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 survival data and adopt an accelerated failure time (AFT) model. An exponential squared loss is adopted to achieve robustness. A sparse group penalization approach, which respects the "main effects, interactions" hierarchy, is adopted for estimation and identification. Consistency properties are rigorously established. Simulation shows that the proposed method outperforms direct competitors. In data analysis, the proposed method makes biologically sensible findings.
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…
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…
A novel approach for dealing with censored competing risks regression data is proposed. This is implemented by a mixture of accelerated failure time (AFT) models for a competing risks scenario within a cluster-weighted modelling (CWM) framework. Specifically, we make use of the log-normal AFT model here but any commonly used AFT model can be utilized. The alternating expectation conditional maximization algorithm (AECM) is used for parameter estimation and bootstrapping for standard error estimation. Finally, we present our results on some simulated and real competing risks data.
The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations provide promising tools to make the accelerate failure time models more attractive in practice. For semiparametric multivariate accelerated failure time models, we propose a generalized estimating equation approach to account for the multivariate dependence through working correlation structures. The marginal error distributions can be either identical as in seq…
The generalized log-gamma (GLG) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology. In this paper, we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a GLG distribution in the presence of censoring. We also introduced estimators with the same properties for accelerated failure time models with censored observations and error distribution belonging to the GLG family. We prove that the proposed estimators are asymptotically fully efficient and examine the maximum mean square e…
This paper considers robust modeling of the survival time for cancer patients. Accurate prediction can be helpful for developing therapeutic and care strategies. We propose a unified Expectation-Maximization approach combined with the L1-norm penalty to perform variable selection and obtain parameter estimation simultaneously for the accelerated failure time model with right-censored survival data. Our approach can be used with general loss functions, and reduces to the well-known Buckley-James method when the squared-error loss is used without regularization. To mitigate the effects of outlie…
For survival data with high-dimensional covariates, results generated in the analysis of a single dataset are often unsatisfactory because of the small sample size. Integrative analysis pools raw data from multiple independent studies with comparable designs, effectively increases sample size, and has better performance than meta-analysis and single-dataset analysis. In this study, we conduct integrative analysis of survival data under the accelerated failure time (AFT) model. The sparsity structures of multiple datasets are described using the homogeneity and heterogeneity models. For variabl…
Nonparametric and semiparametric methods are commonly used in survival analysis to mitigate the bias due to model misspecification. However, such methods often cannot estimate upper-tail survival quantiles when a sizable proportion of the data are censored, in which case parametric likelihood-based estimators present a viable alternative. In this article, we extend a popular family of parametric survival models which make the Accelerated Failure Time (AFT) assumption to account for heteroscedasticity in the survival times. The conditional variances can depend on arbitrary covariates, thus addi…
In medical studies, the collected covariates usually contain underlying outliers. For clustered /longitudinal data with censored observations, the traditional Gehan-type estimator is robust to outliers existing in response but sensitive to outliers in the covariate domain, and it also ignores the within-cluster correlations. To take account of within-cluster correlations, varying cluster sizes, and outliers in covariates, we propose weighted Gehan-type estimating functions for parameter estimation in the accelerated failure time model for clustered data. We provide the asymptotic properties of…
Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, i.e. shorten or extend the time to event. Commonly used parametric AFT models are limited in the underlying shapes that they can capture. In this article, we propose a general parametric AFT model, and in particular concentrate on using restricted cubic splines to model the baseline to provide substantial flexibility. We then extend the model to accommo…
Debiased Machine Learning for Partially Linear Accelerated Failure Time Models
University of California, Los Angeles（加州大学洛杉矶分校）；Phoenix VA Health Care System (111E)（凤凰城退伍军人健康护理系统(111E)）；VA Greater Los Angeles Health Care（大洛杉矶地区退伍军人健康护理系统）
针对右删失下部分线性AFT模型，本文构建首个基于秩的去偏机器学习框架，通过正交化U统计量等技术实现有效推断，模拟与All of Us数据应用验证了其性能与实用性。
Recent advances in causal mediation analysis have formalized conditions for estimating direct and indirect effects in various contexts. These approaches have been extended to a number of models for survival outcomes including accelerated failure time (AFT) models which are widely used in a broad range of health applications given their intuitive interpretation. In this setting, it has been suggested that under standard assumptions, the "difference" and "product" methods produce equivalent estimates of the indirect effect of exposure on the survival outcome. We formally show that these two meth…
Competing Accelerated Failure Time Models for Multiple Concurrent Failure Mechanisms
Xi’an Jiaotong-Liverpool University（西交利物浦大学）；University of Liverpool（利物浦大学）；Beijing University of Chinese Medicine（北京中医药大学）；University of Wisconsin, Madison（威斯康星大学麦迪逊分校）
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）
We develop a constructive approach for $\ell_0$-penalized estimation in the sparse accelerated failure time (AFT) model with high-dimensional covariates. Our proposed method is based on Stute's weighted least squares criterion combined with $\ell_0$-penalization. This method is a computational algorithm that generates a sequence of solutions iteratively, based on active sets derived from primal and dual information and root finding according to the KKT conditions. We refer to the proposed method as AFT-SDAR (for support detection and root finding). An important aspect of our theoretical result…
Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are often non-differentiable, which poses a computational challenge in high-dimensional settings. In this article, we propose a new alternating direction method of multipliers algorithm for fitting semiparametric AFT models by minimizing a penalized rank-based loss function. Our algorithm scales well in both the number of subjects and number of predictors; and …
The problem of estimating the probability p=P(g(X<0) is considered when X represents a multivariate stochastic input of a monotone function g. First, a heuristic method to bound p is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of p is considered based on a sequential stochastic exploration of the input space. A maximum likelihood estimator of p based on successive dependent Bernoulli data is defined and its theoretical convergence properties are studied. Under intuitive or mild conditions, the estimation is faster and more robust t…
Robust Survival Estimation under Interval Censoring: Expectation-Maximization and Bayesian Accelerated Failure Time Assessment via Simulation and Application
Carnegie Mellon University（卡内基梅隆大学）；Columbia University（哥伦比亚大学）；Tongji University（同济大学）；University of Illinois Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
Evaluating the performance of autonomous vehicles (AV) and their complex subsystems to high precision under naturalistic circumstances remains a challenge, especially when failure or dangerous cases are rare. Rarity does not only require an enormous sample size for a naive method to achieve high confidence estimation, but it also causes dangerous underestimation of the true failure rate and it is extremely hard to detect. Meanwhile, the state-of-the-art approach that comes with a correctness guarantee can only compute an upper bound for the failure rate under certain conditions, which could li…
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…
The proportional hazards model represents the most commonly assumed hazard structure when analysing time to event data using regression models. We study a general hazard structure which contains, as particular cases, proportional hazards, accelerated hazards, and accelerated failure time structures, as well as combinations of these. We propose an approach to apply these different hazard structures, based on a flexible parametric distribution (Exponentiated Weibull) for the baseline hazard. This distribution allows us to cover the basic hazard shapes of interest in practice: constant, bathtub, …
Dependent survival data arise in many contexts. One context is clustered survival data, where survival data are collected on clusters such as families or medical centers. Dependent survival data also arise when multiple survival times are recorded for each individual. Frailty models is one common approach to handle such data. In frailty models, the dependence is expressed in terms of a random effect, called the frailty. Frailty models have been used with both Cox proportional hazards model and the accelerated failure time model. This paper reviews recent developments in the area of frailty mod…
