Multi-stage transitional models with random effects and their application to the Einstein aging study

Abstract

Longitudinal studies of aging often gather repeated observations of cognitive status to describe the development of dementia and to assess the influence of risk factors. Clinical progression to dementia is often conceptualized by a multi-stage model of several transitions that synthesizes time-varying effects. In this study, we assess the influence of risk factors on the transitions among three cognitive status: cognitive stability (normal cognition for age), memory impairment, and clinical dementia. We have developed a shared random effects model that not only links the propensity of transitions and to the probability of informative missingness due to death, but also incorporates heterogeneous transition between subjects. We evaluate four approaches using generalized logit and four using proportional odds models to the first-order Markov transition probabilities as a function of covariates. Random effects were incorporated into these models to account for within-subject correlations. Data from the Einstein Aging Study are used to evaluate the goodness-of-fit of these models using the Akaike information criterion. The best fitting model for each type (generalized logit and proportional odds) is recommended and their results are discussed in more details.

Conflict of interest statement

Conflict of Interest

The authors declare no conflict of interest.

2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Figures

Fig. 1

Possible transitions for the four stages and their regression coefficients γij to be estimated. We have used γjk to denote (αjk,βjk) for j = 1, 2 and k = 1, 2, 3, 4. We are using the normality stage as a reference, so γ11, and γ21, are not estimated.

Fig. 2

Simulated transitions for the generalized logit model logp∼t(k∣j)p∼t(1∣j)=αjk+θju, k = 2, 3 with α12 = −1, α13 = −3, α22 = 1, and α23 = −1.5. The three figures on the left are simulated with θ = θ2 = 1 and u = −1, 1, 2. The three figures on the right are derived with θ = θ2 = −1 and u = −1, 1, 2.