PARAMETRIC ESTIMATION IN COMPETING RISKS AND MULTI-STATE MODELS

The typical research of Alzheimer\u27s 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 \u3c 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

Multinomial logistic regression and prediction accuracy for interval-censored competing risks data

Interval-censored competing risks data are ubiquitous in biomedical research fields. The direct parametric modeling of the cumulative incidence functional (CIF) is appealing due to its intuitive probability interpretation and easy implementation. This dissertation is to study and extend the multinomial logistic regression (MLR) model to interval-censored competing risks data. The MLR model naturally guarantees the additivity property of the event-specific probabilities under competing risks. A cubic B-Spline-based sieve method is then adopted to add flexibility into the proposed MLR model. The second study objective is to develop the prediction error (PE) as a model-free metric to evaluate and validate the prediction accuracy for interval-censored competing risks data. Adopting the method of the pseudo-value estimator, this dissertation work proposes a novel approach to estimate the PE under the interval-censored competing risks setting. Simulation studies are presented to assess performance of the MLR model and the PE in different scenarios. The proposed methods were then applied to a community-based study of cognitive impairment in aging population. Public Health Significance: Interval-censored competing risks data could be often encountered in biomedical research that is essential for public health, such as rehabilitation and pain medicine. The proposed methods provide precise yet flexible modeling of such data with straightforward interpretation on how predictors affect the CIF, as well as useful tools to evaluate and validate the prediction accuracy of the developed models

Aspects of competing risks survival analysis

This thesis is focused on the topic of competing risks survival analysis. The first chapter provides an introduction and motivation with a brief literature review. Chapter 2 considers the fundamental functional of all competing risks data: the crude incidence function. This function is considered in the light of the counting process framework which provides powerful mathematics to calculate confidence bands in an analytical form, rather than bootstrapping or simulation. Chapter 3 takes the Peterson bounds and considers what happens in the event of covariate information. Fortunately, these bounds do become tighter in some cases. Chapter 4 considers what can be inferred about the effect of covariates in the case of competing risks. The conclusion is that there exist bounds on any covariate-time transformation. These two preceding chapters are illustrated with a data set in chapter 5. Chapter 6 considers the result of Heckman and Honore (1989) and investigates the question of their generalisation. It reaches the conclusion that the simple assumption of a univariate covariate-time transformation is not enough to provide identifiability. More practical questions of modeling dependent competing risks data through the use of frailty models to induce dependence is considered in chapter 7. A practical and implementable model is illustrated. A diversion is taken into more abstract probability theory in chapter 8 which considers the Bayesian non-parametric tool: P61ya trees. The novel framework of this tool is explained and some results are obtained concerning the limiting random density function and the issues which arise when trying to integrate with a realised P61ya distribution as the integrating measure. Chapter 9 applies the theory of chapters 7 and 8 to a competing risks data set of a prostate cancer clinical trial. This has several continuous baseline covariates and gives the opportunity to use a frailty model discussed in chapter 7 where the unknown frailty distribution is modeled using a P61ya tree which is considered in chapter 8. An overview of the thesis is provided in chapter 10 and directions for future research are considered here

Aspects of competing risks survival analysis

This thesis is focused on the topic of competing risks survival analysis. The first chapter provides an introduction and motivation with a brief literature review. Chapter 2 considers the fundamental functional of all competing risks data: the crude incidence function. This function is considered in the light of the counting process framework which provides powerful mathematics to calculate confidence bands in an analytical form, rather than bootstrapping or simulation. Chapter 3 takes the Peterson bounds and considers what happens in the event of covariate information. Fortunately, these bounds do become tighter in some cases. Chapter 4 considers what can be inferred about the effect of covariates in the case of competing risks. The conclusion is that there exist bounds on any covariate-time transformation. These two preceding chapters are illustrated with a data set in chapter 5. Chapter 6 considers the result of Heckman and Honore (1989) and investigates the question of their generalisation. It reaches the conclusion that the simple assumption of a univariate covariate-time transformation is not enough to provide identifiability. More practical questions of modeling dependent competing risks data through the use of frailty models to induce dependence is considered in chapter 7. A practical and implementable model is illustrated. A diversion is taken into more abstract probability theory in chapter 8 which considers the Bayesian non-parametric tool: P61ya trees. The novel framework of this tool is explained and some results are obtained concerning the limiting random density function and the issues which arise when trying to integrate with a realised P61ya distribution as the integrating measure. Chapter 9 applies the theory of chapters 7 and 8 to a competing risks data set of a prostate cancer clinical trial. This has several continuous baseline covariates and gives the opportunity to use a frailty model discussed in chapter 7 where the unknown frailty distribution is modeled using a P61ya tree which is considered in chapter 8. An overview of the thesis is provided in chapter 10 and directions for future research are considered here.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research Council : Knowle Hill School FundGBUnited Kingdo

Dynamic aspects of competing risks with application to medical data

M.A. Nicolaie focuses in this thesis on inference in survival models for survival data with competing risks. The author introduces a new approach to competing risks data, called vertical modeling. It is built on natural observable quantities in competing risks, that is, it quantifies 1. the chance that a failure occurs, irrespective of its cause and 2. conditionally that a failure occurred, it quantifies the risk that the event of failure is ascertained to a certain type of failure. Another appealing feature of vertical modeling which is discussed is that it deals with competing risks when missing causes of failure occur. Next, the author tackles the topic of dynamic prediction in competing risks, a topical subject nowadays. She uses two different approaches, one which is based on modeling the cause-specific hazards and one which is based on modeling the dynamic pseudo-observations associated to the cumulative incidence functions. The results presented in this thesis provide key messages on the use of competing risks methods in different fields such as epidemiology, medicine, demography.M.A. Nicolaie focuses in this thesis on inference in survival models for survival data with competing risks. The author introduces a new approach to competing risks data, called vertical modeling. It is built on natural observable quantities in competing risks, that is, it quantifies 1. the chance that a failure occurs, irrespective of its cause and 2. conditionally that a failure occurred, it quantifies the risk that the event of failure is ascertained to a certain type of failure. Another appealing feature of vertical modeling which is discussed is that it deals with competing risks when missing causes of failure occur. Next, the author tackles the topic of dynamic prediction in competing risks, a topical subject nowadays. She uses two different approaches, one which is based on modeling the cause-specific hazards and one which is based on modeling the dynamic pseudo-observations associated to the cumulative incidence functions. The results presented in this thesis provide key messages on the use of competing risks methods in different fields such as epidemiology, medicine, demography.Research leading to this thesis was supported by the Netherlands Organization for Scienti c Research Grant ZONMW-912-07-018'Prognostic modeling and dynamic prediction for competing risks and multi-state models'.UBL - phd migration 201

Hierarchical Likelihood Inference on Clustered Competing Risks Data

Frailties models, an extension of the proportional hazards model, are used to model clustered survival data. In some situations there may be competing risks within a cluster. When this happens the basic frailty model is no longer appropriate. Depending on the purpose of the analysis, either the cause-specific hazard frailty model or the subhazard frailty model needs to be used. In this work, hierarchical likelihood (h-likelihood) methods are extended to provide a new method for fitting both types of competing risks frailty models. Methods for model selection as well as testing for covariate and clustering effects are discussed. Simulations show that in cases with little information, the h-likelihood method can perform better than the penalized partial likelihood method for estimating the subhazard frailty model. Additional simulations demonstrate that h-likelihood performs well when estimating the cause-specific hazard frailty model assuming both a univariate and bivariate frailty distribution. A real example from a breast cancer clinical trial is used to demonstrate using h-likelihood to fit both types of competing risks frailty models.Public health significance: When researchers have clustered survival data and the observations within those clusters can experience multiple types of events the popular proportional hazards model is no longer appropriate and can lead to biased estimates. For the results of a clinical study to be meaningful the estimated effects of treatments and other covariates needs to be accurate. H-likelihood methods are an alternative to existing procedures and can provide less bias and more accurate information which will ultimately lead to better patient care

Functional Regression Methods for Densely-Sampled Biomarkers in the ICU

This thesis develops methods for modeling longitudinal predictors by treating them as functional covariates in regression models. First, I introduce Variable-Domain Functional Regression, which extends the generalized functional linear model by allowing for functional covariates that have subject-specific domain widths. I then propose a blueprint for the inclusion of baseline functional predictors in Cox proportional hazards models. Finally, I propose the Historical Cox Model, which introduces a new way of modeling time-varying covariates in survival models by including them as historical functional terms. Methods were motivated by and applied to a study of association between daily measures of the Intensive Care Unit (ICU) Sequential Organ Failure Assessment (SOFA) score and mortality, and are generally applicable to a large number of new studies that record a continuous variables over time