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-paramet...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2017-09, Vol.44 (3), p.798-814
Main Authors: HÄRKÄNEN, TOMMI, BUT, ANNA, HAUKKA, JARI
Format: Article
Language:English
Subjects:
Bayesian analysis
Computer simulation
Empirical analysis
event history
hazard rate
intensity function
International
Lexis diagram
Nonparametric statistics
Poisson process
reversible jump MCMC
Smoothing
Statistical analysis
Studies
survival analysis
Time
Two dimensional models
two‐dimensional
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Summary: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.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12280