Pre‐Smoothing Methods for Transition Probabilities in Complex Non‐Markovian Multistate Models

Summary Multistate models are essential tools in longitudinal data analysis, enabling the estimation of transition probabilities that provide predictive insights into clinical outcomes across stages of disease progression or recovery. Conventional approaches to inference in these models often rely on the Markov assumption, which simplifies computation but may not hold in complex real‐world settings. To address this limitation, we extend the landmark Aalen–Johansen estimator by incorporating pre‐smoothing techniques, offering a robust alternative for estimating transition probabilities in non‐Markovian multistate models, including those with multiple states and reversible transitions. The proposed method effectively reduces estimation variability and mitigates biases arising from the selection of arbitrary landmark times. Through empirical evaluation using three real‐world datasets with distinct multistate structures, we demonstrate that the pre‐smoothed estimator achieves enhanced precision and stability, particularly in the presence of high noise or small sample sizes. To facilitate its application, we provide an R package, presmoothedTP , which implements all the proposed methods.

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Publication Details

Journal
International Statistical Review
Published
2025-07-19
DOI
https://doi.org/10.1111/insr.70002
Primary Topic
Statistical Methods and Inference
Type
article
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article

Pre‐Smoothing Methods for Transition Probabilities in Complex Non‐Markovian Multistate Models

Gustavo Soutinho, Luís Meira‐Machado
International Statistical Review
Statistical Methods and Inference
article

Pre‐Smoothing Methods for Transition Probabilities in Complex Non‐Markovian Multistate Models

Gustavo Soutinho, Luís Meira‐Machado
article en

Abstract

Summary Multistate models are essential tools in longitudinal data analysis, enabling the estimation of transition probabilities that provide predictive insights into clinical outcomes across stages of disease progression or recovery. Conventional approaches to inference in these models often rely on the Markov assumption, which simplifies computation but may not hold in complex real‐world settings. To address this limitation, we extend the landmark Aalen–Johansen estimator by incorporating pre‐smoothing techniques, offering a robust alternative for estimating transition probabilities in non‐Markovian multistate models, including those with multiple states and reversible transitions. The proposed method effectively reduces estimation variability and mitigates biases arising from the selection of arbitrary landmark times. Through empirical evaluation using three real‐world datasets with distinct multistate structures, we demonstrate that the pre‐smoothed estimator achieves enhanced precision and stability, particularly in the presence of high noise or small sample sizes. To facilitate its application, we provide an R package, presmoothedTP , which implements all the proposed methods.

International Statistical Review
Universidade Portucalense (PT), University of Minho (PT)
Openalex Percentile: Top 81%
Statistical Methods and Inference
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Pre‐Smoothing Methods for Transition Probabilities in Complex Non‐Markovian Multistate Models — Gustavo Soutinho, Luís Meira‐Machado · International Statistical Review (2025) | TGRS Research Map | TGRS