Competing‐risks duration models with correlated random effects: an application to dementia patients’ transition histories

Multi-state transition models are widely applied tools to analyze individual event histories in the medical or social sciences. In this paper, we propose the use of (discrete-time) competing-risks duration models to analyze multi-transition data. Unlike conventional Markov transition models, these models allow the estimated transition probabilities to depend on the time spent in the current state. Moreover, the models can be readily extended to allow for correlated transition probabilities. A further virtue of these models is that they can be estimated using conventional regression tools for discrete-response data, such as the multinomial logit model. The latter is implemented in many statistical software packages and can be readily applied by empirical researchers. Moreover, model estimation is feasible, even when dealing with very large data sets, and simultaneously allowing for a flexible form of duration dependence and correlation between transition probabilities. We derive the likelihood function for a model with three competing target states and discuss a feasible and readily applicable estimation method. We also present the results from a simulation study, which indicate adequate performance of the proposed approach. In an empirical application, we analyze dementia patients' transition probabilities from the domestic setting, taking into account several, partly duration-dependent covariates.

[1]  A. Yashin,et al.  Heterogeneity's ruses: some surprising effects of selection on population dynamics. , 1985, The American statistician.

[2]  T. Mroz,et al.  Arbitrarily Normalized Coefficients, Information Sets, and False Reports of Biases in Binary Outcome Models , 2008, The Review of Economics and Statistics.

[3]  Kenneth E. Train,et al.  Discrete Choice Methods with Simulation , 2016 .

[4]  S. Greven,et al.  On the behaviour of marginal and conditional AIC in linear mixed models , 2010 .

[5]  D. Roth,et al.  Modeling Trajectories and Transitions: Results From the New York University Caregiver Intervention , 2011, Nursing research.

[6]  S. Vollset,et al.  Smoking and Deaths between 40 and 70 Years of Age in Women and Men , 2006, Annals of Internal Medicine.

[7]  Daniel Commenges,et al.  Multi-state Model for Dementia, Institutionalization, and Death , 2004 .

[8]  K. Hooker,et al.  Institutional Placement of Persons With Dementia , 2007, Journal of family nursing.

[9]  R. Holle,et al.  Excess costs of dementia disorders and the role of age and gender - an analysis of German health and long-term care insurance claims data , 2012, BMC Health Services Research.

[10]  B. Winblad,et al.  Institutionalization in the elderly: the role of chronic diseases and dementia. Cross-sectional and longitudinal data from a population-based study. , 2001, Journal of clinical epidemiology.

[11]  Elmar Brähler,et al.  Prediction of institutionalization in the elderly. A systematic review. , 2010, Age and ageing.

[12]  Jaroslaw Harezlak,et al.  An illness-death stochastic model in the analysis of longitudinal dementia data. , 2003, Statistics in medicine.

[13]  R. Lipton,et al.  Multi‐stage transitional models with random effects and their application to the Einstein aging study , 2011, Biometrical journal. Biometrische Zeitschrift.

[14]  J. Kalbfleisch,et al.  Marginal likelihoods based on Cox's regression and life model , 1973 .

[15]  D McDaid,et al.  The economic impact of dementia in Europe in 2008—cost estimates from the Eurocode project , 2011, International journal of geriatric psychiatry.

[16]  D Commenges,et al.  Incidence and mortality of Alzheimer's disease or dementia using an illness‐death model , 2004, Statistics in medicine.

[17]  R. Prentice,et al.  Regression analysis of grouped survival data with application to breast cancer data. , 1978, Biometrics.

[18]  C. Nicoletti,et al.  The (Mis)Specification of Discrete Duration Models with Unobserved Heterogeneity: A Monte Carlo Study , 2009 .

[19]  J. Vaupel,et al.  The impact of heterogeneity in individual frailty on the dynamics of mortality , 1979, Demography.

[20]  J Zhang,et al.  Risk factors for nursing home use after hospitalization for medical illness. , 1996, The journals of gerontology. Series A, Biological sciences and medical sciences.

[21]  P. Haan,et al.  Estimation of Multinomial Logit Models with Unobserved Heterogeneity using Maximum Simulated Likelihood , 2006 .

[22]  J. Goodwin,et al.  Risk of continued institutionalization after hospitalization in older adults. , 2011, The journals of gerontology. Series A, Biological sciences and medical sciences.

[23]  Lei Yu,et al.  Shared random effects analysis of multi‐state Markov models: application to a longitudinal study of transitions to dementia , 2007, Statistics in medicine.

[24]  Herbert Matschinger,et al.  Predictors of nursing home admission of individuals without a dementia diagnosis before admission - results from the Leipzig Longitudinal Study of the Aged (LEILA 75+) , 2010, BMC health services research.

[25]  Rolf Holle,et al.  Predictors of Institutionalization of Dementia Patients in Mild and Moderate Stages: A 4-Year Prospective Analysis , 2013, Dementia and Geriatric Cognitive Disorders Extra.

[26]  S. Rabe-Hesketh,et al.  Reliable Estimation of Generalized Linear Mixed Models using Adaptive Quadrature , 2002 .

[27]  D. Cox Regression Models and Life-Tables , 1972 .

[28]  S. Mitchell,et al.  Medicare expenditures among nursing home residents with advanced dementia. , 2011, Archives of internal medicine.

[29]  C. Berr,et al.  Prevalence of dementia in the elderly in Europe , 2005, European Neuropsychopharmacology.

[30]  F. Jessen,et al.  Predictors of Institutionalisation in Incident Dementia – Results of the German Study on Ageing, Cognition and Dementia in Primary Care Patients (AgeCoDe Study) , 2012, Dementia and Geriatric Cognitive Disorders.

[31]  C. Bhat Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model , 2001 .

[32]  Tim Futing Liao,et al.  Multinomial Logit Models , 1994 .

[33]  F. Buntinx,et al.  The process of definitive institutionalization of community dwelling demented vs non demented elderly: data obtained from a network of sentinel general practitioners , 2009, International journal of geriatric psychiatry.

[34]  R. Holle,et al.  Are community-living and institutionalized dementia patients cared for differently? Evidence on service utilization and costs of care from German insurance claims data , 2013, BMC Health Services Research.