Using Lexis Objects for Multi-State Models in R

The fourth and fifth papers in the special issue of Journal of Statistical Software concern Lexis objects in the R package Epi and are by Martin Plummer and Bendix Carstensen. The first paper is mainly a general introduction to Lexis objects whereas the second paper looks specifically at their use for multi-state models. Lexis diagrams, which have a long history, provide a way of illustrating data with multiple time scales and have been promoted by Niels Keiding among others.

The Lexis function makes initial exploration of multi-state data easier, by allowing plotting of events on different timescales so that, for instance, the correct time scale(s) for analysis can be chosen. Lexis objects can also be passed to mstate.

The authors consider the problem is determining whether two baseline transition intensities are proportional. A model allowing proportionality is straightforward to implement as it just involves putting the two transition intensities in the same strata of a Cox model and adding an extra indicator variable to denote which transition intensity an event derives from. However, if one is interested in formally testing an assumption of proportionality there is a difficulty because the Cox model factorizes the baseline intensities out. The authors therefore propose full likelihood modelling where the baseline intensities are assumed to be piecewise constant within short time intervals but follow a smooth spline function. Testing proportionality of intensities can then be performed through a standard likelihood ratio test.