Frontiers in Survival Analysis: Models, Inference, and Tools

Most existing cure models assume homogeneous latent cause structures and rely primarily on scalar covariates. We propose a functional two-component cure model that incorporates functional covariates and allows heterogeneous latent cause distributions through a mixture of power series distributions. This model generalizes both the mixture cure model and the promotion time cure model to functional data with a cured fraction. We employ an expectation–maximization algorithm and a semiparametric penalized spline approach to estimate dynamic functional coefficients for both incidence and latency components, enforcing smoothness via roughness penalties. Simulation studies show satisfactory performance in parameter and baseline survival estimation. The clinical utility of the proposed method is illustrated using National Health and Nutrition Examination Survey 2003–2006 data, where minute-level physical activity trajectories were analyzed in relation to all-cancer mortality through 2019, adjusting for biological factors. The results highlight how latent mixing structures capture unobserved population heterogeneity and how daily activity patterns are associated with cancer mortality risk. 

In time-to-event data of recent cancer clinical trials, it is often the case that some patients never experience the event of interest even after a sufficiently long follow-up period. Patients who are not susceptible to the event of interest are considered cured, and the rest of the population uncured. Summarizing the data for the cured and uncured populations separately will help in understanding the data.
The median survival time is often used to summarize the survival time of the uncured population. In survival analysis with a cured population, parametric cure models are commonly used, and the median survival time for the uncured population is often estimated parametrically. A non-parametric estimate of the median survival time can be obtained without the risk of model misspecification. Maller and Zhou proposed a point estimate of a non-parametric survival function for the uncured population, but the interval estimation has not been detailed.
In this study, we approximated the standard error of the median survival time based on the Kaplan-Meier estimate using the delta method and constructed confidence intervals. We evaluated their performance via a Monte Carlo simulation. 

Recurrent events are frequently observed in biomedical studies, and often they consist of more than one type of events of interests. Marginal analysis of each type of recurrent event is useful but cannot address questions on the relationship between different types of recurrent events. In this work, we study a dynamic association model. Our estimating equations are constructed based on the stochastic processes embedded with bivariate recurrent events data. The proposed estimation can be implemented by an efficient and stable algorithm. Our proposals are illustrated via simulation studies and an application to a real dataset. 

This work develops a statistical framework for regression analysis with ordinal outcomes, where the important covariates are subject to right censoring and a portion of the population is cured, meaning that the cured individuals will never experience an event. We propose a two-stage regression analysis method for cross-sectionally sampled data with an ordinal outcome, measured at the time of sampling. The proposed approach, first, models the probability of being cured and the distribution of the time-to-event covariate for the uncured individuals. In the second stage, we estimate the ordinal outcome regression, using either a proportional odds regression model or an adjacent categories regression. Our approach accounts for censored covariates and for the presence of cured subjects in the data, which improves estimation efficiency compared to the complete case analysis and removes bias compared to naive analysis. We provide identifiability conditions for our approach, develop asymptotic distribution of our estimator and investigate its performance in simulations. Finally, we apply it to the Adult Perthes' Disease data. An R package implementing our approach is also developed. 

Progression-free survival (PFS) is a common endpoint in oncology trials, yet its estimation becomes challenging when progression is interval-censored and death is right-censored. Standard approaches, such as the Aalen–Johansen estimator fail to respect the clinical ordering constraint that progression must occur prior to death. We propose a nonparametric maximum likelihood estimator (NPMLE) for the joint cumulative distribution function of progression and death, employing a sieve approach with I- and M-splines to ensure monotonicity and clinical interpretability. The proposed method is fit via convex optimization and accommodates both right- and interval-censoring mechanisms. Simulation studies under a Clayton copula framework demonstrate that the proposed estimator gives unbiased estimates of PFS and cause-specific cumulative incidence functions with substantially reduced bias as compared to standard approaches. This work provides a practical and theoretically rigorous tool for analyzing interval-censored progression endpoints in oncology and offers a foundation for extensions to evaluation in the context of competing risks. 

Background:
Clinical trials for Huntington disease (HD) increasingly aim to intervene before the onset of irreversible neurodegeneration. Achieving this goal requires identifying individuals at higher risk of transitioning between Huntington Disease Integrated Staging System (HD-ISS) stages and understanding how such risk stratification may improve clinical trial efficiency.

Methods:
We analyzed data from the Enroll-HD observational study (Periodic Dataset 7; 2012--2024) to model time to HD-ISS stage transitions (Stage 0 → 1, 1 → 2, and 2 → 3). Parametric accelerated failure time (AFT) models were fitted using candidate distributions selected via AIC/BIC and comparison with Kaplan--Meier estimates. Predictive performance of candidate markers---including CAP score, prognostic index normalized (PIN), composite Unified Huntington's Disease Rating Scale (cUHDRS), and individual components (CAG repeat length, TMS, SDMT)---was evaluated using the area under the receiver operating characteristic curve (AUC) with cross-validation. Individuals were stratified into risk quartiles based on the strongest predictor for each transition. These risk groups were then used to evaluate clinical trial enrichment strategies through sample size calculations under AFT-based treatment effect assumptions.

Results:
The generalized gamma distribution provided the best fit across stage transitions. CAP score was the strongest predictor for the Stage 0 → 1 transition (cross-validated AUC 0.87), whereas PIN was most predictive for Stage 1 → 2 (AUC 0.64), and cUHDRS for Stage 2 → 3 (AUC 0.54). Risk stratification demonstrated substantially shorter transition times among higher-risk quartiles. Enrichment strategies that restricted enrollment to higher-risk subgroups markedly reduced required sample sizes. For example, in a one-year trial targeting the Stage 0 → 1 transition, restricting enrollment to the highest CAP quartile reduced required sample size by approximately four-fold for detecting a moderate treatment effect.

Conclusions:
Predictive markers of HD progression can identify individuals at elevated risk of stage transition. Incorporating risk stratification into trial enrollment may substantially improve the efficiency of HD clinical trials targeting early disease stages.