{"title":"Gradient boosting machine for survival prediction in studies with general failure-time outcome-dependent sampling design.","authors":"Haolin Li, Haibo Zhou, Jianwen Cai","doi":"10.1007/s10985-026-09732-y","DOIUrl":"10.1007/s10985-026-09732-y","url":null,"abstract":"<p><p>Outcome-dependent sampling (ODS) designs are widely used in epidemiological and biomedical research as cost-effective alternatives to full cohort studies. While existing research has focused on parameter estimation and inference under specific models, survival prediction in ODS settings remains underexplored. In this paper, we propose a gradient boosting machine tailored for survival prediction in studies conducted using general failure-time ODS designs. Our approach integrates a weighting scheme to correct for sampling bias and improves predictive accuracy. We introduce a weighted empirical risk based on the integrated Brier score for hyperparameter tuning and establish its convergence to the corresponding integrated Brier-score risk. The proposed method is evaluated through extensive simulations and applied to the Cancer Incidence and Mortality of Uranium Miners Study, and is shown to have improved effectiveness in survival prediction. This work advances machine learning methods for ODS studies, offering valuable insights for personalized medicine and clinical decision-making in failure-time ODS settings.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13668957/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149185620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Estimating heterogeneous treatment effects with survival outcomes via a deep survival learner.","authors":"Yuming Sun, Jian Kang, Yi Li","doi":"10.1007/s10985-026-09734-w","DOIUrl":"10.1007/s10985-026-09734-w","url":null,"abstract":"<p><p>Estimating heterogeneous treatment effects in survival settings is complicated by right censoring as well as the time-varying nature of the estimand. While the conditional average treatment effect (CATE) provides a natural target, most existing approaches focus on a single prespecified time point and do not account for temporal trajectory, leading to instability in estimation. We propose a deep survival learner (DSL) for estimating heterogeneous treatment effects with right-censored outcomes. The method is based on a doubly robust pseudo-outcome whose conditional expectation identifies time-specific CATEs under standard assumptions. This construction remains unbiased if either the outcome model or the treatment assignment model is correctly specified, when properly accounting for censoring. To estimate CATEs over a clinically relevant time spectrum, DSL employs a multi-output deep neural network with shared representations, enabling joint estimation of treatment effect trajectories. From a theoretical perspective, we derive error bounds for both pointwise and joint estimation over time. We show that joint estimation can leverage temporal structure to control estimation error without incurring much additional approximation cost under smoothness conditions, leading to improved stability relative to separate estimation. Cross-fitting is incorporated to reduce overfitting and mitigate bias arising from flexible nuisance estimation. Simulation studies demonstrate favorable finite-sample performance, particularly under nuisance model misspecification. Applied to the Boston Lung Cancer Study, DSL reveals heterogeneity in the effects of perioperative chemotherapy across patient characteristics and over time.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13672394/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Shape-constrained semiparametric maximum likelihood for backward time under an accelerated failure time model.","authors":"Jing Qin","doi":"10.1007/s10985-026-09730-0","DOIUrl":"https://doi.org/10.1007/s10985-026-09730-0","url":null,"abstract":"<p><p>We investigate semiparametric maximum likelihood inference for backward (current-duration, backward-recurrence) times arising in cross-sectional (prevalent-cohort) sampling under an accelerated failure time (AFT) model for the underlying forward lifetime. A key observation is that, after a suitable transformation, the baseline density of backward times is intrinsically monotone non-increasing. Exploiting this shape constraint yields a profile likelihood estimator for the regression parameter β together with a nonparametric maximum likelihood estimator (NPMLE) of the monotone density via the Grenander estimator. Because the Grenander estimator is known to behave poorly near the origin-often causing instability in AFT parameter estimation-we additionally consider a log-concavity constraint on the backward density, which leads to substantially more stable estimation in practice. We present a rigorous formulation of the likelihood, provide sufficient conditions for identifiability, and establish consistency of the profile MLE. We further highlight the importance of restricting the parameter space for β to a compact set: this is essential for both identifiability and numerical stability, as the likelihood may otherwise be flat or ill-behaved. Finally, we propose a practical multi-start estimation procedure that integrates shape-restricted projection of the nonparametric component with derivative-free optimization of the parametric component.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149002759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"No cure for cure models: killed by competing risks.","authors":"Hein Putter, Per Kragh Andersen","doi":"10.1007/s10985-026-09729-7","DOIUrl":"10.1007/s10985-026-09729-7","url":null,"abstract":"<p><p>Cure models have become increasingly popular over the last couple of decades. An appealing element of cure models is the idea that part of the population is immune to the event of interest. We argue that, in medical applications, the use of cure models is limited. Thus, true cure cannot exist if the event of interest includes death, as death is inevitable, and if death is excluded then competing risks must be accounted for. In this case, we find it more natural to model the cumulative incidence of both the event of interest and competing events over time, avoiding unreliable estimates at infinity and using observed data. Further, we point out two more technical difficulties with cure models arising, first, from the fact that cure models rely on identifying plateaus in survival curves at the tail, where data may be sparse and unreliable and, second, the mixture cure model faces issues with practical identifiability of covariate effects in the incidence model (probability of cure), especially alongside proportional hazards assumptions in the latency model (survival model, conditionally on not being cured). We also comment on hybrid extensions of the classical single event cure model that allow for both competing risks and a cured fraction. We support our arguments with real and simulated data. Full data and code are available online.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 4","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13562180/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148931743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Siddharth Roy, Anindya Roy, Megan A Clarke, Ana Gradissimo, Robert D Burk, Nicolas Wentzensen, Danping Liu
{"title":"A latent health process model for dynamic risk prediction with application to an HPV study.","authors":"Siddharth Roy, Anindya Roy, Megan A Clarke, Ana Gradissimo, Robert D Burk, Nicolas Wentzensen, Danping Liu","doi":"10.1007/s10985-026-09723-z","DOIUrl":"10.1007/s10985-026-09723-z","url":null,"abstract":"<p><p>Individuals with an elevated risk of disease (ex., HPV infection) are often monitored with increased screening along with the collection of additional biomarkers to improve risk assessment at each screening visit. These individuals may experience disease progression, but may also transition back to a low-risk status (ex., clearing an infection). However, standard joint modeling approaches for dynamic risk prediction for these at-risk individuals have several limitations. First, it is challenging to flexibly link a noisy longitudinal biomarker to both interval-censored disease progression and remission without restrictive assumptions on the association structure and survival process. Furthermore, for non-terminal events, standard joint modeling approaches often ignore biomarkers collected after the event, meaning biomarker models do not account for the event status. We propose to model the health status of at-risk individuals as an underlying stochastic process constrained between two thresholds: an upcrossing representing a transition to low-risk status and a downcrossing representing disease progression. We link the change in the health process to a longitudinal biomarker whose trajectory can change based on the event. Simulations and a real data set demonstrate the flexibility of our proposed approach, showing substantial improvements in risk estimates by capturing an event's impact on the biomarker trajectory and utilizing two thresholds to account for the competing risks of disease progression and remission.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Competing risk model with a nonparametric form of relative risks.","authors":"Youngjin Cho, Pang Du","doi":"10.1007/s10985-026-09728-8","DOIUrl":"10.1007/s10985-026-09728-8","url":null,"abstract":"<p><p>Competing risks, referring to multiple mutually exclusive cause-specific events in survival data, are commonly seen in medical and engineering studies. In the presence of covariates, the Cox proportional hazards model is the most common approach to modeling covariate effects as the relative risk component for each cause-specific hazard function. However, the linear form of covariate effects in the existing models can be too restrictive to satisfy in practice. In this work, we propose a Cox regression model for competing risk survival data where the relative risk of each cause-specific hazard takes a flexible nonparametric form. The effects of multiple covariates are modeled under a smoothing spline ANOVA framework allowing for nonparametric effect components among covariates. For each cause-specific hazard, we develop an estimation procedure based on the optimization of penalized partial likelihood. We show that our spline estimators of the log relative risk functions can achieved the optimal nonparametric rates of convergence. Through simulation studies, we demonstrate the numerical performance of the proposed method. We then apply our approach to a multiple myeloma dataset, where the effects of gene expressions on cancer and non-cancer related death are investigated. The nonlinear trend revealed in our analysis offers a strong support to the need of a nonparametric modeling approach like ours.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13490231/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Herbert P Susmann, Nicholas T Williams, Richard Liu, Jessica G Young, Iván Díaz
{"title":"Computationally and statistically efficient estimation of time-smoothed counterfactual curves.","authors":"Herbert P Susmann, Nicholas T Williams, Richard Liu, Jessica G Young, Iván Díaz","doi":"10.1007/s10985-026-09727-9","DOIUrl":"10.1007/s10985-026-09727-9","url":null,"abstract":"<p><p>Longitudinal causal inference is concerned with defining, identifying, and estimating the effect of a time-varying intervention on a time-varying outcome that is indexed by a follow-up time. In an observational study, Robins's generalized g-formula can identify causal effects induced by a broad class of time-varying interventions. Various methods for estimating the generalized g-formula have been posed for different outcome types, such as a failure event indicator by a specified time (e.g. mortality by 5 year follow-up), as well as continuous or dichotomous/multi-valued outcomes measures at a specified time (e.g. blood pressure in mmHg or an indicator of high blood pressure at 5-year follow-up). Multiply-robust, data-adaptive estimators leverage flexible nonparametric estimation algorithms while allowing for statistical inference. However, extant methods do not accommodate pooling estimation across time points when multiple outcomes are measured over time, which can lead to substantial loss of precision. We propose a novel multiply-robust estimator of the generalized g-formula that accommodates pooled estimation over numerous available outcome measures, which we refer to as time-smoothing. Our approach accommodates any intervention that can be described as a Longitudinal Modified Treatment Policy, a flexible class suitable for binary, multi-valued, and continuous longitudinal treatments. Our method produces an estimate of the effect curve: the causal effect of the intervention on the outcome at each measurement time, taking into account censoring and non-monotonic outcome missingness patterns. In simulations we find that the proposed algorithm outperforms extant multiply-robust approaches for effect curve estimation in scenarios with high degrees of outcome missingness and when there is low covariate overlap. We apply the method to study longitudinal effects of union membership on wages. The proposed estimator is available in the LMTP package at https://github.com/lmtp/tree/curve .</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148800749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Correction to: Nonparametric estimation of conditional survival function with time-varying covariates using DeepONet.","authors":"Bingqing Hu, Bin Nan","doi":"10.1007/s10985-026-09724-y","DOIUrl":"10.1007/s10985-026-09724-y","url":null,"abstract":"","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13473235/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148762857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Transition dynamics modeling of pre-trained accelerometry representations for time to diagnosis of Parkinson's disease.","authors":"Huiming Xie, Fei Xue, Xiao Wang","doi":"10.1007/s10985-026-09721-1","DOIUrl":"10.1007/s10985-026-09721-1","url":null,"abstract":"<p><p>Early identification of Parkinson's disease is critical for timely intervention. Disruptions in sleep architecture and changes in physical activity patterns have been reported years before motor symptom onset, yet prodromal behavioral changes spanning sleep and daytime activity patterns are subtle and difficult to detect with conventional clinical tools. Wearable sensors provide a scalable means of monitoring these behaviors in natural settings, but extracting meaningful, interpretable features from high-frequency, unlabeled time series remains a major challenge. We present an end-to-end framework for assessing Parkinson's disease risk from wrist-worn accelerometry via automated feature extraction and survival modeling of time to diagnosis. Behavioral states are derived from unlabeled data using pretrained models including random forests with hidden Markov models for physical activity classification and a self-supervised learning based sleep staging model. We jointly model both sleep stage and physical activity sequences using hierarchical nonstationary Markov chains stratified by time of day and temporal resolution, characterizing individual-level behavioral rhythms and transition dynamics. Gradient-boosted Cox proportional hazards models are then used to estimate Parkinson's disease risk from these transition-based features. Applied to accelerometer data from the UK Biobank, our approach outperforms baselines that exclude dynamic modeling or rely on traditional functional data analysis, while providing interpretable predictors from long sequences of wearable sensor data. This demonstrates the potential of integrating pretrained AI models, temporal sequence modeling, and survival analysis to detect early behavioral signatures of neurodegeneration.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13433425/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wenhao Li, Shikun Wang, Zhe Yin, Brad C Astor, Wei Yang, Tom H Greene, Liang Li
{"title":"Backward joint model for the joint dynamic prediction of time-to-event and longitudinal data: basic formulation and new developments.","authors":"Wenhao Li, Shikun Wang, Zhe Yin, Brad C Astor, Wei Yang, Tom H Greene, Liang Li","doi":"10.1007/s10985-026-09725-x","DOIUrl":"10.1007/s10985-026-09725-x","url":null,"abstract":"<p><p>Dynamic prediction of future clinical outcomes based on longitudinally measured predictors plays a crucial role in disease management and patient counseling, particularly when conventional static models are inadequate. Joint modeling of longitudinal and time-to-event data provides a useful framework for addressing this challenge. In this paper, we present a comprehensive development of the recently proposed backward joint model (BJM; Shen and Li, 2021), which factorizes the likelihood into the distribution of time-to-event data and the conditional distribution of longitudinal data given the event time. This structure facilitates computation and is well-suited for multivariate longitudinal data. We introduce several novel developments to the BJM, including the extrapolation and two-part specifications, as well as the incorporation of competing risks. We also address an important yet underexplored problem in the literature: predicting future longitudinal trajectories conditional on predicted event times. Additionally, we explore the connection between BJM and existing joint modeling approaches. All these extensions preserve the computational advantages of the basic BJM formulation, including one-dimensional numerical integration, convex optimization via the EM algorithm, and a quick procedure for consistent estimation using standard software. We evaluate the method's performance through simulation studies and illustrate its utility in a chronic kidney disease application.</p>","PeriodicalId":49908,"journal":{"name":"Lifetime Data Analysis","volume":"32 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13433653/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148664744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}