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Non‐parametric Bayesian Intensity Model: Exploring Time‐to‐Event Data on Two Time Scales

Time‐to‐event data have been extensively studied in many areas. Although multiple time scales are often observed, commonly used methods are based on a single time scale. Analysing time‐to‐event data on two time scales can offer a more extensive insight into the phenomenon. We introduce a non‐parametric Bayesian intensity model to analyse two‐dimensional point process on Lexis diagrams. After a simple discretization of the two‐dimensional process, we model the intensity by a one‐dimensional piecewise constant hazard functions parametrized by the change points and corresponding hazard levels. Our prior distribution incorporates a built‐in smoothing feature in two dimensions. We implement posterior simulation using the reversible jump Metropolis–Hastings algorithm and demonstrate the applicability of the method using both simulated and empirical survival data. Our approach outperforms commonly applied models by borrowing strength in two dimensions.