The accelerated failure time (AFT) model is a commonly used tool in analyzing survival data. In public health studies, data is often collected from medical service providers in different locations. Survival rates from different locations often present geographically varying patterns. In this paper, we focus on the accelerated failure time model with spatially varying coefficients. We compare three types of the priors for spatially varying coefficients. A model selection criterion, logarithm of the pseudo-marginal likelihood (LPML), is developed to assess the fit of AFT model with different priors. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. Finally, we apply our model to SEER data on prostate cancer in Louisiana and demonstrate the existence of spatially varying effects on survival rates from prostate cancer data.
This paper deals with unobserved heterogeneity in the survival dataset through Accelerated Failure Time (AFT) models under both frameworks--Bayesian and classical. The Bayesian approach of dealing with unobserved heterogeneity has recently been discussed in Vallejos and Steel (2017), where mixture models are used to diminish the effect that anomalous observations or some kinds of covariates which are not included in the survival models. The frailty models also deal with this kind of unobserved variability under classical framework and have been used by practitioners as alternative to Bayesian.…
Bayesian joint modelling using semiparametric accelerated failure time approaches
The University of Queensland’s Clinical Trials Capability (ULTRA)（昆士兰大学临床试验能力中心（ULTRA））；NHMRC Clinical Trial Centre, University of Sydney（悉尼大学国家健康与医学研究委员会临床试验中心）；Australian and New Zealand Urogenital and Prostate (ANZUP) Cancer Trials Group（澳大利亚和新西兰泌尿生殖和前列腺癌症试验组）
Robust Survival Estimation under Interval Censoring: Expectation-Maximization and Bayesian Accelerated Failure Time Assessment via Simulation and Application
A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly-used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many other approaches, all manner of censored survival times are simultaneously accommodated including uncensored, interval censored, current-status, left and right censored, and mixtures of these. Left-truncated data are also accommodated leading to models for time-dependent covariates. Both georeferenced (location exactly observed) and areally observed (locati…
We study the causal effect of winning an Oscar Award on an actor or actress's survival. Does the increase in social rank from a performer winning an Oscar increase the performer's life expectancy? Previous studies of this issue have suffered from healthy performer survivor bias, that is, candidates who are healthier will be able to act in more films and have more chance to win Oscar Awards. To correct this bias, we adapt Robins' rank preserving structural accelerated failure time model and $g$-estimation method. We show in simulation studies that this approach corrects the bias contained in pr…
This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the non-terminal and the terminal failure times given the observed covariates. Semi-parametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided EM algorithm, and variances are estimated by weighted bootstrap. The model is presented in the context of existing frailty-bas…
Major disasters such as wildfire, tornado, hurricane, tropical storm, flooding cause disruptions in infrastructure systems such as power outage, disruption to water supply system, wastewater management, telecommunication failures, and transportation facilities. Disruptions in electricity infrastructures has a negative impact on every sector of a region, such as education, medical services, financial, recreation. In this study, we introduce a novel approach to investigate the factors which can be associated with longer restoration time of power service after a hurricane. We consider three types…
For complex diseases, beyond the main effects of genetic (G) and environmental (E) factors, gene-environment (G-E) interactions also play an important role. Many of the existing G-E interaction methods conduct marginal analysis, which may not appropriately describe disease biology. Joint analysis methods have been developed, with most of the existing loss functions constructed based on likelihood. In practice, data contamination is not uncommon. Development of robust methods for interaction analysis that can accommodate data contamination is very limited. In this study, we consider censored su…
Individuals often respond differently to identical treatments, and characterizing such variability in treatment response is an important aim in the practice of personalized medicine. In this article, we describe a non-parametric accelerated failure time model that can be used to analyze heterogeneous treatment effects (HTE) when patient outcomes are time-to-event. By utilizing Bayesian additive regression trees and a mean-constrained Dirichlet process mixture model, our approach offers a flexible model for the regression function while placing few restrictions on the baseline hazard. Our non-p…
Graphics processing units (GPUs) are widely used in many high-performance computing (HPC) applications such as imaging/video processing and training deep-learning models in artificial intelligence. GPUs installed in HPC systems are often heavily used, and GPU failures occur during HPC system operations. Thus, the reliability of GPUs is of interest for the overall reliability of HPC systems. The Cray XK7 Titan supercomputer was one of the top ten supercomputers in the world. The failure event times of more than 30,000 GPUs in Titan were recorded and previous data analysis suggested that the fai…
Many highly reliable products are designed to function for years without failure. For such systems accelerated degradation testing may provide significance information about the reliability properties of the system. In this paper, we propose the $c$-optimality criterion for obtaining optimal designs of constant-stress accelerated degradation tests where the degradation path follow a linear mixed effects model. The present work is mainly concerned with developing optimal desings in terms of the time variable rather than considering an optimal design of the stress variable which is usually consi…
Accelerated degradation tests are used to provide accurate estimation of lifetime properties of highly reliable products within a relatively short testing time. There data from particular tests at high levels of stress (e.\,g.\ temperature, voltage, or vibration) are extrapolated, through a physically meaningful model, to obtain estimates of lifetime quantiles under normal use conditions. In this work, we consider repeated measures accelerated degradation tests with multiple stress variables, where the degradation paths are assumed to follow a linear mixed effects model which is quite common i…
The main objective of accelerated life tests (ALTs) is to predict fraction failings of products in the field. However, there are often discrepancies between the predicted fraction failing from the lab testing data and that from the field failure data, due to the yet unobserved heterogeneities in usage and operating conditions. Most previous research on ALT planning and data analysis ignores the discrepancies, resulting in inferior test plans and biased predictions. In this paper we model the heterogeneous environments together with their effects on the product failures as a frailty term to lin…
Accelerated degradation testing (ADT) is one of the major approaches in reliability engineering which allows accurate estimation of reliability characteristics of highly reliable systems within a relatively short time. The testing data are extrapolated through a physically reasonable statistical model to obtain estimates of lifetime quantiles at normal use conditions. The Gamma process is a natural model for degradation, which exhibits a monotone and strictly increasing degradation path. In this work, optimal experimental designs are derived for ADT with two response components. We consider th…
Software development innovations and advances in computing have enabled more complex and less costly computations in medical research (survival analysis), engineering studies (reliability analysis), and social sciences event analysis (historical analysis). As a result, many semi-parametric modeling efforts emerged when it comes to time-to-event data analysis. In this context, this work presents a flexible Bernstein polynomial (BP) based framework for survival data modeling. This innovative approach is applied to existing families of models such as proportional hazards (PH), proportional odds (…
