Monday, 21 March 2011

Joint model with latent state for longitudinal and multistate data

Dantan, Joly, Dartigues and Jacqmin-Gadda have a new paper in Biostatistics. There is a wide literature on joint models of survival with longitudinal data with some extensions for joint competing-risks survival and longitudinal data (e.g. Elashoff et al). Dantan et al develop a joint model for multi-state survival data and longitudinal data. The standard approach to these joint models is to have a random effect that it shared across the model for the survival data (e.g. appearing as a frailty) and the longitudinal model (e.g. random slopes and intercepts in a generalized linear mixed model). Rather than follow this convention, Dantan et al allow a slightly more direct correspondence between the survival and longitudinal parts. Specifically, they have a progressive 4-state multi-state model relating to healthy, pre-diagnosis, illness and death states. The pre-diagnosis state is unobservable and entry into this state corresponds to the time a which the slope of decline in the longitudinal biomarker changes. The model is an extension on the random change-point model proposed by Jacqmin-Gadda et al (Biometrics, 2006), as here it is not necessary to make unrealistic assumptions about death being non-informative censoring for illness.

For the PAQUID dataset on cognitive decline, the baseline transition intensities are of Weibull form for healthy to pre-diagnosis and pre-diagnosis to illness (the latter being Weibull w.r.t time since pre-diagnosis). The hazard of death is assumed to depend only on age (via piecewise constant intensities) and the value of the longitudinal marker, Y(t), but not explicitly on the current disease state. This assumption seems to be primarily for computational reasons.

A limitation of the approach taken in the paper is that dementia is only diagnosed at clinic visits, so in effect is interval censored between the current and last clinic visit. The authors just assume entry into the dementia state occurred at the midpoint between clinic visits. Through simulation in the supplementary materials the authors show this doesn't cause serious bias.
However, a further issue is that the dependency of the dementia age on the observed value of the marker at a clinic visit would presumably mean the assumption of independence between dementia age and observation errors conditional on the random effects (slopes, intercepts and change-time) would be inappropriate. To what extent is the apparent increase in the decline of cognition before diagnosis due to such an artifact?

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