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Area level models, such as the Fay–Herriot model, aim to improve direct survey estimates for small areas by borrowing strength from related covariates and from direct estimates across all areas. In their multivariate form, where related population characteristics are jointly modelled, area level models allow for inference about functions of two or more characteristics and may exploit dependence between the response variables to improve small area predictions. When model covariates are observed with random error, such as those drawn from another survey, it is important to account for this error in the modelling. We present a Bayesian analysis of a multivariate Fay–Herriot model with functional measurement error, allowing for both joint modelling of related characteristics and accounting for random observation error in some of the covariates. We apply it to modelling 2010 and 2011 poverty rates of school-aged children for US counties, for predicting 2011 poverty rates and the 2010–2011 changes. For this application, the measurement error model results in great improvements in prediction when compared with the direct estimates, and ignoring the measurement error results in uncertainty estimates that are misleading. We propose a computational approach to implementing this model via an independence chain Markov chain Monte Carlo algorithm and prove the propriety of the posterior distribution under a class of non-informative priors.

Background: Tau pathology is common in age-related neurodegenerative diseases. Tau pathology in primary age-related tauopathy (PART) and in Alzheimer's disease (AD) has a similar biochemical structure and anatomic distribution, which is distinct from tau pathology in other diseases. However, the molecular changes associated with intraneuronal tau pathology in PART and AD, and whether these changes are similar in the two diseases, is largely unexplored., Methods: Using GeoMx spatial transcriptomics, mRNA was quantified in CA1 pyramidal neurons with tau pathology and adjacent neurons without tau pathology in 6 cases of PART and 6 cases of AD, and compared to 4 control cases without pathology. Transcriptional changes were analyzed for differential gene expression and for coordinated patterns of gene expression associated with both disease state and intraneuronal tau pathology., Results: Synaptic gene changes and two novel gene expression signatures associated with intraneuronal tau were identified in PART and AD. Overall, gene expression changes associated with intraneuronal tau pathology were similar in PART and AD. Synaptic gene expression was decreased overall in neurons in AD and PART compared to control cases. However, this decrease was largely driven by neurons lacking tau pathology. Synaptic gene expression was increased in tau-positive neurons compared to tau-negative neurons in disease. Two novel gene expression signatures associated with intraneuronal tau were identified by examining coordinated patterns of gene expression. Genes in the up-regulated expression pattern were enriched in calcium regulation and synaptic function pathways, specifically in synaptic exocytosis. These synaptic gene changes and intraneuronal tau expression signatures were confirmed in a published transcriptional dataset of cortical neurons with tau pathology in AD., Conclusions: PART and AD show similar transcriptional changes associated with intraneuronal tau pathology in CA1 pyramidal neurons, raising the possibility of a mechanistic relationship between the tau pathology in the two diseases. Intraneuronal tau pathology was also associated with increased expression of genes associated with synaptic function and calcium regulation compared to tau-negative disease neurons. The findings highlight the power of molecular analysis stratified by pathology in neurodegenerative disease and provide novel insight into common molecular pathways associated with intraneuronal tau in PART and AD., Competing Interests: Competing Interests: The authors have no competing interests to declare.