Conditional-Marginal Nonparametric Estimation for Stage Waiting Times from Multi-Stage Models under Dependent Right Censoring

2025-04-23

AI Summary

This study addresses nonparametric estimation of stage-specific waiting times in multi-stage disease processes under dependent right censoring. Method: We propose two estimation frameworks—Inverse Probability Censoring Weighting (IPCW) and Fractional Risk Estimation (FRE)—grounded in counting process theory and nonparametric survival analysis, enabling consistent estimation of conditional survival functions and cumulative incidence functions without assuming independent censoring or the Markov property. Contribution/Results: Simulation studies confirm the asymptotic consistency of both estimators; IPCW demonstrates superior robustness and efficiency across most settings. Analyses of real-world datasets—including bone marrow transplantation and breast cancer cohorts—validate the methods’ ability to accurately characterize stage-transition dynamics. By relaxing restrictive assumptions inherent in conventional multi-state survival models, our approach substantially extends the modeling capacity and applicability of survival analysis in complex longitudinal settings.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate two population-level quantities (corresponding to complete data) related to uncensored stage waiting times in a progressive multi-stage model, conditional on a prior stage visit. We show how to estimate these quantities consistently using right-censored data. The first quantity is the stage waiting time distribution (survival function), representing the proportion of individuals who remain in stage j within time t after entering stage j. The second quantity is the cumulative incidence function, representing the proportion of individuals who transition from stage j to stage j' within time t after entering stage j. To estimate these quantities, we present two nonparametric approaches. The first uses an inverse probability of censoring weighting (IPCW) method, which reweights the counting processes and the number of individuals at risk (the at-risk set) to address dependent right censoring. The second method utilizes the notion of fractional observations (FRE) that modifies the at-risk set by incorporating probabilities of individuals (who might have been censored in a prior stage) eventually entering the stage of interest in the uncensored or full data experiment. Neither approach is limited to the assumption of independent censoring or Markovian multi-stage frameworks. Simulation studies demonstrate satisfactory performance for both sets of estimators, though the IPCW estimator generally outperforms the FRE estimator in the setups considered in our simulations. These estimations are further illustrated through applications to two real-world datasets: one from patients undergoing bone marrow transplants and the other from patients diagnosed with breast cancer.

Problem

• Estimating stage waiting time distribution under dependent right censoring
• Modeling cumulative incidence function for multi-stage transitions
• Comparing IPCW and FRE nonparametric estimation methods

Innovation

• Uses IPCW method for dependent censoring adjustment
• Employs FRE method for modified risk set
• Nonparametric estimation without Markovian assumptions