A nonstationary Markov transition model for computing the relative risk of dementia before death

Yu et al have a new paper in Statistics in Medicine. This is concerned with estimating the risk of dementia before death. A 5 state multi-state model is used, with three transient states representing levels of cognitive impairment, plus two absorbing states dementia and death. Unlike other recent dementia studies using multi-state models, improvements, as well as deteriation, in cognitive ability are assumed possible. A discrete-time approach is taken. This has some advantages in terms of the flexibility in modelling possible in terms of incorporating non-homogeneity over time and a frailty term - the Markov assumption. A drawback of using a discrete-time approach in the current study was that the study did not have equally spaced observation times, but it was necessary to assume this was the case for the discrete-time model. This is likely to cause some bias.

The main theoretical development in the paper is expressions for the mean and variance of the time spent in each transient state before absorption in the non-homogeneous case.

Vertical modeling: A pattern mixture approach for competing risks modeling

Nicolaie, van Houwelingen and Putter have a new paper in Statistics in Medicine. This presents a new approach to modeling competing risks data. In essence this involves splitting the model in two parts: firstly model all cause survival, e.g. P(T >=t), secondly model P(D | T=t), the probability of a particular type of failure given a failure at time t, which they term as the relative hazard. The cause specific hazards and cumulative incidence functions can be retrieved under this formulation. A multinomial type model is applied to the relative hazards, with time dependency modelled using either piecewise constant functions or cubic splines. All cause survival can be modelled through any standard survival model e.g. a proportional hazards model. Vertical modeling provides a third approach particularly useful in cases where a proportional hazards assumption is not appropriate on either the cause-specific hazards (the classical approach) or on the sub-distribution hazard (Fine-Gray model).

Whilst it would be relatively straightforward to implement a vertical model using existing R packages, there are plans to include vertical modeling within the mstate package.

Estimating disease progression using panel data

Micha Mandel has a new paper in Biostatistics. This considers estimation for panel observed data relating to MS progression. The underlying process can have backward transitions, so reaching a higher state is not in itself considered as evidence of progression. Instead, the patient is required to have stayed in the higher state for some period of time (e.g. 6 months). The quantities of interest in the study is therefore the time taken to first have stayed in state 3 for 6 months. For a continuous time, time-homogeneous Markov process expressions for the mean time and the distribution function are obtained.

As noted by Mandel, the estimates obtained are strongly dependent on the Markov assumption and time homogeneity. This is demonstrated in a simulation study. Mandel notes that more methods for semi-Markov models are required, the recent paper on phase-type semi-Markov models may be of use. Indeed, in the simulations Mandel actually uses phase-type distributions to create a semi-Markov process. However, the MS dataset may be too small to reliably estimate a semi-Markov model.

Informative observation times are a potential problem in the MS study. Mandel shows that observations that occur away from the scheduled 26-week gap time, are more likely to involve a transition, suggesting these observation times are informative. As a result, only observations within a 4 week period of the scheduled visit time are included in the analysis.

A comparison with a discrete-time Markov model approach showed that estimates based on assuming a discrete-time process gave larger estimates of the hitting times.