Joint Modeling of Self-Rated Health and Changes in Physical Functioning

Hubbard, Inoue and Diehr have a new paper in press in JASA. This applies the time-transformation model proposed by Hubbard et al (Biometrics, 2008). The data are panel observed with an assessment of disability at each observation plus a self-rated measure of health. The disability measure is assumed to be a 5 state time non-homogeneous Markov model, with 4 levels of disability and death as an absorbing state. Backward transitions between disability levels are permitted. Two parametric forms for the time transformation were considered: a power transformation implying monotonicity of all intensities with time, and a two parameter transformation implying the intensities are all unimodal. The non-parametric transformation proposed in Hubbard et al (2008) are not considered here.

Disability is jointly modelled with the self-rated measure of health which is dichotomised as healthy or unhealthy. This health outcome may depend on both the current and past values of disability and other covariates. There would be obvious problems of missing data if the past history of disability is included due to the panel observation. The authors only consider models where the health outcome depends on current (+ predicted future) levels of disability but not past levels. Linear logistic models are used to relate the health outcome to the observed levels of disability and other covariates. Rudimentary goodness-of-fit for the multi-state model is carried out using the prevalence-counts method of Gentleman et al (Stats in Med, 1994), while the logistic model is assessed using the Hosmer-Lemeshow test.

Model diagnostics for multi-state models

Titman and Sharples have a new review paper in SMMR. This considers methods for assessing fit in parametric, panel observed multi-state models. The primary focus is on the assessment of time homogeneous Markov models, although there is also a section on hidden Markov models that occur if states are considered to be observed with classification error. Methods for fitting more complicated models such as non-homogeneous and random effects models are also reviewed. A simple graphical generalization of the prevalence counts method of Gentleman et al (Stats in Med, 1994) is also developed.

Estimating dementia-free life expectancy for Parkinsons patients using Bayesian inference and microsimulation

Van den Hout and Matthews have a new paper in Biostatistics involving a random-effects Markov model with time (age) dependent intensities. The methodology is close to that used by Pan et al and Wu et al, using a WinBUGS/OpenBUGS Bayesian approach. They use a three-state illness-death model without recovery. A more sophisticated multivariate log-normal random effect on the effects of age on the intensities is used with a Wishart prior is used on the covariance matrix, which is more appropriate than the Gamma(e,e) type priors used by Pan et al. Like their recent Applied Statistics paper, time dependencies in the intensities are accounted for by assuming an individual that is observed at times t1 and t2 has a constant matrix of intensities between those points, but different assumptions are used to calculate life expectancies. The main methodological development is obtaining life expectancy estimates through 'microsimulation.' This is deemed necessary because there are two levels of variation: variation in the posterior of the parameters and variation from the random effects distribution conditional on the parameters. 'Microsimulation' (or simulation) just approximates the integral over the random effects distribution.