Cheng K. Lee, Jenq-Daw Lee
A survival model is derived from the exponential function using the concept of fractional differentiation. The hazard function of the proposed model generates various shapes of curves including increasing, increasing-constant-increasing, increasing-decreasing-increasing, and so-called bathtub hazard curve. The model also contains a parameter that is the maximum of the survival time.
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Model Identifiability for Bivariate Failure Time Data with Competing Risk: Non-parametric Cause-specific Hazards and Gamma Frailty
本研究探讨了带有竞争风险的二元生存数据在非参数基线特定原因风险和不同Gamma脆弱性分布下的模型可识别性，证明了双非参数模型的不可识别性，并验证了四种Gamma脆弱性模型在一般假设下的可识别性。
Model-Induced Hazard Geometry and Functional Representations in Survival Analysis
该研究针对生存分析，通过模型诱导的切空间等形式化风险几何约束，扩展AFT时间尺度并建立风险函数的推断方法，经模拟和肺癌应用验证了模型限制对风险函数表示的传播。
Rethinking Individual Risk and Aggregation in Survival Analysis: A Latent Mechanism Framework
本文提出一个潜在机制框架，明确个体风险与生存数据之间的关系，揭示生存分析中异质性、可识别性和解释的统一理解。
Neural Frailty Machine: Beyond proportional hazard assumption in neural survival regressions
本研究提出神经脆弱性机（NFM）框架，结合乘性脆弱性思想与神经网络处理生存回归的异质性和非线性依赖，推导出两种高效训练的模型，在理论上提供收敛速率保证，实验中在6个基准数据集上性能优于现有最优生存模型。
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…
Higher criticism for rare and weak non-proportional hazard deviations in survival analysis
本文提出基于高阶批评的生存数据比较方法，对罕见且弱的非比例风险差异敏感，功效优于对数秩检验，并在理论框架下分析了渐近功效与相变特性。
We present a new estimator of the restricted mean survival time in randomized trials where there is right censoring that may depend on treatment and baseline variables. The proposed estimator leverages prognostic baseline variables to obtain equal or better asymptotic precision compared to traditional estimators. Under regularity conditions and random censoring within strata of treatment and baseline variables, the proposed estimator has the following features: (i) it is interpretable under violations of the proportional hazards assumption; (ii) it is consistent and at least as precise as the …
The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan-Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards commonly a log-rank test is performed in order to investigate whether there is a difference in survival, or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inf…
Local differential privacy in survival analysis using private failure indicators
本文提出在局部差分隐私下，通过私有化失败指标并用非参数核估计器估计累积风险函数，证明其一致性及极小极大最优性。
Relative Survival Analysis Using Bayesian Decision Tree Ensembles
本研究提出基于贝叶斯加性回归树的相对生存分析方法，扩展至比例与非比例风险场景，结合英国结肠癌数据验证其可识别癌症生存不平等的驱动因素。
In a survival analysis context we suggest a new method to estimate the piecewise constant hazard rate model. The method provides an automatic procedure to find the number and location of cut points and to estimate the hazard on each cut interval. Estimation is performed through a penalized likelihood using an adaptive ridge procedure. A bootstrap procedure is proposed in order to derive valid statistical inference taking both into account the variability of the estimate and the variability in the choice of the cut points. The new method is applied both to simulated data and to the Mayo Clinic …
Modifying Survival Models To Accommodate Thresholding Behavior
针对受外部物理过程约束时生存模型过于僵化的问题，本文提出可刻画累积风险与事件发生关系、尤其能捕捉阈值行为的改进生存模型，并通过生理学应用验证其实用性。
We consider Bayesian hierarchical models for survival analysis, where the survival times are modeled through an underlying diffusion process which determines the hazard rate. We show how these models can be efficiently treated by means of Markov chain Monte Carlo techniques.
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 appears in various fields such as medicine, economics, engineering, and business. Recent studies showed that the Ordinary Differential Equation (ODE) modeling framework unifies many existing survival models while the framework is flexible and widely applicable. However, naively applying the ODE framework to survival analysis problems may model fiercely changing density function which may worsen the model's performance. Though we can apply L1 or L2 regularizers to the ODE model, their effect on the ODE modeling framework is barely known. In this paper, we propose hazard gradie…
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 two harmonized efficacy studies to prevent HIV infection through multiple infusions of the monoclonal antibody VRC01, a key objective is to evaluate whether the serum concentration of VRC01, which changes cyclically over time along with the infusion schedule, is associated with the rate of HIV infection. Simulation studies are needed in the development of such survival models. In this paper, we consider simulating event time data with a continuous time-varying covariate whose values vary with time through multiple drug administration cycles, and whose effect on survival changes differently …
Spatial Proportional Hazards Model with Differential Regularization
本文提出一种具有差异正则化的空间比例危害模型，通过非参数函数建模空间效应，并利用有限元方法和筛法保证估计的一致性和渐近正态性，实验证明其优于现有方法。
One of the central goals in precision health is the understanding and interpretation of high-dimensional biological data to identify genes and markers associated with disease initiation, development, and outcomes. Though significant effort has been committed to harness gene expression data for multiple analyses while accounting for time-to-event modeling by including survival times, many traditional analyses have focused separately on non-negative matrix factorization (NMF) of the gene expression data matrix and survival regression with Cox proportional hazards model. In this work, Cox proport…
Monitoring time to event in registry data using CUSUMs based on relative survival models
提出基于生存对数似然比的 CUSUM 程序，在死因信息缺失时利用相对生存模型监测登记数据中生存时间分布的变化，并扩展至超额风险设置。
Dynamical Survival Analysis for Modeling Hazard Functions with Nonlinear Systems
本文提出基于高阶微分方程的动态生存分析框架，用于建模具有非线性和振荡特性的危险函数，通过贝叶斯推断和模拟研究验证了其在捕捉时间风险模式方面的有效性。
The Cox regression, a semi-parametric method of survival analysis, is extremely popular in biomedical applications. The proportional hazards assumption is a key requirement in the Cox model. To accommodate non-proportional hazards, we propose to parameterise the shape parameter of the baseline hazard function using the additional, separate Cox-regression term which depends on the vector of the covariates. We call this model the double-Cox model. The R programs for fitting the double-Cox model are available on Github. We formally introduce the double-Cox model with shared frailty and investigat…
Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the covariates and are convenient as they do not require estimation of the baseline hazard rate. Recent approaches have involved learning non-linear representations of the input covariates and demonstrate improved performance. In this paper we argue against such deep parameterizations for survival analysis and experimentally demonstrate that more interpretable semi-par…
ADHAM: Additive Deep Hazard Analysis Mixtures for Interpretable Survival Regression
提出ADHAM可解释加性生存模型，通过条件潜在结构定义子组并合并相似组，在保持预测性能的同时提供人群、子组和个体层面的可解释性见解。
One-sample survival tests in the presence of non-proportional hazards in oncology clinical trials
本文提出了一种结合分段指数模型和加速危害模型的生存检验方法，用于评估单臂试验中治疗效果，通过模拟研究验证了其在不同场景下的优越性。
Extending Cox Proportional Hazards Model with Symbolic Non-Linear Log-Risk Functions for Survival Analysis
提出GCPH模型，利用KAN实现符号化非线性对数风险函数，扩展Cox模型，兼顾可解释性与预测性能，在合成数据和公开基准上验证了其竞争力。
Comparison of the Cox proportional hazards model and Random Survival Forest algorithm for predicting patient-specific survival probabilities in clinical trial data
本研究基于RCT数据集全面比较了Cox回归与RSF在预测生存概率中的表现，发现仅依赖C index评估具局限性，总体性能指标更合理，且RSF替代分裂规则在非比例风险下更优。
Simulation-based assessment of a Bayesian survival model with flexible baseline hazard and time-dependent effects
本研究通过仿真评估基于M样条的灵活贝叶斯生存模型（survextrap R包），在肿瘤临床试验数据上验证其对复杂基线风险和时间效应拟合良好，并为模型选择及默认设置提供指导。
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…
On harmonic oscillator hazard functions
本研究提出一种基于阻尼简谐振子正性约束的参数化风险模型，具备闭式风险与累积风险函数，可捕捉多种风险形态并刻画生存函数尾部，通过真实数据验证了其在生存分析中的适用性。
Unobserved individual heterogeneity is a common challenge in population cancer survival studies. This heterogeneity is usually associated with the combination of model misspecification and the failure to record truly relevant variables. We investigate the effects of unobserved individual heterogeneity in the context of excess hazard models, one of the main tools in cancer epidemiology. We propose an individual excess hazard frailty model to account for individual heterogeneity. This represents an extension of frailty modelling to the relative survival framework. In order to facilitate the infe…
The conventional nonparametric tests in survival analysis, such as the log-rank test, assess the null hypothesis that the hazards are equal at all times. However, hazards are hard to interpret causally, and other null hypotheses are more relevant in many scenarios with survival outcomes. To allow for a wider range of null hypotheses, we present a generic approach to define test statistics. This approach utilizes the fact that a wide range of common parameters in survival analysis can be expressed as solutions of differential equations. Thereby we can test hypotheses based on survival parameter…
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 …
In the process of clinical diagnosis and treatment, the restricted mean survival time (RMST), which reflects the life expectancy of patients up to a specified time, can be used as an appropriate outcome measure. However, the RMST only calculates the mean survival time of patients within a period of time after the start of follow-up and may not accurately portray the change in a patient's life expectancy over time. The life expectancy can be adjusted for the time the patient has already survived and defined as the conditional restricted mean survival time (cRMST). A dynamic RMST model based on …
Medical practitioners use survival models to explore and understand the relationships between patients' covariates (e.g. clinical and genetic features) and the effectiveness of various treatment options. Standard survival models like the linear Cox proportional hazards model require extensive feature engineering or prior medical knowledge to model treatment interaction at an individual level. While nonlinear survival methods, such as neural networks and survival forests, can inherently model these high-level interaction terms, they have yet to be shown as effective treatment recommender system…
CoxSE: Exploring the Potential of Self-Explaining Neural Networks with Cox Proportional Hazards Model for Survival Analysis
CoxSE通过自解释神经网络和Cox比例风险模型提升生存分析的可解释性和鲁棒性，混合模型在稳定性与一致性方面表现最佳。
The Cox model, which remains as the first choice in analyzing time-to-event data even for large datasets, relies on the proportional hazards (PH) assumption. When survival data arrive sequentially in chunks, a fast and minimally storage intensive approach to test the PH assumption is desirable. We propose an online updating approach that updates the standard test statistic as each new block of data becomes available, and greatly lightens the computational burden. Under the null hypothesis of PH, the proposed statistic is shown to have the same asymptotic distribution as the standard version co…
Bayesian calendar-time survival analysis with epidemic curve priors and variant-specific infection hazards
本文提出一种基于流行曲线先验和变种特异性感染危险的贝叶斯日历时间生存分析方法，用于评估干预措施对感染风险的影响。
Dynamic survival analysis: modelling the hazard function via ordinary differential equations
本文提出一种基于自治常微分方程组对风险函数动态进行参数化建模的通用方法，支持解析或数值求解，兼容贝叶斯与最大似然估计，并通过模拟和真实数据案例验证其性能与可解释性。
Understanding the factors that explain differences in survival times is an important issue for establishing policies to improve national health systems. Motivated by breast cancer data arising from the Surveillance Epidemiology and End Results program, we propose a covariate-adjusted proportional hazards frailty model for the analysis of clustered right-censored data. Rather than incorporating exchangeable frailties in the linear predictor of commonly-used survival models, we allow the frailty distribution to flexibly change with both continuous and categorical cluster-level covariates and mod…
Dimension reduction for integrative survival analysis
提出带“到集合的距离”惩罚的受约束最大偏似然降维方法，在多群体 Cox 生存模型中兼顾低秩与稀疏，并通过泛癌分析和外部验证证明其预测优势。
In the analysis of survival data, it is usually assumed that any unit will experience the event of interest if it is observed for a sufficient long time. However, one can explicitly assume that an unknown proportion of the population under study will never experience the monitored event. The promotion time model, which has a biological motivation, is one of the survival models taking this feature into account. The promotion time model assumes that the failure time of each subject is generated by the minimum of N latent event times which are independent with a common distribution independent of…
Survival models are a popular tool for the analysis of time to event data with applications in medicine, engineering, economics, and many more. Advances like the Cox proportional hazard model have enabled researchers to better describe hazard rates for the occurrence of single fatal events, but are unable to accurately model competing events and transitions. Common phenomena are often better described through multiple states, for example: the progress of a disease modeled as healthy, sick and dead instead of healthy and dead, where the competing nature of death and disease has to be taken into…
survextrap: a package for flexible and transparent survival extrapolation
本文介绍了R包survextrap，通过贝叶斯M-spline模型联合分析个体与汇总生存数据，实现灵活透明的长期生存外推，支持比例/非比例风险及治愈等机制，为健康技术评估提供全面工具。
A Scalable Nonparametric Continuous-Time Survival Model through Numerical Quadrature
本文提出QSurv模型，通过高斯-勒让德数值积分实现非参数连续时间生存建模，无需时间离散化或限制分布假设，有效捕捉非平稳危险动态，实验表明其在即时危险函数估计上具有优势。
Antibodies, an essential part of our immune system, develop through an intricate process to bind a wide array of pathogens. This process involves randomly mutating DNA sequences encoding these antibodies to find variants with improved binding, though mutations are not distributed uniformly across sequence sites. Immunologists observe this nonuniformity to be consistent with "mutation motifs", which are short DNA subsequences that affect how likely a given site is to experience a mutation. Quantifying the effect of motifs on mutation rates is challenging: a large number of possible motifs makes…
For many diseases it is reasonable to assume that the hazard rate is not constant across time, but also that it changes in different time intervals. To capture this, we work here with a piecewise survival model. One of the major problems in such piecewise models is to determine the time points of change of the hazard rate. From the practical point of view this can provide very important information as it may reflect changes in the progress of a disease. We present piecewise Weibull regression models with covariates. The time points where change occurs are assumed unknown and need to be estimat…
In heterogeneous cohorts and those where censoring by non-primary risks is informative many conventional survival analysis methods are not applicable; the proportional hazards assumption is usually violated at population level and the observed crude hazard rates are no longer estimators of what they would have been in the absence of other risks. In this paper, we develop a fully Bayesian survival analysis to determine the probabilistically optimal description of a heterogeneous cohort and we propose a novel means of recovering hazard rates and survival functions `decontaminated' of the effects…
A Cosine-Projection Framework for Choosing Among Cox HR, D-RMST, and Average-Hazard Tests in Survival Trials
本文提出余弦投影框架，推导Cox HR、D-RMST、RAH检验的渐近相对效率，揭示删失和入组对效率排序的影响，经CheckMate 057试验和模拟验证，为生存试验检验选择提供统一方法。
Stochastic volatility often implies increasing risks that are difficult to capture given the dynamic nature of real-world applications. We propose using arc length, a mathematical concept, to quantify cumulative variations (the total variability over time) to more fully characterize stochastic volatility. The hazard rate, as defined by the Cox proportional hazards model in survival analysis, is assumed to be impacted by the instantaneous value of a longitudinal variable. However, when cumulative variations pose a significant impact on the hazard, this assumption is questionable. Our proposed B…
We present a general approach to synthesizing evidence of time-to-event endpoints in meta-analyses of aggregate data (AD). Our work goes beyond most previous meta-analytic research by using reconstructed survival data as a source of information. A Bayesian multilevel regression model, called the "meta-analysis of reconstructed survival data" (MARS), is introduced, by modeling and integrating reconstructed survival information with other types of summary data, to estimate the hazard ratio function and survival probabilities. The method attempts to reduce selection bias, and relaxes the presumpt…
An accurate model of patient-specific kidney graft survival distributions can help to improve shared-decision making in the treatment and care of patients. In this paper, we propose a deep learning method that directly models the survival function instead of estimating the hazard function to predict survival times for graft patients based on the principle of multi-task learning. By learning to jointly predict the time of the event, and its rank in the cox partial log likelihood framework, our deep learning approach outperforms, in terms of survival time prediction quality and concordance index…
Communication-efficient distributed hazard difference estimation for heterogeneous multi-site survival data
FedRD是一种通信高效的联邦学习框架，用于分布式生存数据中的风险差估计，提供置信区间和假设检验能力，优于本地和联邦基线方法。
In comparative research on time-to-event data for two groups, when two survival curves cross each other, it may be difficult to use the log-rank test and hazard ratio (HR) to properly assess the treatment benefit. Our aim was to identify a method for evaluating the treatment benefits for two groups in the above situation. We quantified treatment benefits based on an intuitive measure called the area between two survival curves (ABS), which is a robust measure of treatment benefits in clinical trials regardless of whether the proportional hazards assumption is violated or two survival curves cr…
We describe a new approach to estimating relative risks in time-to-event prediction problems with censored data in a fully parametric manner. Our approach does not require making strong assumptions of constant proportional hazard of the underlying survival distribution, as required by the Cox-proportional hazard model. By jointly learning deep nonlinear representations of the input covariates, we demonstrate the benefits of our approach when used to estimate survival risks through extensive experimentation on multiple real world datasets with different levels of censoring. We further demonstra…
A Novel Stratified Analysis Method for Testing and Estimating Overall Treatment Effects on Time-to-Event Outcomes Using Average Hazard with Survival Weight
针对生存加权平均风险（AH）在分层分析中的空白，本文提出一种基于标准化的新型分层方法，可同时以绝对差值和相对指标总结调整分层因素后的组间治疗效应，弥补传统分层方法类似Cochran-Mantel-Haenszel和分层Cox的局限性。
Smooth Transformation Models for Survival Analysis: A Tutorial Using R
本文介绍平滑变换模型框架在R中统一处理多种生存模型，包括非比例风险、相依删失等复杂场景，并利用直肠癌试验数据演示实现。
A neutral comparison of statistical methods for time-to-event analyses under non-proportional hazards
针对非比例风险下事件时间分析无最优共识方法的问题，通过多场景模拟对比多种统计方法的I类错误、效能与置信区间覆盖率，发现可解释性与效能存在权衡，为临床试验分析提供方法选择参考。
We use recurrent-events survival analysis techniques and methods to analyze the duration of Olympic records. The Kaplan-Meier estimator is used to perform preliminary tests and recurrent event survivor function estimators proposed by Wang & Chang (1999) and Pena et al. (2001) are used to estimate survival curves. Extensions of the Cox Proportional Hazards model are employed as well as a discrete-time logistic model for repeated events to estimate models and quantify parameter significance. The logistic model was the best fit to the data according to the Akaike Information Criterion (AIC). We d…
Assessing Delayed Treatment Benefits of Immunotherapy Using Long-Term Average Hazard: A Novel Test/Estimation Approach
针对免疫疗法延迟治疗效应，提出基于长期平均风险（LT-AH）的检验/估计方法，整合限制平均生存时间与平均风险思想，提高检验功效，提供稳健且可解释的治疗效应估计。
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