Our article (Härkänen, But and Haukka, 2017, Nonparametric Bayesian Intensity Model: Exploring Time-to-Event Data on Two Time Scales) will appear in the Scandinavian Journal of Statistics soon. The lexis example as well as the example on reading the output using the simulated data can be found in the Download section.
The Lexis prior incorporates multidimensional smoothing of the hazard surface. We demonstrated in our paper that this approach provides more accurate results than some common unidimensional methods such as the Poisson regression with splines, because the Lexis prior borrows strength in more than one dimension. This method can be useful not only in analyzing multiple time scales but also in case of ordinal covariates defining a stratification in a hazard model. In the latter case one can assume that the hazard functions of the neighbouring covariate categories are similar thus there is some continuity over the hazard functions.
The smoothing is especially useful in case of relatively small number of observations per stratum as the smoothing reduces the risk of false positive findings. When using other existing methods, the common approach is to merge strata in order to have a larger number of observations, but this approach can hide the actual change points, which can be avoided in our approach.