Disentangling sex-dependent effects of APOE on diverse trajectories of cognitive decline in Alzheimer's disease

Current diagnostic systems for Alzheimer's disease (AD) rely upon clinical signs and symptoms, despite the fact that the multiplicity of clinical symptoms renders various neuropsychological assessments inadequate to reflect the underlying pathophysiological mechanisms. Since putative neuroimaging biomarkers play a crucial role in understanding the etiology of AD, we sought to stratify the diverse relationships between AD biomarkers and cognitive decline in the aging population and uncover risk factors contributing to the diversities in AD. To do so, we capitalized on a large amount of neuroimaging data from the ADNI study to examine the inflection points along the dynamic relationship between cognitive decline trajectories and whole-brain neuroimaging biomarkers, using a state-of-the-art statistical model of change point detection. Our findings indicated that the temporal relationship between AD biomarkers and cognitive decline may differ depending on the synergistic effect of genetic risk and biological sex. Specifically, tauopathy-PET biomarkers exhibit a more dynamic and age-dependent association with Mini-Mental State Examination scores (p<0.05), with inflection points at 72, 78, and 83 years old, compared with amyloid-PET and neurodegeneration (cortical thickness from MRI) biomarkers. In the landscape of health disparities in AD, our analysis indicated that biological sex moderates the rate of cognitive decline associated with APOE4 genotype. Meanwhile, we found that higher education levels may moderate the effect of APOE4, acting as a marker of cognitive reserve.

A New Class of Weighted CUSUM Statistics

A change point is a location or time at which observations or data obey two different models: before and after. In real problems, we may know some prior information about the location of the change point, say at the right or left tail of the sequence. How does one incorporate the prior information into the current cumulative sum (CUSUM) statistics? We propose a new class of weighted CUSUM statistics with three different types of quadratic weights accounting for different prior positions of the change points. One interpretation of the weights is the mean duration in a random walk. Under the normal model with known variance, the exact distributions of these statistics are explicitly expressed in terms of eigenvalues. Theoretical results about the explicit difference of the distributions are valuable. The expansions of asymptotic distributions are compared with the expansion of the limit distributions of the Cramér-von Mises statistic and the Anderson and Darling statistic. We provide some extensions from independent normal responses to more interesting models, such as graphical models, the mixture of normals, Poisson, and weakly dependent models. Simulations suggest that the proposed test statistics have better power than the graph-based statistics. We illustrate their application to a detection problem with video data.

High Dimensional Change Point Inference: Recent Developments and Extensions

Change point analysis aims to detect structural changes in a data sequence. It has always been an active research area since it was introduced in the 1950s. In modern statistical applications, however, high-throughput data with increasing dimensions are ubiquitous in fields ranging from economics, finance to genetics and engineering. For those problems, the earlier works are typically no longer applicable. As a result, the problem of testing a change point for high dimensional data sequences has been an important yet challenging task. In this paper, we first focus on models for at most one change point, and review recent state-of-art techniques for change point testing of high dimensional mean vectors and compare their theoretical properties. Based on that, we provide a survey of some extensions to general high dimensional parameters beyond mean vectors as well as strategies for testing multiple change points in high dimensions. Finally, we discuss some open problems for possible future research directions.

Structural change detection in ordinal time series

Change-point detection in health care data has recently obtained considerable attention due to the increased availability of complex data in real-time. In many applications, the observed data is an ordinal time series. Two kinds of test statistics are proposed to detect the structural change of cumulative logistic regression model, which is often used in applications for the analysis of ordinal time series. One is the standardized efficient score vector, the other one is the quadratic form of the efficient score vector with a weight function. Under the null hypothesis, we derive the asymptotic distribution of the two test statistics, and prove the consistency under the alternative hypothesis. We also study the consistency of the change-point estimator, and a binary segmentation procedure is suggested for estimating the locations of possible multiple change-points. Simulation results show that the former statistic performs better when the change-point occurs at the centre of the data, but the latter is preferable when the change-point occurs at the beginning or end of the data. Furthermore, the former statistic could find the reason for rejecting the null hypothesis. Finally, we apply the two test statistics to a group of sleep data, the results show that there exists a structural change in the data.