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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 a general non-Markov (NM) state transition probability estimator by Titman, which has not yet been done for any other general NM 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 a two-sample liver cirrhosis dataset 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 (AJ) 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 AJ 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 a general non-Markov (NM) state transition probability estimator by Titman, which has not yet been done for any other general NM 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 a two-sample liver cirrhosis dataset 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 (AJ) 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 AJ 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
VL - 47
SP - 572
EP - 586
JO - Scandinavian Journal of Statistics
JF - Scandinavian Journal of Statistics
SN - 0303-6898
IS - 2
ER -