Comparison of Estimators for Multi-State Models in Potentially Non-Markov Processes
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arXiv
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| Format: | Preprint |
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2025
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| author | Drenda, Carolin Dobler, Dennis Munko, Merle Titman, Andrew |
| author_facet | Drenda, Carolin Dobler, Dennis Munko, Merle Titman, Andrew |
| contents | Various estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the Aalen-Johansen estimator is generally only consistent under the rather restrictive Markov assumption, the landmark Aalen-Johansen estimator can handle non-Markov multi-state models. However, the landmark Aalen-Johansen estimator leads to a strict data reduction and, thus, to an increased variance. The hybrid Aalen-Johansen estimator serves as a compromise by, firstly, checking with a log-rank-based test whether the Markov assumption is satisfied. Secondly, landmarking is only applied if the Markov assumption is rejected. In this work, we propose a new hybrid Aalen-Johansen estimator which uses a Cox model instead of the log-rank-based test to check the Markov assumption in the first step. Furthermore, we compare the four estimators in an extensive simulation study across Markov, semi-Markov, and distinct non-Markov settings. In order to get deep insights into the performance of the estimators, we consider four different measures: bias, variance, root mean squared error, and coverage rate. Additionally, further influential factors on the estimators such as the form and degree of non-Markov behaviour, the different transitions, and the starting time are analysed. The main result of the simulation study is that the hybrid Aalen-Johansen estimators yield favourable results across various measures and settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparison of Estimators for Multi-State Models in Potentially Non-Markov Processes Drenda, Carolin Dobler, Dennis Munko, Merle Titman, Andrew Methodology Various estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the Aalen-Johansen estimator is generally only consistent under the rather restrictive Markov assumption, the landmark Aalen-Johansen estimator can handle non-Markov multi-state models. However, the landmark Aalen-Johansen estimator leads to a strict data reduction and, thus, to an increased variance. The hybrid Aalen-Johansen estimator serves as a compromise by, firstly, checking with a log-rank-based test whether the Markov assumption is satisfied. Secondly, landmarking is only applied if the Markov assumption is rejected. In this work, we propose a new hybrid Aalen-Johansen estimator which uses a Cox model instead of the log-rank-based test to check the Markov assumption in the first step. Furthermore, we compare the four estimators in an extensive simulation study across Markov, semi-Markov, and distinct non-Markov settings. In order to get deep insights into the performance of the estimators, we consider four different measures: bias, variance, root mean squared error, and coverage rate. Additionally, further influential factors on the estimators such as the form and degree of non-Markov behaviour, the different transitions, and the starting time are analysed. The main result of the simulation study is that the hybrid Aalen-Johansen estimators yield favourable results across various measures and settings. |
| title | Comparison of Estimators for Multi-State Models in Potentially Non-Markov Processes |
| topic | Methodology |
| url | https://arxiv.org/abs/2510.24453 |