A novel hybrid MCMC method for interval-censored data

Interval-censored data analysis is a hot topic in biomedical statistics and survival analysis and draws much research interest. There are several methods existing in the literature to approach interval-censored data, for example, the Non-Parametric Maximum Likelihood Estimator (NPMLE), the Momentum Estimator, and the generalized log-rank test. Markov chain Monte Carlo (MCMC) methods provides an alternative and prospective solution to this problem due to its generality and simplicity. To avoid random walk behavior, Hybrid Monte Carlo Markov chain (HMCMC) methods introduce an auxiliary momentum vector and implement Hamiltonian dynamics where the potential function is the target density. In this paper, a novel HMCMC schema that combines the Hamiltonian method and the Gibbs sampling is set forth. The new algorithm is then adopted to parameter estimation of interval-censored data. Numerical experiments demonstrate that the new HMCMC schema outperforms other methods not only in accuracy of parameters estimation, but also in computational efficiency.