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.

maxLik: A package for maximum likelihood estimation

Arne Henningsen and Ott Toomet have a new paper in Computational Statistics. The paper isn't directly related to multi-state modelling, but rather is on their package, maxLik, for general maximum likelihood estimation. Primarily their package is a wrapper for existing optimization packages in R such as optim and nlm. However, they do in addition provide an implementation of the BHHH (Berndt, Hall, Hall and Hausman) algorithm. This is a quasi-Newton algorithm in a similar vein to Fisher scoring, but rather than use the Expected Fisher information, it uses the mean of the outer product of the scores of each observation. Like the BFGS algorithm, a line search is performed to find the step length at each iteration.

For panel observed Markov multi-state models the Fisher scoring algorithm proposed by Kalbfleisch and Lawless (1985, JASA) and generalised by Gentleman et al (1994, Stat Med) is superior to BHHH. However, for data with a mixture of panel observed observations and exact times of absorption (e.g. death), the Fisher scoring algorithm cannot be applied. Here BHHH seems to perform significantly better than the BFGS algorithm supplying first derivatives.