Hidden three-state survival model for bivariate longitudinal count data

A model is presented that describes bivariate longitudinal count data by conditioning on a progressive illness-death process where the two living states are latent. The illness-death process is modelled in continuous time, and the count data are described by a bivariate extension of the binomial distribution. The bivariate distributions for the count data approach include the correlation between two responses even after conditioning on the state. An illustrative data analysis is discussed, where the bivariate data consist of scores on two cognitive tests, and the latent states represent two stages of underlying cognitive function. By including a death state, possible association between cognitive function and the risk of death is accounted for

Change point models for cognitive tests using semi-parametric maximum likelihood

Random-effects change point models are formulated for longitudinal data obtained from cognitive tests. The conditional distribution of the response variable in a change point model is often assumed to be normal even if the response variable is discrete and shows ceiling effects. For the sum score of a cognitive test, the binomial and the beta-binomial distributions are presented as alternatives to the normal distribution. Smooth shapes for the change point models are imposed. Estimation is by marginal maximum likelihood where a parametric population distribution for the random change point is combined with a non-parametric mixing distribution for other random effects. An extension to latent class modelling is possible in case some individuals do not experience a change in cognitive ability. The approach is illustrated using data from a longitudinal study of Swedish octogenarians and nonagenarians that began in 1991. Change point models are applied to investigate cognitive change in the years before deat

Accounting for self-protective responses in randomized response data from a social security survey using the zero-inflated Poisson model

In 2004 the Dutch Department of Social Affairs conducted a survey to assess the extent of noncompliance with social security regulations. The survey was conducted among 870 recipients of social security benefits and included a series of sensitive questions about regulatory noncompliance. Due to the sensitive nature of the questions the randomized response design was used. Although randomized response protects the privacy of the respondent, it is unlikely that all respondents followed the design. In this paper we introduce a model that allows for respondents displaying self-protective response behavior by consistently giving the nonincriminating response, irrespective of the outcome of the randomizing device. The dependent variable denoting the total number of incriminating responses is assumed to be generated by the application of randomized response to a latent Poisson variable denoting the true number of rule violations. Since self-protective responses result in an excess of observed zeros in relation to the Poisson randomized response distribution, these are modeled as observed zero-inflation. The model includes predictors of the Poisson parameters, as well as predictors of the probability of self-protective response behavior.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS135 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Active Cognitive Lifestyle Associates with Cognitive Recovery and a Reduced Risk of Cognitive Decline

Education and lifestyle factors linked with complex mental activity are thought to affect the progression of cognitive decline. Collectively, these factors can be combined to create a cognitive reserve or cognitive lifestyle score. This study tested the association between cognitive lifestyle score and cognitive change in a population-based cohort of older persons from five sites across England and Wales. Data came from 13,004 participants of the Medical Research Council Cognitive Function and Ageing Study who were aged 65 years and over. Cognition was assessed at multiple waves over 16 years using the Mini-Mental State Examination. Subjects were grouped into four cognitive states (no impairment, slight impairment, moderate impairment, severe impairment) and cognitive lifestyle score was assessed as a composite measure of education, mid-life occupation, and current social engagement. A multi-state model was used to test the effect of cognitive lifestyle score on cognitive transitions. Hazard ratios for cognitive lifestyle score showed significant differences between those in the upper compared to the lower tertile with a more active cognitive lifestyle associating with: a decreased risk of moving from no to slight impairment (0.58, 95% CI (0.45, 0.74)); recovery from a slightly impaired state back to a non-impaired state (2.93 (1.35, 6.38)); but an increased mortality risk from a severely impaired state (1.28 (1.12, 1.45)). An active cognitive lifestyle is associated with a more favorable cognitive trajectory in older persons. Future studies would ideally incorporate neuroradiological and neuropathological data to determine if there is causal evidence for these associations

Estimating dementia-free life expectancy for Parkinson's patients using Bayesian inference and microsimulation

Interval-censored longitudinal data taken from a Norwegian study of individuals with Parkinson's disease are investigated with respect to the onset of dementia. Of interest are risk factors for dementia and the subdivision of total life expectancy (LE) into LE with and without dementia. To estimate LEs using extrapolation, a parametric continuous-time 3-state illness–death Markov model is presented in a Bayesian framework. The framework is well suited to allow for heterogeneity via random effects and to investigate additional computation using model parameters. In the estimation of LEs, microsimulation is used to take into account random effects. Intensities of moving between the states are allowed to change in a piecewise-constant fashion by linking them to age as a time-dependent covariate. Possible right censoring at the end of the follow-up can be incorporated. The model is applicable in many situations where individuals are followed over a long time period. In describing how a disease develops over time, the model can help to predict future need for health care

Analysing cognitive test data: Distributions and non-parametric random effects

An important assumption in many linear mixed models is that the conditional distribution of the response variable is normal. This assumption is violated when the models are fitted to an outcome variable that counts the number of correctly answered questions in a questionnaire. Examples include investigations of cognitive decline where models are fitted to Mini Mental State Examination scores, the most widely used test to measure global cognition. Mini Mental State Examination scores take integer values in the 0–30 range, and its distribution has strong ceiling and floor effects. This article explores alternative distributions for the outcome variable in mixed models fitted to mini mental state examination scores from a longitudinal study of ageing. Model fit improved when a beta-binomial distribution was chosen as the distribution for the response variable

Transitions across cognitive states and death among older adults in relation to education:A multistate survival model using data from six longitudinal studies

INTRODUCTION: This study examines the role of educational attainment, an indicator of cognitive reserve, on transitions in later life between cognitive states (normal Mini-Mental State Examination (MMSE), mild MMSE impairment, and severe MMSE impairment) and death. METHODS: Analysis of six international longitudinal studies was performed using a coordinated approach. Multistate survival models were used to estimate the transition patterns via different cognitive states. Life expectancies were estimated. RESULTS: Across most studies, a higher level of education was associated with a lower risk of transitioning from normal MMSE to mild MMSE impairment but was not associated with other transitions. Those with higher levels of education and socioeconomic status had longer nonimpaired life expectancies. DISCUSSION: This study highlights the importance of education in later life and that early life experiences can delay later compromised cognitive health. This study also demonstrates the feasibility and benefit in conducting coordinated analysis across multiple studies to validate findings