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Dynamic inference for non-Markov transition probabilities under random right-censoring

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Dynamic inference for non-Markov transition probabilities under random right-censoring. / Dobler, Dennis; Titman, Andrew Charles.

In: Scandinavian Journal of Statistics, 14.01.2020.

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@article{3f8fe2041be34586af6e6aa6b0215a89,
title = "Dynamic inference for non-Markov transition probabilities under random right-censoring",
abstract = "The main contribution of this article is the verification of} weak convergence of the general non-Markov state transition probability estimator by Titman (2015) which has not yet been done for any other general non-Markov estimator. A similar theorem is shown for the bootstrap, yielding resampling-based inference methods for statistical functionals. Formulas of the involved covariance functions are presented in detail. Particular applications include the conditional expected length of stay in a specific state, given occupation of another state in the past, and the construction of time-simultaneous confidence bands for the transition probabilities. The expected lengths of stay in the two-sample liver cirrhosis data-set by Andersen et al (1993) are compared and confidence intervals for their difference are constructed. With borderline significance and in comparison to the placebo group, the treatment group has an elevated expected length of stay in the healthy state given an earlier disease state occupation. In contrast, the Aalen--Johansen estimator-based confidence interval, which relies on a Markov assumption, leads to a drastically different conclusion. Also, graphical illustrations of confidence bands for the transition probabilities demonstrate the biasedness of the Aalen-Johansen estimator in this data example. The reliability of these results is assessed in a simulation study.",
keywords = "confidence bands, Markov assumption, multistate model, restricted conditional expected length of stay, right censoring, weak convergence",
author = "Dennis Dobler and Titman, {Andrew Charles}",
year = "2020",
month = jan
day = "14",
doi = "10.1111/sjos.12443",
language = "English",
journal = "Scandinavian Journal of Statistics",
issn = "0303-6898",
publisher = "Blackwell-Wiley",

}

RIS

TY - JOUR

T1 - Dynamic inference for non-Markov transition probabilities under random right-censoring

AU - Dobler, Dennis

AU - Titman, Andrew Charles

PY - 2020/1/14

Y1 - 2020/1/14

N2 - The main contribution of this article is the verification of} weak convergence of the general non-Markov state transition probability estimator by Titman (2015) which has not yet been done for any other general non-Markov estimator. A similar theorem is shown for the bootstrap, yielding resampling-based inference methods for statistical functionals. Formulas of the involved covariance functions are presented in detail. Particular applications include the conditional expected length of stay in a specific state, given occupation of another state in the past, and the construction of time-simultaneous confidence bands for the transition probabilities. The expected lengths of stay in the two-sample liver cirrhosis data-set by Andersen et al (1993) are compared and confidence intervals for their difference are constructed. With borderline significance and in comparison to the placebo group, the treatment group has an elevated expected length of stay in the healthy state given an earlier disease state occupation. In contrast, the Aalen--Johansen estimator-based confidence interval, which relies on a Markov assumption, leads to a drastically different conclusion. Also, graphical illustrations of confidence bands for the transition probabilities demonstrate the biasedness of the Aalen-Johansen estimator in this data example. The reliability of these results is assessed in a simulation study.

AB - The main contribution of this article is the verification of} weak convergence of the general non-Markov state transition probability estimator by Titman (2015) which has not yet been done for any other general non-Markov estimator. A similar theorem is shown for the bootstrap, yielding resampling-based inference methods for statistical functionals. Formulas of the involved covariance functions are presented in detail. Particular applications include the conditional expected length of stay in a specific state, given occupation of another state in the past, and the construction of time-simultaneous confidence bands for the transition probabilities. The expected lengths of stay in the two-sample liver cirrhosis data-set by Andersen et al (1993) are compared and confidence intervals for their difference are constructed. With borderline significance and in comparison to the placebo group, the treatment group has an elevated expected length of stay in the healthy state given an earlier disease state occupation. In contrast, the Aalen--Johansen estimator-based confidence interval, which relies on a Markov assumption, leads to a drastically different conclusion. Also, graphical illustrations of confidence bands for the transition probabilities demonstrate the biasedness of the Aalen-Johansen estimator in this data example. The reliability of these results is assessed in a simulation study.

KW - confidence bands

KW - Markov assumption

KW - multistate model

KW - restricted conditional expected length of stay

KW - right censoring

KW - weak convergence

U2 - 10.1111/sjos.12443

DO - 10.1111/sjos.12443

M3 - Journal article

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

ER -