulation studies were conducted to examine the finite sample performance of the proposed methodology. Finally, the proposed method was applied to MD STARnet data to assess the impact of shortening fractions and steroid use on the onsets of scoliosis and mental health issues.

Patients who were previously diagnosed with prostate cancer usually undergo a routine clinical monitoring that involves measuring the Prostate-specific antigen (PSA). The trajectory of this biomarker over time serves as an indication of cancer recurrence. If the PSA value begins to increase, the cancer is said to be more likely to recur and thus, the patient is advised to start a treatment. There are two reasons for stopping the patient follow-up and this poses a certain challenge. One of them is starting a salvage hormone therapy and another is actual recurrence of cancer. When analyzing such data, we need to account for informative dropout, otherwise, neglecting it may lead to increased bias in estimation of the PSA trajectory. Thus, hormone therapy serves as a censoring event, which is a defining feature of survival analysis. Motivated by the PSA data, we need to efficiently describe the dropout mechanism using the joint model. The survival submodel is based on the Weibull distribution and we use the Bayesian inference to fit this model, more specifically, we use the R-INLA package, which is a much faster alternative to MCMC-based inference. The fact that our joint model with a linear bivariate Gaussian association structure is a latent Gaussian model (LGM) allows us to use this inferential tool. Based on this work, we are then able to develop dynamic predictions of prostate cancer recurrence. Making accurate prognosis for cancer data is clinically impactful and could ultimately contribute to the development of precision medicine.

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Complex systems composed of many substructures include various structural joints connecting the substructures together. These mechanical connections play a significant role in predicting the dynamic characteristics of the assembled systems accurately. Therefore, equivalent dynamic models of joints that consist of stiffness and damping elements should be developed and the joint parameters should be determined for an accurate vibration analysis. Since it is difficult to estimate joint parameters accurately by using a pure analytical approach, it is a general practice to use experimental measurements to model joints connecting substructures. In this study an experimental identification method is suggested. In this approach the frequency response functions (FRFs) of substructures and the coupled structure are measured and FRF decoupling method is used to identify equivalent dynamic characteristics of bolted joints. Since rotational degrees of freedom (RDOF) in connection dynamics is very important, a structural joint is modeled with translational, rotational and cross-coupling stiffness and damping terms. FRF synthesis and finite-difference formulations are used for the estimation of unmeasured FRFs and RDOF related FRFs, respectively. The validity and application of the proposed method are demonstrated both numerically and experimentally. In simulation studies, simulated experimental values are used, and it is seen that the identification results are prone to high errors due to noise in measurement and the matrix inversions in the identification equations. In order to reduce the effect of noise, it is proposed to extract the joint properties by taking the average of the results obtained at several frequencies in the frequency regions sensitive to joint parameters. Yet, it is observed in practical applications that experimental errors combine with the measurement noise and the identification results still may not be so accurate. In order to solve this problem, an update algorithm is developed. In the approach proposed, the identified dynamic parameters are used as initial estimates and then optimum dynamic parameters representing the joint are obtained by using an optimization algorithm. The application of the proposed method is performed on a bolted assembly. It is shown with experimental studies that this method is very successful in identifying bolted joint parameters. The accuracy and applicability of the identification method suggested are illustrated by using a dynamically identified bolt in a new structure, and showing that the calculated FRFs in which identified joint parameters are used, match perfectly with the measured ones for the new structure. In this study, the effects of bolt size and quality of bolts, as well as the bolt torque on the joint properties are also studied by making a series of experiments and identifying the joint parameters for each case.

Pour de nombreuses pathologies chroniques,l’amélioration de la prise en charge des patients passe par une meilleure compréhension de la progression de la pathologie et par la capacité à pronostiquer précocement la survenue d’événements délétères.L’évolution de l’état de santé des patients peut être appréciée à travers des mesures répétées d’un marqueur longitudinal, comme la créatinine sérique en transplantation rénale.Ce travail de thèse en Epidémiologie et Biostatistique appliqué à la transplantation rénale s’intéresse aux modèles conjoints pour données longitudinales et de temps d’évènement. Ces derniers présentent de nombreux avantages mais ils restent encore peu utilisés en pratique. Dans une première partie du travail, nous proposons d’utiliser cette méthodologie afin d’étudier le rôle spécifique des déterminants de santé sur l’évolution du sérum de créatinine et/ou sur le risque d’échec de greffe. Cette modélisation apporte une vision épidémiologique très riche et met en évidence certains facteurs qui pourraient être intéressants à intégrer dans la prise en charge des patients puisqu’ils semblent associés au risque d’échec de greffe sans reflet préalable sur le marqueur de suivi, la créatinine sérique.Dans une seconde partie, nous nous sommes intéressés aux prédictions dynamiques. Calculables à partir d’un modèle conjoint, les prédictions sont dites dynamiques car elles se mettent à jour tout au long du suivi en fonction de l’information longitudinale récoltée jusqu’au temps de prédiction. L’utilité clinique de ce type de score dynamique doit être évaluée et repose en partie sur des performances adéquates en termes de calibration et de discrimination. Des outils d’évaluation,tels que le Brier Score ou la courbe ROC, ont déjà été développés. En complément de ces indicateurs, nous proposons le développement d’un indicateur de type R² afin de pallier certaines de leurs limites / For many chronic diseases, the monitoring of patients can be improved by a better understanding of disease growth and the ability to predict the occurrence of major events. Health status evolution can be measured by repeated measurements of a longitudinal marker, as serumcreatinine in renal transplantation.This thesis work in epidemiology and biostatistics applied to renal transplantation focuses on jointmodels for longitudinal and time-to-event data.These models have various benefits but their use is still uncommon in practice. In a first part, we use this methodology to identify the specific role of risk factors on serum creatinine evolution and/or graftfailure risk. We give a rich epidemiological overview and highlights some features which deserve additional attention as they seemassociated with graft failure risk without previousmodification of the longitudinal marker, the serumcreatinine. In a second part, we focus on dynamic predictions, which can be estimated from a jointmodel. They are called dynamic because of an update performed at each new measurement of the longitudinal marker. The clinical usefulness of this type of predictions has to be evaluated and should be based on good accuracy in terms of discrimination and calibration. To assess the prognostic capacities, the Brier Score or the ROCcurve have already been developed. To complete them, we propose an R² type indicator in order to complement some limitations of previous tools.

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.

Due to tuberculosis (TB) being one of the top ten diseases in Africa with the highest mortality rate, a crucial objective is to find the appropriate medication to cure patients and prevent people from contracting the disease. Since this statistic is not improving sufficiently, it is evident that there is a need for new anti-TB drugs. One of the main challenges in developing new and effective drugs for the treatment of TB is to identify the combinations of effective drugs when subsequent testing of patients in pivotal clinical trials are performed. During the early weeks of the treatment of TB, trials of the early bactericidal activity assess the decline in colony-forming unit (CFU) count of Mycobacterium TB in the sputum of patients containing smear-microscopy-positive pulmonary TB. A previously published dataset containing CFU counts of treated patients over 56 days is used to perform joint modeling of the nonlinear data over time and the patients’ sputum culture conversion (i.e., the time-to-event outcome). It is clear from the results obtained that there is an association between the longitudinal and time-to-event outcomes. / Mini Dissertation ( MSc (Advanced Data Analytics))--University of Pretoria, 2021. / South African Medical Research Council (SAMRC) / Statistics / MSc (Advanced Data Analytics) / Restricted

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