Flexible hazard ratio curves for continuous predictors in multi-state models: an application to breast cancer data

Cadarso-Suarez, Meira-Machado, Kneib and Gude have a long-awaited paper (it was accepted in October 2008) newly published in Statistical Modelling. This proposes the use of P-splines to allow smooth transition intensities and smooth functionals of covariates in a Cox-Markov or Cox-semi-Markov multi-state model.

The principal difficulty in fitting these models lies in obtaining appropriate values for the penalization parameters. However, since for right-censored data, both the Cox-Markov and Cox-semi-Markov models allow factorization of the likelihood into parts relating to the constituent transition intensities, methods from univariate survival analysis can be used. The R packages survival and BayesX are both used in the analysis.

Estimating life expectancy of demented and institutionalized subjects from interval-censored observations of a multi-state model

Joly, Durand, Helmer and Commenges have a new paper in Statistical Modelling. This concerns the estimation of life expectancy in patients with dementia. Unlike similar analysis by Van den Hout and Matthews, here there are 5 states rather than 3 since they consider instiutionalization as an additional event. Age at death is known up to right-censoring but other transitions are interval censored. Like previous papers by Joly and Commenges, a penalized likelihood approach is taken. The penalized likelihood is approximated by cubic M-splines, with the degree of penalization chosen via an approximate cross-validation score. This allows smooth, flexible non-homogeneous intensities. A Markov assumption is assumed but semi-Markov models can also be fitted provided the model is progressive.

Life expectancies are found by integrating the estimated transition probabilities. Like Van den Hout and Matthews, a parametric bootstrap approach based on simulating from the asymptotic normal distribution of the parameters is used to obtain confidence bands. However, these will typically underestimate variability because the penalization factor is taken to be fixed.