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Nonparametric tests for transition probabilities in nonhomogeneous Markov processes.

ABSTRACT: This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time non-homogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an L ²-norm-based test and a Kolmogorov-Smirnov-type test. Significance level assessment is based on rigorous procedures, which are justified through the use of modern empirical process theory. Moreover, the L ²-norm and the Kolmogorov-Smirnov-type tests are shown to be consistent for every fixed alternative hypothesis. The proposed tests are also extended to more complex situations such as cases with incompletely observed absorbing states and non-Markov processes. Simulation studies show that the test statistics perform well even with small sample sizes. Finally, the proposed tests are applied to data on the treatment of early breast cancer from the European Organization for Research and Treatment of Cancer (EORTC) trial 10854, under an illness-death model.

SUBMITTER: Bakoyannis G

PROVIDER: S-EPMC7173284 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Nonparametric tests for transition probabilities in nonhomogeneous Markov processes.

Bakoyannis Giorgos G

Journal of nonparametric statistics 20191219 1

This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time non-homogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an L 2-norm-based test and a Kolmogorov-Smirnov-type test. Significance level assessment is based on rigorous procedures, which are justified through the use of modern empirical process theory. Moreover, the ...[more]

PMID: 32317843

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Project description:Screening tests are widely recommended for the early detection of disease among asymptomatic individuals. While detecting disease at an earlier stage has the potential to improve outcomes, screening also has negative consequences, including false positive results which may lead to anxiety, unnecessary diagnostic procedures, and increased healthcare costs. In addition, multiple false positive results could discourage participating in subsequent screening rounds. Screening guidelines typically recommend repeated screening over a period of many years, but little prior research has investigated how often individuals receive multiple false positive test results. Estimating the cumulative risk of multiple false positive results over the course of multiple rounds of screening is challenging due to the presence of censoring and competing risks, which may depend on the false positive risk, screening round, and number of prior false positive results. To address the general challenge of estimating the cumulative risk of multiple false positive test results, we propose a nonhomogeneous multistate model to describe the screening process including competing events. We developed alternative approaches for estimating the cumulative risk of multiple false positive results using this multistate model based on existing estimators for the cumulative risk of a single false positive. We compared the performance of the newly proposed models through simulation studies and illustrate model performance using data on screening mammography from the Breast Cancer Surveillance Consortium. Across most simulation scenarios, the multistate extension of a censoring bias model demonstrated lower bias compared to other approaches. In the context of screening mammography, we found that the cumulative risk of multiple false positive results is high. For instance, based on the censoring bias model, for a high-risk individual, the cumulative probability of at least two false positive mammography results after 10 rounds of annual screening is 40.4.

Dataset Information

Nonparametric tests for transition probabilities in nonhomogeneous Markov processes.

Publications

Nonparametric tests for transition probabilities in nonhomogeneous Markov processes.

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