People are living longer than ever before, and with this arises new complications and challenges for humanity. Among the most pressing of these challenges is of understanding the role of aging in the development of dementia. This paper is motivated by the Mayo Clinic Study of Aging data for 4742 subjects since 2004, and how it can be used to draw inference on the role of aging in the development of dementia. We construct a hidden Markov model (HMM) to represent progression of dementia from states associated with the buildup of amyloid plaque in the brain, and the loss of cortical thickness. A hierarchical Bayesian approach is taken to estimate the parameters of the HMM with a truly time-inhomogeneous infinitesimal generator matrix, and response functions of the continuous-valued biomarker measurements are cut-point agnostic. A Bayesian approach with these features could be useful in many disease progression models. Additionally, an approach is illustrated for correcting a common bias in delayed enrollment studies, in which some or all subjects are not observed at baseline. Standard software is incapable of accounting for this critical feature, so code to perform the estimation of the model described below is made available online.

Objective Diagnostic criteria from 2002 classify transverse myelitis (TM) as idiopathic or disease associated but predate the discovery of aquaporin-4 (AQP4)–immunoglobulin G (IgG) and myelin oligodendrocyte glycoprotein (MOG)-IgG, which associate with TM. Prior incidence estimates of idiopathic TM (ITM) range from 1 to 6.2 per 1 million. We sought to determine whether the population-based incidence and prevalence of ITM were reduced by testing patients with ITM for AQP4/MOG-IgG and reclassifying seropositive cases as having disease-associated TM. Methods For this observational study, we retrospectively identified all cases of incident (January 1, 2003–December 31, 2016) and prevalent (December 31, 2016) ITM in Olmsted County (85% white) by using the Rochester Epidemiology Project medical records linkage system. ITM was defined by the 2002 Transverse MyelitisConsortium Working Group diagnostic criteria. Available sera were tested for AQP4-IgG and MOG-IgG. Results Twenty-four patients (incident 22, prevalent 17) initially met 2002 ITM criteria (longitudinally extensive TM [LETM] 6). Sera were tested for AQP4-IgG in 22 of 24 (92%) and MOG-IgG in 21 of 24 (88%). Three seropositive cases (AQP4-IgG 2, MOG-IgG 1) were identified and reclassified as having disease-associated TM, accounting for 14% of total incident and 12% of total prevalent cases. AQP4-IgG and MOG-IgG seropositive cases represented 50% (3 of 6) of idiopathic LETM. After reclassification of seropositive patients, the final ITM incidence was 8.6 per 1,000,000 and prevalence was 7.9 per 100,000. Three cases of ITM (14%) subsequently fulfilled multiple sclerosis criteria within the study period. Conclusions The availability of AQP4-IgG and MOG-IgG modestly reduced ITM incidence and prevalence, which remained higher than previously reported in this predominantly white population. Incorporation of these biomarkers into future revisions of TM diagnostic criteria should be considered.

Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design matrix is collinear. To overcome this challenge, an entirely new perspective on variable selection is presented within a generalized fiducial inference framework. This new procedure is able to effectively account for linear dependencies among subsets of covariates in a high-dimensional setting where $p$ can grow almost exponentially in $n$, as well as in the classical setting where $p\le n$. It is shown that the procedure very naturally assigns small probabilities to subsets of covariates which include redundancies by way of explicit $L_{0}$ minimization. Furthermore, with a typical sparsity assumption, it is shown that the proposed method is consistent in the sense that the probability of the true sparse subset of covariates converges in probability to 1 as $n\to\infty$, or as $n\to\infty$ and $p\to\infty$. Very reasonable conditions are needed, and little restriction is placed on the class of possible subsets of covariates to achieve this consistency result.

As evidenced by various recent and significant papers within the frequentist literature, along with numerous applications in macroeconomics, genomics, and neuroscience, there continues to be substantial interest in understanding the theoretical estimation properties of high‐dimensional vector autoregression (VAR) models. To date, however, while Bayesian VAR (BVAR) models have been developed and studied empirically (primarily in the econometrics literature), there exist very few theoretical investigations of the repeated‐sampling properties for BVAR models in the literature, and there exist no generalized fiducial investigations of VAR models. In this direction, we construct methodology via the ‐admissible subsets (EAS) approach for inference based on a generalized fiducial distribution of relative model probabilities over all sets of active/inactive components (graphs) of the VAR transition matrix. We provide a mathematical proof of pairwise and strong graphical selection consistency for the EAS approach for stable VAR(1) models, and demonstrate empirically that it is an effective strategy in high‐dimensional settings.