---
title: "Non-Parametric Mediation Analysis in Non-Markov Illness-Death Models"
id: "pubmed-42538523"
canonical_url: "https://medichelpline.com/clinical-feed/pubmed-42538523"
content_type: "clinical_feed_article"
specialty: "Infectious Disease"
source_name: "PubMed / NCBI"
source_url: "https://pubmed.ncbi.nlm.nih.gov/42538523/"
doi: "10.1002/sim.70685"
published_at: "2026-08-01T00:00:00.000Z"
evidence_level: "Journal Article"
license: "CC-BY-NC-4.0 / Informational Use"
---
# Non-Parametric Mediation Analysis in Non-Markov Illness-Death Models
## Provenance & Clinical Metadata
- **Canonical URL:** https://medichelpline.com/clinical-feed/pubmed-42538523
- **Specialty:** [Infectious Disease](https://medichelpline.com/clinical-feed/infectious-disease.md)
- **Primary Source:** PubMed / NCBI
- **Source URL:** [Original Journal Publication](https://pubmed.ncbi.nlm.nih.gov/42538523/)
- **DOI:** [10.1002/sim.70685](https://doi.org/10.1002%2Fsim.70685)
- **Published At:** 2026-08-01T00:00:00.000Z
- **Evidence Rating:** Journal Article
## Executive GIST (TL;DR)
- The study presents a **non-parametric mediation analysis** of a **non-Markov** illness-death model. - Previous models lacked causal interpretations or relied on strong Markov assumptions. - A new definition of **counterfactual hazard** is introduced, accommodating the complexity of intermediate events. - The research develops an **identification formula** utilizing the probability density function of intermediate event times. - Direct and indirect effects of exposure on terminal events, mediated or unmediated by intermediate events, are defined. - **Kernel estimators** for these effects are proposed, with an evaluation of their performance through **numerical simulations**. - Application of the method reveals that the impact of **hepatitis C** on mortality is not mediated by septicemia in the initial 15 years post-exposure. - The study holds significance for understanding disease progression and outcomes associated with chronic conditions like hepatitis C.
## Clinical Analysis & Structured Key Points
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Affiliations Expand ### Affiliations * 1 Institute of Statistics and Data Science, National Tsing Hua University, Hsinchu, Taiwan. * 2 Institute of Statistical Science, Academia Sinica, Taipei, Taiwan. * 3 Department of Statistics, National Taipei University, New Taipei, Taiwan. * PMID: **42538523** * DOI: [ 10.1002/sim.70685 ](https://doi.org/10.1002/sim.70685) Item in Clipboard # Non-Parametric Mediation Analysis of Non-Markov Illness-Death Model Li-Sheng Zhuang et al. Stat Med. 2026 Aug. Show details Display options Display options Format Abstract PubMed PMID Stat Med Actions * [ Search in PubMed ](https://pubmed.ncbi.nlm.nih.gov/?term=%22Stat+Med%22%5Bjour%5D&sort=date&sort_order=desc) * [ Search in NLM Catalog ](https://www.ncbi.nlm.nih.gov/nlmcatalog?term=%22Stat+Med%22%5BTitle+Abbreviation%5D) * [ Add to Search ](https://pubmed.ncbi.nlm.nih.gov/42538523/) . 2026 Aug;45(18-19):e70685. doi: 10.1002/sim.70685. ### Authors [Li-Sheng Zhuang](https://pubmed.ncbi.nlm.nih.gov/?term=Zhuang+LS&cauthor_id=42538523)[ 1 ](https://pubmed.ncbi.nlm.nih.gov/42538523/#short-view-affiliation-1 "Institute of Statistics and Data Science, National Tsing Hua University, Hsinchu, Taiwan.")[ 2 ](https://pubmed.ncbi.nlm.nih.gov/42538523/#short-view-affiliation-2 "Institute of Statistical Science, Academia Sinica, Taipei, Taiwan."), [Jih-Chang Yu](https://pubmed.ncbi.nlm.nih.gov/?term=Yu+JC&cauthor_id=42538523)[ 3 ](https://pubmed.ncbi.nlm.nih.gov/42538523/#short-view-affiliation-3 "Department of Statistics, National Taipei University, New Taipei, Taiwan."), [Yen-Tsung Huang](https://pubmed.ncbi.nlm.nih.gov/?term=Huang+YT&cauthor_id=42538523)[ 2 ](https://pubmed.ncbi.nlm.nih.gov/42538523/#short-view-affiliation-2 "Institute of Statistical Science, Academia Sinica, Taipei, Taiwan.") ### Affiliations * 1 Institute of Statistics and Data Science, National Tsing Hua University, Hsinchu, Taiwan. * 2 Institute of Statistical Science, Academia Sinica, Taipei, Taiwan. * 3 Department of Statistics, National Taipei University, New Taipei, Taiwan. * PMID: **42538523** * DOI: [ 10.1002/sim.70685 ](https://doi.org/10.1002/sim.70685) Item in Clipboard Cite Display options Display options Format Abstract PubMed PMID ## Abstract The illness-death model is widely used to characterize disease progression over time. Previous work focuses either on estimation without causal interpretation or on causal interpretation under a strong Markov assumption where the terminal event depends on the status but not the timing of the intermediate event. To bridge the research gap, we propose a new definition of counterfactual hazard that relaxes the Markov assumption by considering the entire history of the intermediate event. We derive an identification formula that involves an integral with respect to the probability density function of the intermediate event time. Direct and indirect effects refer to the influence of an exposure on the terminal event not mediated by, and mediated through, the intermediate event, respectively. We propose non-parametric kernel estimators for the two effects and study their asymptotic properties. We conduct numerical simulations to examine the proposed estimators' finite-sample performance. Applying the method to a hepatitis study where the Markov assumption is violated, we show that the effect of hepatitis C on mortality is not mediated through septicemia during the first 15 years of follow-up. **Keywords:** causal inference; illness‐death model; kernel density estimation; mediation analysis; non‐Markov assumption. © 2026 John Wiley & Sons Ltd. [PubMed Disclaimer](https://pubmed.ncbi.nlm.nih.gov/disclaimer/) ## References 1. 1. P. K. Andersen, Ø. Borgan, R. D. Gill, and N. Keiding, Statistical Models Based on Counting Processes (Springer‐Verlag, 1993). 2. 1. P. Hougaard, “Multi‐State Models: A Review,” Lifetime Data Analysis 5 (1999): 239–264. 3. 1. Y.‐T. Huang, C.‐L. Jen, H.‐I. Yang, et al., “Lifetime Risk and Sex Difference of Hepatocellular Carcinoma Among Patients With Chronic Hepatitis b and c,” Journal of Clinical Oncology 29, no. 27 (2011): 3643–3650. 4. 1. O. O. Aalen and S. Johansen, “An Empirical Transition Matrix for Non‐Homogeneous Markov Chains Based on Censored Observations,” Scandinavian Journal of Statistics 5, no. 3 (1978): 141–150. 5. 1. J. de Uña‐Álvarez and L. Meira‐Machado, “Nonparametric Estimation of Transition Probabilities in the Non‐Markov Illness–Death Model: A Comparative Study,” Biometrics 71, no. 2 (2015): 364–375. 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