Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been used to study quality of care for patients with acute health conditions, such as pneumonia and heart failure, with analyses typically based on a logistic-Normal generalized linear mixed model. Applying this model to the study readmission among patients with increasingly prevalent advanced health conditions such as pancreatic cancer is problematic, however, because it ignores death as a competing risk. A more appropriate analysis is to imbed such studies within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. In this paper we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data. The framework permits parametric or non-parametric specifications for a range of model components, including baseline hazard functions and distributions for key random effects, giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters including hospital-specific random effects. The proposed framework is used to study the risk of readmission among 5,298 Medicare beneficiaries diagnosed with pancreatic cancer at 112 hospitals in the six New England states between 2000-2009, specifically to investigate the role of patient-level risk factors and to characterize variation in risk across hospitals that is not explained by differences in patient case-mix

Investigating the Epidemiology of bovine Tuberculosis in the European Badger

Global health is becoming increasingly reliant on our understanding and management of wildlife disease. An estimated 60% of emerging infectious diseases in humans are zoonotic and with human-wildlife interactions set to increase as populations rise and we expand further into wild habitats there is pressure to seek modelling frameworks that enable a deeper understanding of natural systems. Survival and mortality are fundamental parameters of interest when investigating the impact of disease with far reaching implications for species conservation, management and control. Survival analysis has traditionally been dominated by non- and semi-parametric methods but these can sometimes miss subtle yet important dynamics. Survival and mortality trajectory analysis can alleviate some of these problems by fitting fully parametric functions that describe lifespan patterns of mortality and survival. In the first part of this thesis we investigate the use of survival and mortality trajectories in epidemiology and uncover novel patterns of age-, sex- and infection-specific mortality in a wild population of European badgers (Meles meles) naturally infected with Mycobacterium bovis, the causative agent of bovine tuberculosis (bTB). Limitations of dedicated software packages to conduct such analyses led us to investigate alternative methods to build models from first principles and we found the NIMBLE package to offer an attractive blend of flexibility and speed. We create a novel parameterisation of the Siler model to enable more flexible model specification but encounter the common problem of competing models having comparable fits to the data. Multi-model inference approaches can alleviate some of these issues but require efficient methods to carry out model comparisons; we present an approach based on the estimation of the marginal likelihood through importance sampling and demonstrate its application through a series of simulation- and case-studies. The approach works well for both census and capture-mark-recapture (CMR) data, both of which are common within ecological research, but we uncover challenges in recording and modelling early life mortality dynamics that occur as a result of the CMR sampling process. The final part of the thesis looks at another alternative approach for model comparison that doesn’t require direct estimation of the marginal likelihood, Reversible Jump Markov Chain Monte Carlo (RJMCMC), which is particularly efficient when models to be compared are nested and the problem can reduce to one of variable selection. In the final chapter we carry out an investigation of age-, sex-, infection- and inbreeding-specific variation in survival and mortality in a wild population of European badgers naturally infected with bovine Tuberculosis. Using the methods and knowledge presented through the earlier chapters of this thesis we uncover patterns of mortality consistent with both the mutation accumulation and antagonistic pleiotropy theories of senescence but most interestingly uncover antagonistic pleiotropic effects of inbreeding on age-specific mortality in a wild population for the first time. This thesis provides a number of straightforward approaches to Bayesian survival analysis that are widely applicable to ecological research and can offer greater insight and uncover subtle patterns of survival and mortality that traditional methods can overlook. Our investigation into the epidemiology of bovine Tuberculosis and in particular the effects of inbreeding have far-reaching implications for the control of this disease. This research can also inform future conservation efforts and management strategies as all species are likely to be at increasing risk of inbreeding in an age of dramatic global change, rapid habitat loss and isolation

Modelling Survival Data to Account for Model Uncertainty: A Single Model or Model Averaging?

This study considered the problem of predicting survival, based on three alternative models: a single Weibull, a\ud mixture of Weibulls and a cure model. Instead of the common procedure of choosing a single ???best??? model, where\ud ???best??? is defined in terms of goodness of fit to the data, a Bayesian model averaging (BMA) approach was adopted to\ud account for model uncertainty. This was illustrated using a case study in which the aim was the description of\ud lymphoma cancer survival with covariates given by phenotypes and gene expression. The results of this study indicate\ud that if the sample size is sufficiently large, one of the three models emerge as having highest probability given the\ud data, as indicated by the goodness of fit measure; the Bayesian information criterion (BIC). However, when the sample\ud size was reduced, no single model was revealed as ???best???, suggesting that a BMA approach would be appropriate.\ud Although a BMA approach can compromise on goodness of fit to the data (when compared to the true model), it can\ud provide robust predictions and facilitate more detailed investigation of the relationships between gene expression\ud and patient survival

Parametric mixture model of three components for modelling heterogeneos survival data

Previous studies showed that two components of survival mixture model performed better than pure classical parametric survival model. However there are crucial needs for three components of survival mixture model due to the behaviour of heterogeneous survival data which commonly comprises of more than two distributions. Therefore in this study two models of three components of survival mixture model were developed. Model 1 is three components of parametric survival mixture model of Gamma distributions and Model 2 is three components of parametric survival mixture model of Exponential, Gamma and Weibull distributions. Both models were estimated using the Expectation Maximization (EM) and validated via simulation and empirical studies. The simulation was repeated 300 times by incorporating three different sample sizes: 100, 200, 500; three different censoring percentages: 10%, 20%, 40%; and two different sets of mixing probabilities: ascending (10%, 40%, 50%) and descending (50%, 30%, 20%). Several sets of real data were used in the empirical study and models comparisons were implemented. Model 1 was compared with pure classical parametric survival model, two and four components parametric survival mixture models of Gamma distribution, respectively. Model 2 was compared with pure classical parametric survival models and three components parametric survival mixture models of the same distribution. Graphical presentations, log likelihood (LL), Akaike Information Criterion (AIC), Mean Square Error (MSE) and Root Mean Square Error (RMSE) were used to evaluate the performance. Simulation findings revealed that both models performed well at large sample size, small percentage of censoring and ascending mixing probabilities. Both models also produced smaller errors compared to other type of survival models in the empirical study. These indicate that both of the developed models are more accurate and provide better option to analyse heterogeneous survival data

A Hierarchical Model for Heterogenous Reliability Field Data

When analyzing field data on consumer products, model-based approaches to inference require a model with sufficient flexibility to account for multiple kinds of failures. The causes of failure, while not interesting to the consumer per se, can lead to various observed lifetime distributions. Because of this, standard lifetime models, such as using a single Weibull or lognormal distribution, may be inadequate. Usually cause-of-failure information will not be available to the consumer and thus traditional competing risk analyses cannot be performed. Furthermore, when the information carried by lifetime data are limited by sample size, censoring, and truncation, estimates can be unstable and suffer from imprecision. These limitations are typical, for example, lifetime data for high-reliability products will naturally tend to be right-censored. In this article, we present a method for joint estimation of multiple lifetime distributions based on the generalized limited failure population (GLFP) model. This five-parameter model for lifetime data accommodates lifetime distributions with multiple failure modes: early failures (sometimes referred to in the literature as “infant mortality”) and failures due to wearout. We fit the GLFP model to a heterogenous population of devices using a hierarchical modeling approach. Borrowing strength across subpopulations, our method enables estimation with uncertainty of lifetime distributions even in cases where the number of model parameters is larger than the number of observed failures. Moreover, using this Bayesian method, comparison of different product brands across the heterogenous population is straightforward because estimation of arbitrary functionals is easy using draws from the joint posterior distribution of the model parameters. Potential applications include assessment and comparison of reliability to inform purchasing decisions. Supplementary materials for this article are available online

Bayesian methods for the design and analysis of complex follow-up studies

My doctoral research focused on two topics: i) models for the analysis of multi-state time-to-event data; and ii) decision-theoretic approaches for the design of clinical trials with a survival endpoint. For the first, I developed stochastic processes useful for the Bayesian non-parametric analysis of follow-up studies where patients may experience multiple events relevant to their prognosis. For the second, I developed an approach that uses data from early clinical trials to specify the statistical test used in a confirmatory survival study, accounting for the possible failure of standard assumptions. In this thesis, I describe 3 research papers that report my contributions. Part of my work has been conducted while a visiting researcher at the Dana-Farber Cancer Institute, Boston, Massachusetts (United States of America)

Joint analysis of longitudinal and time to event data using accelerated failure time models: A Bayesian approach

Joint modeling is a collection of statistical methods to properly handle a longitudinal response while investigating its effects on time to the occurrence of an event. Joint modeling also allows an investigation of the effects of baseline covariates on both the longitudinal response and the event process. In practice, the inspiration of biostatistical research arises from clinical and biomedical studies. The data collected from these studies have always been getting attention due to their particular features that need special consideration when doing an analysis. New statistical methods have developed over time to handle an analysis of such data coming from these sources. A typical clinical study often involves collecting repeated measurements on a biomarker (e.g., lvmi measurements) along with an observation of the time to the occurrence of an event (e.g., death), resulting in a joint modeling setup, a model becomes increasingly popular in clinical studies. Joint models can be formulated with a probability distribution (parametric models) or without assuming a probability distribution (Cox model or semi-parametric Cox PH model) for time-to-event process. In general, parametric models are pivotal in the joint modeling of longitudinal and time-to-event data. A non-parametric or semi-parametric model usually leads to an underestimation of standard errors of the parameter estimates in the joint analysis. However, selection for the joint model framework is quite limited in the literature. The best choice for the selection of longitudinal model can be made based on the observed longitudinal data, and the best survival model can be selected based on the survival data, using standard model selection procedures for these models. In this thesis, we develop and implement a Bayesian joint model framework, consisting of longitudinal process involving continuous longitudinal outcome and two parametric accelerated failure time (AFT) models (Log-logistic (model 1) and Weibull (model 2)) for survival process. We introduce a link between the parametric AFT survival processes and the longitudinal process via one parameter of association corresponding to shared random effects. A linear mixed-effect model approach is used for the analysis of longitudinal process with the normality assumption of longitudinal response along with normal and independent distribution assumption for both random effects and the error term of the longitudinal process. Finally, Bayesian approach using the Markov chain Monte Carlo method with the Gibbs Sampler technique is adopted for the statistical inference. The motivating ideas behind our work on Bayesian joint models using parametric AFT event processes are: (a) although there are well-known techniques to test the proportionality assumption for the Cox PH model, checking this assumption for joint modeling has received less attention in the literature. To our knowledge, no statistical package is available to check the PH assumption under the joint modeling setup. AFT models are particularly useful when the PH assumption is in question, (b) there are two integrals involved in the specification of joint models: (1) a unidimensional integral with respect to time which is relatively straightforward to approximate using numerical techniques, and (2) a multidimensional integral with respect to random effects which is the main computational burden to fit a joint model. It is relatively straightforward to handle (2) under the Bayesian framework, implemented using Markov Chain Monte Carlo (MCMC) techniques, (c) Bayesian approach does not depend on asymptotic approximation for statistical inference and (d) availability of software makes Bayesian implementation for complicated models relatively more straightforward and simpler than frequentist methods. We also develop computational algorithms to fit the proposed Bayesian joint model approach and implemented it in WinBUGS (a Bayesian software) and R software. Analysis are performed with an application to aortic heart valve replacement surgery data (available in joineR package in R software) to illustrate the performance of our two proposed models with the aim of comparing the efficiency of two types of valves based on tissue type (Stentless porcine tissue or Homograft) implanted during surgery and the association between internal covariate (longitudinal response: log.lvmi) and the occurrence of an event (death) after the surgery. Model selection is performed using the deviance information criterion (DIC). Study analysis results for both joint models indicate the statistically significant and strong association between internal covariate (longitudinal response: log.lvmi) and the relative risk of death after aortic valve replacement surgery. Results show that one gm/m^2 increase in the value of log.lvmi after the surgery reduces the relative risk of death by about 62 % (model 1) and 60 % (model 2), respectively, after controlling for other factors. Moreover, age of the patient (age) and preoperative left ventricular ejection fraction (lv) are found statistically significant for the risk of death after surgery. However, we found no significant difference between the efficiency of two types of valves implanted during surgery based on tissue type (Stentless porcine tissue or Homograft) associated with reducing the risk of death in the patients after surgery. Finally, based on DIC, we recommend, Bayesian joint AFT model with Weibull distribution fits the motivated data set more efficiently than Bayesian joint AFT model with Log-Logistic distribution. Developing joint models using AFT event processes, writing the model in a hierarchical framework for Bayesian implementation and developing computational algorithms to fit proposed joint models is the novelty of this thesis

Statistical Reliability with Applications

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data. The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood estimation and likelihood ratio testing. Degradation data are more prevalent in experiments in which failure is rare and test time is limited. Special regression techniques for degradation data can be used to draw inference on the underlying lifetime distribution, even if failures are rarely observed. The last part of the chapter discusses reliability for systems. Along with the components that comprise the system, reliability analysis must take account of the system configuration and (stochastic) component dependencies. System reliability is illustrated with an analysis of logistics systems (e.g., moving goods in a system of product sources and retail outlets). Robust reliability design can be used to construct a supply chain that runs with maximum efficiency or minimum cost