Dynamic risk assessment is an important tool for healthcare providers to inform treatment selection and optimize patient outcomes. Frequent evaluation of clinical status provides invaluable information on adverse event risk and/or treatment urgency, based on the changes in predictive biomarkers. Landmark analysis is a useful approach for dynamic risk assessment that obviates the complexity of jointly modeling longitudinal covariates and time-to-event outcome. Traditional landmark methods often rely on the proportional hazards assumption and assume independent censoring. We propose novel methods to broaden the scope of landmark analysis by directly modeling the restricted residual mean survival time (RRMST) at each landmark date while accommodating dependent censoring. Advantages of RMST models include removing the assumption that the (hazard) model is correct at every time point; RMST models instead consider a single capped survival time. Moreover, investigators may prefer the area under the survival curve to the hazard function as a metric in terms of interpretability. We derive the asymptotic properties of our proposed estimators and validate their performance in finite samples through extensive simulations. We apply the proposed methods to analyze outcomes under natural end-stage liver disease (ESLD) history (i.e., in the absence of liver transplantation).
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.
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.
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.
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.
