Background: Dilated Cardiomyopathy (DCM) is the most common functional type of cardiomyopathy in children with significant morbidity and the leading indication for cardiac transplant over 5 years of age. Identification of baseline risk factors for failing medical management by etiologic grouping remain to be elucidated in a large populationbased study. The competing risk for heart death between all-cause mortality and heart transplantation is often overestimated in the literature and may obscure additional novel risk factors associated with poor clinical outcomes. Methods: The National Heart Lung and Blood Institute Pediatric Cardiomyopathy Registry collected longitudinal data from 1731 children with DCM in North America from 1990 to 2007. Composite endpoint (CEP) was the earlier occurrence of death or heart transplant. Univariate and multivariate predictors were identified from demographic and echocardiographic data (expressed as z-scores) collected within 30 days of diagnosis. A competing risk analysis was performed calculating cumulative incidence and identifying novel prognostic factors. All analyses were performed by etiologic group. Results: Multivariate Cox regression identified the highest mortality risk among children with idiopathic disease (N=1192, CEP: 41%) when diagnosed over age 6 years, and with congestive heart failure (CHF) and decreased left ventricular fractional shortening (FS). Risk factors for those with myocarditis (N=272, CEP: 26%) were older age, CHF, and increased left ventricular (LV) end-diastolic dimension (EDD); while for neuromuscular disease (N=139, CEP: 40%), it was a decreased FS and increased EDD. Only univariate predictors were identified for children with familial isolated cardiomyopathy (N=79, CEP: 44%) including: CHF, increased EDD, end-systolic dimension, or LV mass, and decreased FS or ejection fraction), while for children with inborn errors of metabolism (N=43, CEP: 33%) risk factors included: a positive family history of cardiomyopathy or genetic syndromes. The group of children with malformation syndromes (N=6, CEP: 50%) was not large enough to model. Comparison of cause-specific event rates between Kaplan-Meier and cumulative incidence demonstrated an overestimation with the former method. Competing risk multivariate regression showed similar models to those for CEP, with the following exceptions: for neuromuscular disease, an increased EDD had a larger hazard ratio for transplant than for death; for idiopathic disease, an increased EDD was associated with transplant, but not with death, and growth retardation (height-for-age zscore) was associated with death but not transplant. Conclusions: Within etiologic grouping, demographics and echocardiographic values at diagnosis have varying predictive value. Generally, the presence of symptomatic disease in the form of CHF, echocardiographic evidence of more severe DCM, and increased age were indicative of worse outcomes. These results help to validate those from conflicting studies; however, they suggest that etiology modifies the importance of particular factors. Analysis of competing risk provides an alternate interpretation of studies with composite endpoints and assists in the transfer of clinically relevant information. For children with idiopathic and neuromuscular disease, the degree of dilation had a differential effect that has gone unrecognized. The novel finding of reduced stature and its effect on mortality suggests a potential for treatment and mitigation of poor outcomes in idiopathic DCM. Both increased dilation and reduced stature could be used to improve the triage process and refer children to cardiac transplantation who otherwise might die prematurely and unnecessarily. Subsequent studies on the utility of these factors and their effect on improving survival are warranted.

<p>Subjects enrolled in a clinical trial may experience a competing risk event which alters the risk of the primary event of interest. This differs from when subject information is censored, which is non-informative. In order to calculate the cumulative incidence function (CIF) for the event of interest, competing risks and censoring must be treated appropriately; otherwise estimates will be biased. There are two commonly used methods of calculating a confidence interval (CI) for the CIF for the event of interest which account for censoring and competing risk: the Kalbfleisch-Prentice (KP) method and the Counting Process (CP) method. The goal of this paper is to understand the variances associated with the two methods to improve our understanding of the CI. This will allow for appropriate estimation of the CIF CI for a single-arm cohort study that is currently being conducted. Previous work has failed to address this question because researchers typically focus on comparing two treatment arms using statistical tests that compare cause-specific hazard functions and do not require a CI for the CIF. The two methods were compared by calculating CIs for the CIF using data from a previous related study, using bootstrapping, and a simulation study with varying event rates and competing risk rates. The KP method usually estimated a larger CIF and variance than the CP method. When event rates were low (5%), the CP method is recommended as it yields more consistent results than the KP method. The CP method is recommended for the proposed study since event rates are expected to be moderate (5-10%).</p> / Master of Science (MS)

It is of interest that researchers study competing risks in which subjects may fail from any one of K causes. Comparing any two competing risks with covariate effects is very important in medical studies. This thesis develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. In the thesis, the omnibus tests are derived under the additive risk model, that is an alternative to the proportional hazard model, with by a weighted difference of estimates of cumulative cause-specific hazard rates. Simultaneous confidence bands for the difference of two conditional cumulative incidence functions are also constructed. A simulation procedure is used to sample from the null distribution of the test process in which the graphical and numerical techniques are used to detect the significant difference in the risks. A melanoma data set is used for the purpose of illustration.

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

The typical research of Alzheimer's disease includes a series of cognitive states. Multi-state models are often used to describe the history of disease evolvement. Competing risks models are a sub-category of multi-state models with one starting state and several absorbing states. Analyses for competing risks data in medical papers frequently assume independent risks and evaluate covariate effects on these events by modeling distinct proportional hazards regression models for each event. Jeong and Fine (2007) proposed a parametric proportional sub-distribution hazard (SH) model for cumulative incidence functions (CIF) without assumptions about the dependence among the risks. We modified their model to assure that the sum of the underlying CIFs never exceeds one, by assuming a proportional SH model for dementia only in the Nun study. To accommodate left censored data, we computed non-parametric MLE of CIF based on Expectation-Maximization algorithm. Our proposed parametric model was applied to the Nun Study to investigate the effect of genetics and education on the occurrence of dementia. After including left censored dementia subjects, the incidence rate of dementia becomes larger than that of death for age < 90, education becomes significant factor for incidence of dementia and standard errors for estimates are smaller. Multi-state Markov model is often used to analyze the evolution of cognitive states by assuming time independent transition intensities. We consider both constant and duration time dependent transition intensities in BRAiNS data, leading to a mixture of Markov and semi-Markov processes. The joint probability of observing a sequence of same state until transition in a semi-Markov process was expressed as a product of the overall transition probability and survival probability, which were simultaneously modeled. Such modeling leads to different interpretations in BRAiNS study, i.e., family history, APOE4, and sex by head injury interaction are significant factors for transition intensities in traditional Markov model. While in our semi-Markov model, these factors are significant in predicting the overall transition probabilities, but none of these factors are significant for duration time distribution.

Competing risks occur often in survival analysis. In present work, we study different ap- proaches to modeling competing risks data and use examples to illustrate the most impor- tant results. In the competing risks setting it is often of interest to calculate the cumulative incidence of a specific event. We first study non-parametric estimation and then present three approaches to regression modeling. We use simple numerical example to demonstrate the use of non-parametric methods and perform analysis of real data from Stanford Heart Transplant Program to illustrate and compare the chosen regression models.

Aalen’s additive hazards model has gained increasing attention in recently years because it model all covariate effects as time-varying. In this thesis, our goal is to explore the application of Aalen’s model in assessing treatment effect at a given time point with varying covariate effects. First, based on Aalen’s model, we utilize the direct adjustment method to obtain the adjusted survival of a treatment and comparing two direct adjusted survivals, with univariate survival data. Second, we focus on application of Aalen’s model in the setting of competing risks data, to assess treatment effect on a particular type of failure. The direct adjusted cumulative incidence curve is introduced. We further construct the confidence interval of the difference between two direct adjusted cumulative incidences, to compare two treatments on one risk.

L’hémolyse post transfusionnelle retardée (HPTR) est une complication potentiellement mortelle de la transfusion dans la drépanocytose. Sa fréquence est sous-estimée et aucun facteur prédictif de sa survenue n'a encore été identifié. Nous avons mené une étude observationnelle prospective monocentrique pendant 30 mois. Nous avons inclus 694 épisodes transfusionnels (ET) chez 311 patients adultes drépanocytaires, divisés en ET ponctuels (ETP = 360) et en ET chronique dans le cadre d’un programme (ETC = 334). Au cours de ce suivi, 15 HPTR ont été enregistrées, exclusivement après un ETP. L'incidence cumulative d’HPTR sur 30 mois était de 4,2 % par ETP (IC 95 % [2,6 ; 6,9]) ou 6,8 % par drépanocytaires transfusés (IC 95 % [4,2 ; 11,3]). Le taux d’incidence était de 16,4 HPTR pour 1000 ETP-Année (IC 95 % [10,1 ; 27,2]) ou 27,1 HPTR pour 1000 Personne-Année (IC 95% [16,7 ; 45,0]). Nous avons étudié 11 HPTR supplémentaires afin de construire un score prédictif. Les variables retenues étaient un antécédent d’HPTR, le nombre d’unités précédemment transfusées et l’état d’immunisation pré transfusionnelle. L’adéquation du score était excellente (Hosmer-Lemeshow = 1,40, p = 0,71), sa capacité discriminante très satisfaisante (aire sous la courbe ROC = 0,85 ; p < 0,0001), une valeur prédictive négative de 98,4 % et une valeur prédictive positive de 50,0 %. La validité interne du score, réalisée par Bootstrap, montre une très bonne performance. Nous rapportons, pour la première fois, l'incidence de l’HPTR et montrons qu’elle survient uniquement suite à un ETP. Nous décrivons également un score simple de prédiction d’une HPTR avant un ETP afin de mieux prendre en charge cette transfusion. / Delayed hemolytic transfusion reaction (DHTR) is a life-threatening complication of transfusion in sickle cell disease (SCD). The frequency of DHTR is underestimated and no predictive fac-tors for identifying patients likely to develop DHTR have yet been defined. We conducted a prospective single-center observational study over 30 months. We included 694 transfusion epi-sodes (TE) in 311 adult patients, divided into occasional TE (OTE: 360) and TE during a chronic program (CTE: 334). During follow-up, 15 cases of DHTR were recorded, exclusively after OTEs. DHTR cumulative incidence durin the 30 months was 4.2% per OTE (95% CI [2.6, 6.9]) or 66.8% per patient (95% CI [4.2, 11.3]). The incidence rate was 16.4 DHTR per 1000 OTE-Year (95% CI [10.1, 27.2]) or 27.1 DHTR per 1000 Person-Year (95% CI [16.7 ; 45.0]). We studied 11 additional DHTR cases to construct a score for predicting DHTR after OTE. Fifteen % of the 26 DHTR patients died. The variables retained in the multivariate model were history of DHTR, number of units previously transfused and immunization status before transfusion. The score adequacy was excellent (Hosmer-Lemeshow = 1.40, p = 0.71), very satisfactory dis-criminant capacity (area under ROC curve = 0.85, p <0.0001), negative-predictive value of 98.4% and a positive-predictive value of 50%. The internal validity of the score, realized by Bootstrap, shows a very good performance.We report, for the first time, the incidence of DHTR and we show that DHTR developed only in OTE. We also describe a simple score for predicting DHTR in patients undergoing occasional transfusion, to facilitate the management of blood transfusion in SCD patients.

Les données manquantes sont fréquentes dans les études médicales. Dans les modèles de régression, les réponses manquantes limitent notre capacité à faire des inférences sur les effets des covariables décrivant la distribution de la totalité des réponses prévues sur laquelle porte l'intérêt médical. Outre la perte de précision, toute inférence statistique requière qu'une hypothèse sur le mécanisme de manquement soit vérifiée. Rubin (1976, Biometrika, 63:581-592) a appelé le mécanisme de manquement MAR (pour les sigles en anglais de « manquant au hasard ») si la probabilité qu'une réponse soit manquante ne dépend pas des réponses manquantes conditionnellement aux données observées, et MNAR (pour les sigles en anglais de « manquant non au hasard ») autrement. Cette distinction a des implications importantes pour la modélisation, mais en général il n'est pas possible de déterminer si le mécanisme de manquement est MAR ou MNAR à partir des données disponibles. Par conséquent, il est indispensable d'effectuer des analyses de sensibilité pour évaluer la robustesse des inférences aux hypothèses de manquement.Pour les données multivariées incomplètes, c'est-à-dire, lorsque l'intérêt porte sur un vecteur de réponses dont certaines composantes peuvent être manquantes, plusieurs méthodes de modélisation sous l'hypothèse MAR et, dans une moindre mesure, sous l'hypothèse MNAR ont été proposées. En revanche, le développement de méthodes pour effectuer des analyses de sensibilité est un domaine actif de recherche. Le premier objectif de cette thèse était de développer une méthode d'analyse de sensibilité pour les données longitudinales continues avec des sorties d'étude, c'est-à-dire, pour les réponses continues, ordonnées dans le temps, qui sont complètement observées pour chaque individu jusqu'à la fin de l'étude ou jusqu'à ce qu'il sorte définitivement de l'étude. Dans l'approche proposée, on évalue les inférences obtenues à partir d'une famille de modèles MNAR dits « de mélange de profils », indexés par un paramètre qui quantifie le départ par rapport à l'hypothèse MAR. La méthode a été motivée par un essai clinique étudiant un traitement pour le trouble du maintien du sommeil, durant lequel 22% des individus sont sortis de l'étude avant la fin.Le second objectif était de développer des méthodes pour la modélisation de risques concurrents avec des causes d'évènement manquantes en s'appuyant sur la théorie existante pour les données multivariées incomplètes. Les risques concurrents apparaissent comme une extension du modèle standard de l'analyse de survie où l'on distingue le type d'évènement ou la cause l'ayant entrainé. Les méthodes pour modéliser le risque cause-spécifique et la fonction d'incidence cumulée supposent en général que la cause d'évènement est connue pour tous les individus, ce qui n'est pas toujours le cas. Certains auteurs ont proposé des méthodes de régression gérant les causes manquantes sous l'hypothèse MAR, notamment pour la modélisation semi-paramétrique du risque. Mais d'autres modèles n'ont pas été considérés, de même que la modélisation sous MNAR et les analyses de sensibilité. Nous proposons des estimateurs pondérés et une approche par imputation multiple pour la modélisation semi-paramétrique de l'incidence cumulée sous l'hypothèse MAR. En outre, nous étudions une approche par maximum de vraisemblance pour la modélisation paramétrique du risque et de l'incidence sous MAR. Enfin, nous considérons des modèles de mélange de profils dans le contexte des analyses de sensibilité. Un essai clinique étudiant un traitement pour le cancer du sein de stade II avec 23% des causes de décès manquantes sert à illustrer les méthodes proposées. / Missing data are a common occurrence in medical studies. In regression modeling, missing outcomes limit our capability to draw inferences about the covariate effects of medical interest, which are those describing the distribution of the entire set of planned outcomes. In addition to losing precision, the validity of any method used to draw inferences from the observed data will require that some assumption about the mechanism leading to missing outcomes holds. Rubin (1976, Biometrika, 63:581-592) called the missingness mechanism MAR (for “missing at random”) if the probability of an outcome being missing does not depend on missing outcomes when conditioning on the observed data, and MNAR (for “missing not at random”) otherwise. This distinction has important implications regarding the modeling requirements to draw valid inferences from the available data, but generally it is not possible to assess from these data whether the missingness mechanism is MAR or MNAR. Hence, sensitivity analyses should be routinely performed to assess the robustness of inferences to assumptions about the missingness mechanism. In the field of incomplete multivariate data, in which the outcomes are gathered in a vector for which some components may be missing, MAR methods are widely available and increasingly used, and several MNAR modeling strategies have also been proposed. On the other hand, although some sensitivity analysis methodology has been developed, this is still an active area of research. The first aim of this dissertation was to develop a sensitivity analysis approach for continuous longitudinal data with drop-outs, that is, continuous outcomes that are ordered in time and completely observed for each individual up to a certain time-point, at which the individual drops-out so that all the subsequent outcomes are missing. The proposed approach consists in assessing the inferences obtained across a family of MNAR pattern-mixture models indexed by a so-called sensitivity parameter that quantifies the departure from MAR. The approach was prompted by a randomized clinical trial investigating the benefits of a treatment for sleep-maintenance insomnia, from which 22% of the individuals had dropped-out before the study end. The second aim was to build on the existing theory for incomplete multivariate data to develop methods for competing risks data with missing causes of failure. The competing risks model is an extension of the standard survival analysis model in which failures from different causes are distinguished. Strategies for modeling competing risks functionals, such as the cause-specific hazards (CSH) and the cumulative incidence function (CIF), generally assume that the cause of failure is known for all patients, but this is not always the case. Some methods for regression with missing causes under the MAR assumption have already been proposed, especially for semi-parametric modeling of the CSH. But other useful models have received little attention, and MNAR modeling and sensitivity analysis approaches have never been considered in this setting. We propose a general framework for semi-parametric regression modeling of the CIF under MAR using inverse probability weighting and multiple imputation ideas. Also under MAR, we propose a direct likelihood approach for parametric regression modeling of the CSH and the CIF. Furthermore, we consider MNAR pattern-mixture models in the context of sensitivity analyses. In the competing risks literature, a starting point for methodological developments for handling missing causes was a stage II breast cancer randomized clinical trial in which 23% of the deceased women had missing cause of death. We use these data to illustrate the practical value of the proposed approaches.