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

• Published in: Biometrical journal Vol. 53; no. 6; pp. 938 - 955
• Main Authors: Song, Changhong, Kuo, Lynn, Derby, Carol A., Lipton, Richard B., Hall, Charles B.
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY‐VCH Verlag 01.11.2011; Wiley-VCH; Wiley - VCH Verlag GmbH & Co. KGaA
• Subjects: Aged, 80 and over; Aging; Aging - physiology; Analysis of Variance; Applications; Biology, psychology, social sciences; Biometry - methods; Cognition; Cognition - physiology; Cognitive ability; Correlation analysis; Dementia; Dementia disorders; Evaluation; Exact sciences and technology; Female; General topics; Generalized logit; Humans; Longitudinal studies; Male; Markov Chains; Markov processes; Mathematics; Models, Statistical; Multivariate analysis; Multi‐stage; Probability and statistics; Probability theory and stochastic processes; Proportional odds; Random effects; Regression Analysis; Risk analysis; Risk assessment; Risk Factors; Sciences and techniques of general use; Statistics; Survival Analysis; Transition; Transition probabilities; Biometrics; Correlation; Goodness of fit test; Life science; Psychometrics; Random effects; Statistical association; Akaike information criterion; Multivariate analysis; Covariate; Multi-stage; Statistical method; Proportional odds; Model matching; Correlation analysis; Risk factor; Transition probability; Transition; Random effect; Numerical stability; Generalized logit
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.200900259

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.