An examination of Bayesian statistical approaches to modeling change in cognitive decline in an Alzheimer's disease population

Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete follow-up

Many medical (and ecological) processes involve the change of shape, whereby one trajectory changes into another trajectory at a specific time point. There has been little investigation into the study design needed to investigate these models. We consider the class of fixed effect change-point models with an underlying shape comprised two joined linear segments, also known as broken-stick models. We extend this model to include two sub-groups with different trajectories at the change-point, a change and no change class, and also include a missingness model to account for individuals with incomplete follow-up. Through a simulation study, we consider the relationship of sample size to the estimates of the underlying shape, the existence of a change-point, and the classification-error of sub-group labels. We use a Bayesian framework to account for the missing labels, and the analysis of each simulation is performed using standard Markov chain Monte Carlo techniques. Our simulation study is inspired by cognitive decline as measured by the Mini-Mental State Examination, where our extended model is appropriate due to the commonly observed mixture of individuals within studies who do or do not exhibit accelerated decline. We find that even for studies of modest size (n = 500, with 50 individuals observed past the change-point) in the fixed effect setting, a change-point can be detected and reliably estimated across a range of observation-errors.

Bayesian graphical network analyses reveal complex biological interactions specific to Alzheimer's disease

With different approaches to finding prognostic or diagnostic biomarkers for Alzheimer's disease (AD), many studies pursue only brief lists of biomarkers or disease specific pathways, potentially dismissing information from groups of correlated biomarkers. Using a novel Bayesian graphical network method, with data from the Australian Imaging, Biomarkers and Lifestyle (AIBL) study of aging, the aim of this study was to assess the biological connectivity between AD associated blood-based proteins. Briefly, three groups of protein markers (18, 37, and 48 proteins, respectively) were assessed for the posterior probability of biological connection both within and between clinical classifications. Clinical classification was defined in four groups: high performance healthy controls (hpHC), healthy controls (HC), participants with mild cognitive impairment (MCI), and participants with AD. Using the smaller group of proteins, posterior probabilities of network similarity between clinical classifications were very high, indicating no difference in biological connections between groups. Increasing the number of proteins increased the capacity to separate both hpHC and HC apart from the AD group (0 for complete separation, 1 for complete similarity), with posterior probabilities shifting from 0.89 for the 18 protein group, through to 0.54 for the 37 protein group, and finally 0.28 for the 48 protein group. Using this approach, we identified beta-2 microglobulin (β2M) as a potential master regulator of multiple proteins across all classifications, demonstrating that this approach can be used across many data sets to identify novel insights into diseases like AD.

Prediction models for assessing long-term outcome in Alzheimer's disease: a review

In Alzheimer's disease (AD), placebo-controlled long-term studies of cholinesterase inhibitors (ChEIs) are not permitted for ethical reasons. Therefore, in these studies, patients' outcomes on cognitive and functional assessment scales must be compared with mathematical models or historical data from untreated cohorts. PubMed and previously published long-term extensions of clinical trials and naturalistic studies of ChEIs were examined to identify empirical statistical models and other approaches, such as use of data from historical cohorts or extrapolated changes from extension studies, that were used to draw comparisons between ChEI-treated and untreated patients. The models and methods were described. It is essential to be aware of the limitations of comparisons made with these approaches. Prediction models based on ChEI-treated patients can be used in the studies of new treatments when those treatments are added to ChEIs. More sophisticated models that also accommodate patient-specific characteristics should be developed for comparisons in future long-term AD studies.

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 death.