Bakoyannis Giorgos
Address: Indiana University Fairbanks School of Public Health and School of Medicine, 410 West 10th Street, Suite 3000, Indianapolis, IN 46202.
J Nonparametr Stat. 2020;32(1):131-156. doi: 10.1080/10485252.2019.1705298. Epub 2019 Dec 19.
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 -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 -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.
本文针对具有有限状态空间的连续时间非齐次马尔可夫过程状态间特定转移概率的直接比较，提出了非参数两样本检验。所提出的检验包括线性非参数检验、基于 - 范数的检验和柯尔莫哥洛夫 - 斯米尔诺夫型检验。显著性水平评估基于严格程序，这些程序通过现代经验过程理论得以论证。此外，对于每个固定的备择假设， - 范数检验和柯尔莫哥洛夫 - 斯米尔诺夫型检验被证明是一致的。所提出的检验还扩展到了更复杂的情形，如吸收状态观测不完全的情况和非马尔可夫过程。模拟研究表明，即使样本量较小，检验统计量也表现良好。最后，在疾病 - 死亡模型下，将所提出的检验应用于欧洲癌症研究与治疗组织（EORTC）试验10854中早期乳腺癌治疗的数据。
