We study explained variation under the additive hazards regression model for right-censored data. We consider different approaches for developing such a measure, and focus on one that estimates the proportion of variation in the failure time explained by the covariates. We study the properties of the measure both analytically, and through extensive simulations. We apply the measure to a well-known survival data set as well as the linked Surveillance, Epidemiology and End Results (SEER)-Medicare database for prediction of mortality in early-stage prostate cancer patients using high dimensional claims codes.
Marginal structural models (MSMs) allow for causal analysis of longitudinal data. The MSMs were originally developed as discrete time models. Recently, continuous-time MSMs were presented as a conceptually appealing alternative for survival analysis. In applied analyses, it is often assumed that the theoretical treatment weights are known, but these weights are usually unknown and must be estimated from the data. Here we provide a sufficient condition for a class of continuous-time MSMs to be consistent even when the weights are estimated, and we show how additive hazard models can be used to …
We discuss causal mediation analyses for survival data and propose a new approach based on the additive hazards model. The emphasis is on a dynamic point of view, that is, understanding how the direct and indirect effects develop over time. Hence, importantly, we allow for a time varying mediator. To define direct and indirect effects in such a longitudinal survival setting we take an interventional approach (Didelez (2018)) where treatment is separated into one aspect affecting the mediator and a different aspect affecting survival. In general, this leads to a version of the non-parametric g-…
Survival analysis (SA) is an active field of research that is concerned with time-to-event outcomes and is prevalent in many domains, particularly biomedical applications. Despite its importance, SA remains challenging due to small-scale data sets and complex outcome distributions, concealed by truncation and censoring processes. The piecewise exponential additive mixed model (PAMM) is a model class addressing many of these challenges, yet PAMMs are not applicable in high-dimensional feature settings or in the case of unstructured or multimodal data. We unify existing approaches by proposing D…
We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability distribution, mean and variance. An application to survival analysis and reliability data sets based on confidence bands for estimated hazard rate functions is also provided.
In contrast to the popular Cox model which presents a multiplicative covariate effect specification on the time to event hazards, the semiparametric additive risks model (ARM) offers an attractive additive specification, allowing for direct assessment of the changes or the differences in the hazard function for changing value of the covariates. The ARM is a flexible model, allowing the estimation of both time-independent and time-varying covariates. It has a nonparametric component and a regression component identified by a finite-dimensional parameter. This chapter presents an efficient appro…
Excess hazard modeling is one of the main tools in population-based cancer survival research. Indeed, this setting allows for direct modeling of the survival due to cancer even in the absence of reliable information on the cause of death, which is common in population-based cancer epidemiology studies. We propose a unifying link-based additive modeling framework for the excess hazard that allows for the inclusion of many types of covariate effects, including spatial and time-dependent effects, using any type of smoother, such as thin plate, cubic splines, tensor products and Markov random fiel…
Based on a data set obtained in a dental longitudinal study, conducted in Flanders (Belgium), the joint time to caries distribution of permanent first molars was modeled as a function of covariates. This involves an analysis of multivariate continuous doubly-interval-censored data since: (i) the emergence time of a tooth and the time it experiences caries were recorded yearly, and (ii) events on teeth of the same child are dependent. To model the joint distribution of the emergence times and the times to caries, we propose a dependent Bayesian semiparametric model. A major feature of the propo…
In survival analysis, Cox model is widely used for most clinical trial data. Alternatives include the additive hazard model, the accelerated failure time (AFT) model and a more general transformation model. All these models assume that the effects for all covariates are on the same scale. However, it is possible that for different covariates, the effects are on different scales. In this paper, we propose a shape-invariant hazard regression model that allows us to estimate the multiplicative treatment effect with adjustment of covariates that have non-multiplicative effects. We propose moment-b…
We propose inference procedures for general nonparametric factorial survival designs with possibly right-censored data. Similar to additive Aalen models, null hypotheses are formulated in terms of cumulative hazards. Thereby, deviations are measured in terms of quadratic forms in Nelson-Aalen-type integrals. Different to existing approaches this allows to work without restrictive model assumptions as proportional hazards. In particular, crossing survival or hazard curves can be detected without a significant loss of power. For a distribution-free application of the method, a permutation strate…
Nokia Bell Labs France（诺基亚贝尔实验室法国）；Inria（法国国家信息与自动化研究所）；Safran Tech（赛峰集团技术公司（Safran Tech））
In this paper, we make an experimental comparison of semi-parametric (Cox proportional hazards model, Aalen's additive regression model), parametric (Weibull AFT model), and machine learning models (Random Survival Forest, Gradient Boosting with Cox Proportional Hazards Loss, DeepSurv) through the concordance index on two different datasets (PBC and GBCSG2). We present two comparisons: one with the default hyper-parameters of these models and one with the best hyper-parameters found by randomized search.
Extended cure survival models enable to separate covariates that affect the probability of an event (or `long-term' survival) from those only affecting the event timing (or `short-term' survival). We propose to generalize the bounded cumulative hazard model to handle additive terms for time-varying (exogenous) covariates jointly impacting long- and short-term survival. The selection of the penalty parameters is a challenge in that framework. A fast algorithm based on Laplace approximations in Bayesian P-spline models is proposed. The methodology is motivated by fertility studies where women's …
CoxSE: Exploring the Potential of Self-Explaining Neural Networks with Cox Proportional Hazards Model for Survival Analysis
Center for Applied Intelligent Systems Research (CAISR)（应用智能系统研究中心）；Halmstad University（哈马斯特德大学）；Centre for Environmental and Climate Science（环境与气候科学中心）；Lund University（吕勒奥大学）；Research Institutes of Sweden (RISE)（瑞典研究机构）
Instrumental variable is an essential tool for addressing unmeasured confounding in observational studies. Two stage predictor substitution (2SPS) estimator and two stage residual inclusion(2SRI) are two commonly used approaches in applying instrumental variables. Recently 2SPS was studied under the additive hazards model in the presence of competing risks of time-to-events data, where linearity was assumed for the relationship between the treatment and the instrument variable. This assumption may not be the most appropriate when we have binary treatments. In this paper, we consider the 2SRI e…
Popular parametric and semiparametric hazards regression models for clustered survival data are inappropriate and inadequate when the unknown effects of different covariates and clustering are complex. This calls for a flexible modeling framework to yield efficient survival prediction. Moreover, for some survival studies involving time to occurrence of some asymptomatic events, survival times are typically interval censored between consecutive clinical inspections. In this article, we propose a robust semiparametric model for clustered interval-censored survival data under a paradigm of Bayesi…
Peter the Great St.Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
A new robust algorithm based of the explanation method SurvLIME called SurvLIME-KS is proposed for explaining machine learning survival models. The algorithm is developed to ensure robustness to cases of a small amount of training data or outliers of survival data. The first idea behind SurvLIME-KS is to apply the Cox proportional hazards model to approximate the black-box survival model at the local area around a test example due to the linear relationship of covariates in the model. The second idea is to incorporate the well-known Kolmogorov-Smirnov bounds for constructing sets of predicted …
The "meningitis belt" is a region in sub-Saharan Africa where annual outbreaks of meningitis occur, with large epidemics observed cyclically. While we know that meningitis is heavily dependent on seasonal trends (in particular, weather), the exact pathways for contracting the disease are not fully understood and warrant further investigation. This manuscript examines meningitis trends in the context of survival analysis, quantifying underlying seasonal patterns in meningitis rates through the hazard rate for the population of Navrongo, Ghana. We compare three candidate models: the commonly use…
Many time-to-event studies are complicated by the presence of competing risks. Such data are often analyzed using Cox models for the cause specific hazard function or Fine-Gray models for the subdistribution hazard. In practice regression relationships in competing risks data with either strategy are often complex and may include nonlinear functions of covariates, interactions, high-dimensional parameter spaces and nonproportional cause specific or subdistribution hazards. Model misspecification can lead to poor predictive performance. To address these issues, we propose a novel approach to fl…
University of California, San Diego（加州大学圣地亚哥分校）；Halicioğlu Data Science Institute, University of California, San Diego（加州大学圣地亚哥分校哈利西奥卢数据科学研究所）
Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semi-parametric models, such as the Cox model, have been assumed. These often rely on strong proportionality assumptions of the hazard that might be violated in practice. Moreover, they do not often include covariate information updated over time. We propose a new flexible method for survival prediction: DeepHazard, a neural network for time-varying risks. Our approach is tailored for a wide range of continuous hazards forms, with…
In epidemiological studies of time-to-event data, a quantity of interest to the clinician and the patient is the risk of an event given a covariate profile. However, methods relying on time matching or risk-set sampling (including Cox regression) eliminate the baseline hazard from the likelihood expression or the estimating function. The baseline hazard then needs to be estimated separately using a non-parametric approach. This leads to step-wise estimates of the cumulative incidence that are difficult to interpret. Using case-base sampling, Hanley & Miettinen (2009) explained how the parametr…
Peter the Great St.Petersburg Polytechnic University (SPbPU)（圣彼得堡彼得大帝理工大学）
A new method called SurvLIME for explaining machine learning survival models is proposed. It can be viewed as an extension or modification of the well-known method LIME. The main idea behind the proposed method is to apply the Cox proportional hazards model to approximate the survival model at the local area around a test example. The Cox model is used because it considers a linear combination of the example covariates such that coefficients of the covariates can be regarded as quantitative impacts on the prediction. Another idea is to approximate cumulative hazard functions of the explained m…
Genome-Wide Association Studies (GWAS) explain only a small fraction of heritability for most complex human phenotypes. Genomic heritability estimates the variance explained by the SNPs on the whole genome using mixed models and accounts for the many small contributions of SNPs in the explanation of a phenotype. This paper approaches heritability from a machine learning perspective, and examines the close link between mixed models and ridge regression. Our contribution is twofold. First, we propose estimating genomic heritability using a predictive approach via ridge regression and Generalized…
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…
In this paper we utilize a survival analysis methodology incorporating Bayesian additive regression trees to account for nonlinear and additive covariate effects. We compare the performance of Bayesian additive regression trees, Cox proportional hazards and random survival forests models for censored survival data, using simulation studies and survival analysis for breast cancer with U.S. SEER database for the year 2005. In simulation studies, we compare the three models across varying sample sizes and censoring rates on the basis of bias and prediction accuracy. In survival analysis for breas…
The identification of accident hot spots is a central task of road safety management. Bayesian count data models have emerged as the workhorse method for producing probabilistic rankings of hazardous sites in road networks. Typically, these methods assume simple linear link function specifications, which, however, limit the predictive power of a model. Furthermore, extensive specification searches are precluded by complex model structures arising from the need to account for unobserved heterogeneity and spatial correlations. Modern machine learning (ML) methods offer ways to automate the speci…
Survival data is encountered in a range of disciplines, most notably health and medical research. Although Bayesian approaches to the analysis of survival data can provide a number of benefits, they are less widely used than classical (e.g. likelihood-based) approaches. This may be in part due to a relative absence of user-friendly implementations of Bayesian survival models. In this article we describe how the rstanarm R package can be used to fit a wide range of Bayesian survival models. The rstanarm package facilitates Bayesian regression modelling by providing a user-friendly interface (us…
We discuss the role of misspecification and censoring on Bayesian model selection in the contexts of right-censored survival and concave log-likelihood regression. Misspecification includes wrongly assuming the censoring mechanism to be non-informative. Emphasis is placed on additive accelerated failure time, Cox proportional hazards and probit models. We offer a theoretical treatment that includes local and non-local priors, and a general non-linear effect decomposition to improve power-sparsity trade-offs. We discuss a fundamental question: what solution can one hope to obtain when (inevitab…
Soil Texture Prediction with Bayesian Generalized Additive Models for Spatial Compositional Data
Universitat Politècnica de València（瓦伦西亚理工大学）；Biogipuzkoa Health Research Institute（比奥吉普斯夸健康研究所）；Deusto Physical TherapIker, Faculty of Health Sciences, University of Deusto（德乌斯托大学健康科学学院德乌斯托物理治疗Iker）；School of Science and Technology, IE University（IE大学科学与技术学院）
