Robust Estimation of Mean Functions and Treatment Effects for Recurrent Events Under Event-Dependent Censoring and Termination

Richard Cook et al have a new paper in JASA. This concerns the estimation of mean functions for recurrent events under event dependent censoring. They consider several methods, including a multi-state approach using an estimate based on the Aalen-Johansen estimator of the transition intensities using IPCW to correct for dependent censoring.

Estimating life expectancy in health and ill health by using a hidden Markov model

Van den Hout, Jagger and Matthews have a paper to appear in JRSS C. The paper applies the misclassification hidden Markov model, developed by Satten and Longini and Jackson and Sharples, to modelling of data on cognitive impairment in the elderly and its effect on mortality. Patients with a cognition score (MMSE) below 22 were considered impaired. However, cognitive decline is considered to be progressive so backwards transitions in the dataset are explained through misclassification.

The main aim of the paper is to estimate life expectancies in the non-impaired and impaired states. As mortality will be highly dependent on age, non-homogeneous transition intensities are required. Rather than employ the standard approach of piecewise constant intensities, the authors instead include age as a log-linear time dependent covariate and assume that an individual observed at ages t and u, for t < u, has constant intensity Q(t) for the interval (t,u). This will clearly result in some degree of bias, particularly if observation times are widely spaced. Life expectancy is then calculated by assuming intensities are constant in 1 year intervals. As this is different from how the data were estimated, the bias may be further compounded.

Rudimentary goodness-of-fit is carried out by comparing estimated survival curves from the HMM with a Cox-regression performed directly on the survival data. It is worth noting that this approach could be problematic in certain circumstances because the HMM is not nested within the Cox-regression model, so there might be discrepancies between the curves even if the HMM is correctly specified.

Nonparametric estimation in an "illness-death" model when the transition times are interval-censored and one transition is not observed.

Frydman, Gerds, Groen and Keiding have a paper available as a research report from the Department of Biostatistics, Copenhagen. The paper develops previous work on the non-parametric estimation of interval-censored multi-state data. Here the data in question follow a progressive three-state "illness-death" model but the ill to death transition is never observed. This is because the data arise from clinical observation and the trial ceases if a patient is observed to be in the illness state. Such an observation scheme has strong similarities with data considered by Duffy et al relating to breast cancer screening where a three-stage unidirectional model was assumed and the intermediate state was pre-clinical detectable breast cancer. No data on pre-clinical to clinical breast cancer transitions were available as interest was in the natural progression of the disease. Duffy et al analysed the data parametrically, assuming a time homogeneous Markov model. In contrast Frydman et al fit a non-homogeneous Markov model non-parametrically. Since all transitions are interval censored, they model the process in discrete time.
Update: A paper broadly based upon the research report has now been published in Biometrical Journal. The supplementary materials also includes R code to implement the proposed algorithm.

A multistate approach for estimating the incidence of human immunodeficiency virus by using HIV and AIDS French surveillance data

Sommen, Alioum and Commenges have a new paper in Statistics in Medicine. This applies the penalized likelihood approach to multi-state models, used extensively by the INSERM group, to the area of back-calculation for estimating HIV incidence. The penalization parameters are chosen by minimizing an approximate cross-validation score.