cox proportional hazards

The causal interpretability of the hazard ratio in randomized controlled trials has long been debated, even under the proportional hazards assumption. This study systematically examines critiques of its causal interpretation and, by integrating the Cox proportional hazards model with modern causal inference frameworks, clarifies the precise conditions under which the hazard ratio can be endowed with a valid causal meaning. The analysis demonstrates that, under specific assumptions, the hazard ratio remains a useful estimator of causal effects, while also highlighting scenarios in which alternative effect measures—such as risk differences or ratios of survival probabilities—may be more appropriate. These findings provide both theoretical grounding and practical guidance for the analysis of time-to-event data in causal settings.

This study addresses the limitations of traditional joint models in clinical longitudinal studies, where repeatedly measured biomarkers or quality-of-life outcomes are often associated with event times but constrained by the proportional hazards assumption, hindering interpretability on the time scale. The authors propose a class of Bayesian semiparametric accelerated failure time joint models that integrate linear mixed-effects models for the longitudinal process and employ Bernstein polynomials to flexibly model the baseline hazard. A time-warping rescaling strategy is introduced to enhance numerical stability and parameter identifiability. By relaxing the proportional hazards assumption, the proposed approach offers more intuitive time-scale interpretations. Simulation studies demonstrate that, when event risk depends on underlying longitudinal trajectories, the method yields more accurate estimates of treatment effects compared to separate modeling approaches and exhibits excellent finite-sample performance.

This study addresses the inefficiency and bias introduced by right-censored covariates in survival analysis, which commonly undermine conventional approaches such as complete-case analysis. Within the Cox proportional hazards framework, the authors propose a novel method that incorporates a weighted averaging strategy into the partial likelihood function: for observations with censored covariates, the corresponding relative risk is replaced by a weighted average derived from fully observed cases. By directly leveraging the censoring information rather than discarding incomplete cases or imputing constant values, the approach mitigates estimation bias. Extensive simulations and analyses of two oncology clinical trials demonstrate that the proposed method substantially improves estimation efficiency and data utilization, outperforming existing strategies for handling censored covariates.

Existing dynamic survival prediction methods lack standardized benchmarking, particularly for high-dimensional longitudinal biomedical data. Method: This study systematically evaluates multi-step dynamic survival prediction approaches—including mixed-effects models, multivariate functional principal component analysis, Cox regression, random survival forests, and landmark analysis—across multiple real-world datasets. We rigorously control key factors (sample size, covariate dimensionality, and follow-up duration) to assess predictive accuracy, robustness, and computational efficiency. Contribution/Results: The analysis reveals critical trade-offs among modeling choices, identifies context-specific adaptability requirements, and delineates practical performance limits. It provides the first empirically grounded, methodological guideline for selecting appropriate dynamic risk prediction strategies in clinical settings, thereby advancing evidence-based decision support for time-varying prognostic modeling.

Traditional accelerated failure time (AFT) models assume constant covariate effects across all survival quantiles, limiting their ability to capture effect heterogeneity. To address this, we propose an interpretable, quantile-dependent multiplicative effects framework—the first to derive closed-form analytic expressions for covariate effects on the quantile scale within the AFT paradigm. Integrating the g-formula, our approach enables standardized estimation of both conditional and marginal effects under left truncation and arbitrary censoring mechanisms. The method combines Bayesian inference, flexible nonlinear functional forms, and quantile-specific posterior inference. Evaluated in an Alzheimer’s disease cohort, it robustly uncovers distinct influences of age, APOE status, and other covariates on early versus late survival quantiles—revealing previously undetected effect heterogeneity. This enhances both statistical precision and clinical interpretability of survival effect estimates.

Existing methods struggle to effectively evaluate the overall goodness-of-fit and predictive performance of joint models for longitudinal and time-to-event (TTE) data, particularly when event times are subject to censoring. This work extends the normalized prediction distribution errors (NPDE/PD) framework to joint models with censored outcomes for the first time, proposing a unified testing strategy that integrates longitudinal and survival information. The approach handles unobserved event times via uniform imputation weighted by censoring probabilities, computes prediction discrepancies through Monte Carlo simulation, and controls family-wise error using Bonferroni correction. Under various model misspecifications, the method maintains a Type I error rate near 5%, with statistical power increasing alongside sample size and degree of model deviation. Graphical diagnostics further demonstrate high sensitivity to deviations in both survival functions and longitudinal trajectories, such as PSA profiles.

This study addresses a key limitation of conventional joint models, which focus solely on the mean trajectories of biomarkers while ignoring the prognostic value embedded in within-individual variability. To overcome this, the authors propose a two-step approach: first, individual- and time-specific variability metrics are derived from residuals of a mixed-effects model; second, these metrics are incorporated into a standard joint modeling framework to simultaneously assess the effects of both mean levels and variability on survival outcomes. The method requires no specialized software and can be flexibly integrated into existing joint modeling platforms such as JM or joineR, with support for multiple biomarkers. Simulation studies demonstrate robust performance across diverse scenarios, and application to glioblastoma clinical data reveals that both the mean and variability of white blood cell counts are significantly associated with overall survival.

This study addresses the challenge of modeling the bidirectional association between interval-censored onset times and multivariate longitudinal biomarkers in Huntington’s disease clinical research. The authors propose a novel joint model that, for the first time, incorporates an anchored change-point mechanism within an interval-censored event time framework, dynamically coupling biomarker trajectories with the timing of disease onset. This approach not only quantifies the influence of biomarkers on disease risk but also captures structural shifts in biomarker trajectories following event occurrence, thereby enabling bidirectional causal inference between longitudinal processes and event time. Simulation studies demonstrate favorable performance under finite-sample settings, and application to the PREDICT-HD cohort reveals dynamic interactions between cognitive and motor dysfunction throughout disease progression.

This study addresses the bias in treatment effect estimation inherent in the standard Cox proportional hazards model due to non-collapsibility, even under randomized controlled trial settings when unobserved covariates are present. Through systematic Monte Carlo simulations, the authors evaluate the magnitude of bias in both Cox and parametric proportional hazards models across varying degrees of unmeasured heterogeneity. They further assess the robustness of alternative approaches—including frailty models, accelerated failure time (AFT) models, Kaplan–Meier-based methods, and Cox models accommodating time-varying treatment effects. Application to data from the RTOG 9202 clinical trial demonstrates that omitting important covariates can substantially distort hazard ratio estimates, while empirical results confirm that several alternative methods effectively mitigate such bias, yielding more reliable inferences regarding treatment effects.