Testing transition probability matrix of a multi-state model with censored data

In this paper, we develop procedures to test hypotheses concerning transition probability matrices arising from certain nonhomogeneous Markov processes. It is assumed that the data consist of sample paths, some of which are observed until a certain terminal state, and the other paths are censored. Problems of this type arise in the context of multi-state models relevant to Health Related Quality of Life (HRQoL) and Competing Risks. The test statistic is based on the estimator for the associated intensity matrix. We show that the asymptotic null distribution of the proposed statistic is Gaussian, and demonstrate how the procedure can be adopted for HRQoL studies and competing risks model using real data sets. Finally, we establish that the test statistic for the HRQoL has greatest local asymptotic power against a sequence of proportional hazards alternatives converging to the null hypothesis.