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.