Giorgos Bakoyannis, Assistant Professor
Fairbanks School of Public Health
Department of Biostatistics
Friday, April 12, 2019, 1-2pm, HITS1110
Nonparametric tests for transition probabilities in nonhomogeneous Markov processes
Continuous time nonhomogeneous Markov processes with a finite state space play in important role in modern medicine and public health, such as in clinical trials involving event history data with multiple events. In such trials, inference about specific transitions between events can provide a deeper and more detailed insight about treatment effect compared to the analysis of standard survival outcomes, such as event-free survival. This talk presents nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an L2-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 L2-norm-based and the Kolmogorov-Smirnov-type tests are shown to be consistent against any fixed alternative hypothesis. Consequently, these tests provide good power even in cases where the transition probability curves under comparison cross at one or more time points. 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.