High-dimensional change point detection for mean and location parameters

Change point inference refers to detection of structural breaks of a sequence observation, which may have one or more distributional shifts subject to models such as mean or covariance changes. In this dissertation, we consider the offline multiple change point problem that the sample size is fixed in advance or after observation. In particular, we concentrate on high-dimensional setup where the dimension $p$ can be much larger than the sample size $n$ and traditional distribution assumptions can easily fail. The goal is to employ non-parametric approaches to identify change points without involving intermediate estimation to cross-sectional dependence. In the first part, we consider cumulative sum (CUSUM) statistics that are widely used in the change point inference and identification. We study two problems for high-dimensional mean vectors based on the $\ell^{\infty}$-norm of the CUSUM statistics. For the problem of testing for the existence of a change point in an independent sample generated from the mean-shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data-dependent and it has strong theoretical guarantees under arbitrary dependence structures and mild moment conditions. Specifically, we show that with a boundary removal parameter the bootstrap CUSUM test enjoys the uniform validity in size under the null and it achieves the minimax separation rate under the sparse alternatives when $p \gg n$. Once a change point is detected, we estimate the change point location by maximizing the $\ell^{\infty}$-norm of the generalized CUSUM statistics at two different weighting scales. The first estimator is based on the covariance stationary CUSUM statistics, and we prove its consistency in estimating the location at the nearly parametric rate $n^{-1/2}$ for sub-exponential observations. The second estimator is based on non-stationary CUSUM statistics, assigning less weights on the boundary data points. In the latter case, we show that it achieves the nearly best possible rate of convergence on the order $n^{-1}$. In both cases, dimension impacts the rate of convergence only through the logarithm factors, and therefore consistency of the CUSUM location estimators is possible when $p$ is much larger than $n$. In the presence of multiple change points, we propose a principled bootstrap-assisted binary segmentation (BABS) algorithm to dynamically adjust the change point detection rule and recursively estimate their locations. We derive its rate of convergence under suitable signal separation and strength conditions. The results derived are non-asymptotic and we provide extensive simulation studies to assess the finite sample performance. The empirical evidence shows an encouraging agreement with our theoretical results. In the second part, we analyze the problem of change point detection for high-dimensional distributions in a location family. We propose a robust, tuning-free (i.e., fully data-dependent), and easy-to-implement change point test formulated in the multivariate $U$-statistics framework with anti-symmetric and nonlinear kernels. It achieves the robust purpose in a non-parametric setting when CUSUM statistics are sensitive to outliers and heavy-tailed distributions. Specifically, the within-sample noise is canceled out by anti-symmetry of the kernel, while the signal distortion under certain nonlinear kernels can be controlled such that the between-sample change point signal is magnitude preserving. A (half) jackknife multiplier bootstrap (JMB) tailored to the change point detection setting is proposed to calibrate the distribution of our $\ell^{\infty}$-norm aggregated test statistic. Subject to mild moment conditions on kernels, we derive the uniform rates of convergence for the JMB to approximate the sampling distribution of the test statistic, and analyze its size and power properties. Extensions to multiple change point testing and estimation are discussed with illustration from numeric studies

Enrollment Forecast for Clinical Trials at the Planning Phase with Study-Level Historical Data

Given progressive developments and demands on clinical trials, accurate enrollment timeline forecasting is increasingly crucial for both strategic decision-making and trial execution excellence. Naive approach assumes flat rates on enrollment using average of historical data, while traditional statistical approach applies simple Poisson-Gamma model using timeinvariant rates for site activation and subject recruitment. Both of them are lack of nontrivial factors such as time and location. We propose a novel two-segment statistical approach based on Quasi-Poisson regression for subject accrual rate and Poisson process for subject enrollment and site activation. The input study-level data is publicly accessible and it can be integrated with historical study data from user's organization to prospectively predict enrollment timeline. The new framework is neat and accurate compared to preceding works. We validate the performance of our proposed enrollment model and compare the results with other frameworks on 7 curated studies

A simplified climate change model and extreme weather model based on a machine learning method

The emergence of climate change (CC) is affecting and changing the development of the natural environment, biological species, and human society. In order to better understand the influence of climate change and provide convincing evidence, the need to quantify the impact of climate change is urgent. In this paper, a climate change model is constructed by using a radial basis function (RBF) neural network. To verify the relevance between climate change and extreme weather (EW), the EW model was built using a support vector machine. In the case study of Canada, its level of climate change was calculated as being 0.2241 ("normal"), and it was found that the factors of CO2 emission, average temperature, and sea surface temperature are significant to Canada's climate change. In 2025, the climate level of Canada will become "a little bad" based on the prediction results. Then, the Pearson correlation value is calculated as being 0.571, which confirmed the moderate positive correlation between climate change and extreme weather. This paper provides a strong reference for comprehensively understanding the influences brought about by climate change

Shared decision making in sarcopenia treatment

The implementation of shared decision making (SDM) in management of sarcopenia is still in its nascent stage, especially compared to other areas of medical research. Accumulating evidence has highlighted the importance of SDM in older adults care. The current study overviews general SDM practices and explores the potential advantages and dilemmas of incorporating these concepts into sarcopenia management. We present common patient decision aids available for sarcopenia management and propose future research directions. SDM can be effectively integrated into daily practice with the aid of structured techniques, such as the “seek, help, assess, reach, evaluate” approach, “making good decisions in collaboration” questions, “benefits, risks, alternatives, doing nothing” tool, or “multifocal approach to sharing in shared decision making.” Such techniques fully consider patient values and preferences, thereby enhancing adherence to and satisfaction with the intervention measures. Additionally, we review the barriers to and potential solutions to SDM implementation. Further studies are required to investigate measurement and outcomes, coordination and cooperation, and digital technology, such as remote SDM. The study concludes that sarcopenia management must go beyond the single dimension of “Paternalism” choice. Integrating SDM into clinical practice offers promising opportunities to improve patient care, with patient-centered care and partnership of care approaches positively impacting treatment outcomes