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Efficient algorithms for survival data with multiple outcomes using the frailty model

STATISTICAL METHODS IN MEDICAL RESEARCH 2023年第1期32卷 118-132页

作者： Huang, Xifen Xu, Jinfeng Zhou, Yunpeng Yunnan Normal Univ Sch Math Kunming Yunnan Peoples R China City Univ Hong Kong Dept Biostat Hong Kong Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Peoples R China

Survival data with multiple outcomes are frequently encountered in biomedical investigations. An illustrative example comes from Alzheimer's Disease Neuroimaging Initiative study where the cognitively normal subjects may clinically progress to mild cognitive impairment and/or Alzheimer's disease dementia. Transition time from normal cognition to mild cognitive impairment and that from mild cognitive impairment to Alzheimer's disease are expected to be correlated within subjects and the dependence is often accommodated by the frailty (random effects). Estimation in the frailty model unavoidably involves multiple integrations which may be intractable and hence leads to severe computational challenges, especially in the presence of high-dimensional covariates. In this paper, we propose efficient minorization-maximization algorithms in the frailty model for survival data with multiple outcomes. The alternating direction method of multipliers is further incorporated for simultaneous variable selection and homogeneity pursuit via regularization and fusion. Extensive simulation studies are conducted to assess the performance of the proposed algorithms. An application to the Alzheimer's Disease Neuroimaging Initiative data is also provided to illustrate their practical utilities.

关键词： Alternating direction method of multipliers Alzheimer's Disease Neuroimaging Initiative homogeneity pursuit minorization-maximization algorithm sparsity the frailty model

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Laplace mixture autoregressive models

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STATISTICS & PROBABILITY LETTERS 2016年 110卷 18-24页

作者： Nguyen, Hien D. McLachlan, Geoffrey J. Ullmann, Jeremy F. P. Janke, Andrew L. Univ Queensland Sch Math & Phys St Lucia Qld Australia Univ Queensland Ctr Adv Imaging St Lucia Qld Australia

Autoregressive (AR) models are an important tool in the study of time series data. However, the standard AR model only allows for unimodal marginal and conditional densities, and cannot capture conditional heteroscedasticity. Previously, the Gaussian mixture AR (GMAR) model was considered to remedy these shortcomings by using a Gaussian mixture conditional model. We introduce the Laplace mixture (LMAR) model that utilizes a Laplace mixture conditional model, as an alternative to the GMAR model. We characterize the LMAR model and provide conditions for stationarity. An MM (minorization-maximization) algorithm is then proposed for maximum pseudolikelihood (MPL) estimation of an LMAR model. Conditions for asymptotic inference and a rule for model selection for the MPL estimator are considered. An example analysis of data arising from the calcium imaging of a zebrafish brain is performed. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Laplace distribution Mixture model Autoregressive model minorization-maximization algorithm Calcium imaging Zebrafish brain

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A robust and efficient estimation method for partially nonlinear models via a new MM algorithm

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STATISTICAL PAPERS 2019年第6期60卷 2063-2085页

作者： Jiang, Yunlu Tian, Guo-Liang Fei, Yu Jinan Univ Dept Stat Coll Econ Guangzhou 510632 Guangdong Peoples R China Southern Univ Sci & Technol Dept Math Shenzhen 518055 Peoples R China Yunnan Univ Finance & Econ Sch Math & Stat Kunming 650221 Yunnan Peoples R China

When the observed data set contains outliers, it is well known that the classical least squares method is not robust. To overcome this difficulty, Wang et al. (J Am Stat Assoc 108(502): 632-643, 2013) proposed a robust variable selection method by using the exponential squared loss (ESL) function with a tuning parameter. Although many important statistical models are investigated, to date, in the presence of outliers there is no paper to study the partially nonlinear model by using the ESL function. To fill in this gap, in this paper, we propose a robust and efficient estimation method for the partially nonlinear model based on the ESL function. Under certain conditions, we have shown that the proposed estimators can achieve the best convergence rates. Next, the asymptotic normality of the proposed estimators is established. In addition, we develop a new minorization-maximization algorithm to calculate the estimates for both non-parametric and parametric parts and present a procedure for deriving initial values. Finally, we provide a data-driven approach to select the tuning parameters. Numerical simulations and a real data analysis are used to illustrate that when there are outliers, the proposed ESL method is more robust and efficient for partially nonlinear models than the existing linear approximation method and the composite quantile regression method.

关键词： Exponential squared loss function minorization-maximization algorithm Partially nonlinear model Robustness

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Penalized generalized estimating equations approach to longitudinal data with multinomial responses

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2021年第3期50卷 844-859页

作者： Kamruzzaman, Md Kwon, Oran Park, Taesung Seoul Natl Univ Dept Stat Seoul 08826 South Korea Ewha Womans Univ Dept Nutr Sci & Food Management Seoul 120750 South Korea Seoul Natl Univ Interdisciplinary Program Bioinformat Seoul 08826 South Korea

In high-dimensional longitudinal data with multinomial response, the number of covariates is always much larger than the number of subjects and when modelling such data, variable selection is always an important issue. In this study, we developed the penalized generalized estimating equation for multinomial responses for identifying important variables and estimation of their regression coefficients simultaneously. An iterative algorithm is used to solve the penalized estimating equation by combining the Fisher-scoring algorithm and minorization-maximization algorithm. We used a penalty term to regularize the slope part only because category-specific intercept terms should be included in the multinomial model. We conducted a simulation study to investigate the performance of the proposed method and demonstrated its performance using real dataset.

关键词： High-dimensional data Longitudinal data Multinomial response minorization-maximization algorithm Smoothly Clipped Absolute Deviation penalty Minimax Concave Penalty Variable selection

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Robust variable selection for the varying index coefficient models

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2023年第4期52卷 767-793页

作者： Zou, Hang Jiang, Yunlu Jinan Univ Coll Econ Dept Stat & Data Sci Guangzhou 510632 Peoples R China

Recently, the statistical inference of the varying index coefficient model has been widely concerned. However, to the best of our knowledge, there has no existing robust variable selection method for the varying index coefficient model in the presence of outliers in the response and covariates. To overcome this difficulty, we develop a robust variable selection method for the varying index coefficient model via the exponential squared loss (ESL) function in this article. We first approximate nonparametric functions by B-spline basis functions and then apply the minorization-maximization (MM) algorithm and the Fisher scoring algorithm to calculate the proposed estimators. Under some mild conditions, the theoretical properties of the proposed estimators are established. Furthermore, we propose a data-driven procedure to select the tuning parameters. Some numerical simulations are conducted to illustrate the finite sample performance of the proposed method. Finally, the analysis of New Zealand workforce data reveals the merit of the proposed method.

关键词： Varying index coefficient model Exponential squared loss function Robust variable selection minorization-maximization algorithm

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Modeling intra-individual inter-trial EEG response variability in autism

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STATISTICS IN MEDICINE 2024年第17期43卷 3239-3263页

作者： Dong, Mingfei Telesca, Donatello Guindani, Michele Sugar, Catherine Webb, Sara J. Jeste, Shafali Dickinson, Abigail Levin, April R. Shic, Frederick Naples, Adam Faja, Susan Dawson, Geraldine Mcpartland, James C. Sentuerk, Damla Univ Calif Los Angeles Dept Biostat Los Angeles CA 90095 USA Univ Calif Los Angeles Dept Psychiat & Biobehav Sci Los Angeles CA USA Seattle Childrens Res Inst Ctr Child Hlth Behav & Dev Seattle WA USA Univ Washington Sch Med Dept Psychiat & Behav Sci Seattle WA USA Childrens Hosp Los Angeles Dept Pediat Div Neurol Los Angeles CA USA Boston Childrens Hosp Div Neurol Boston MA USA Harvard Med Sch Div Neurol Boston MA USA Univ Washington Sch Med Dept Pediat Seattle WA USA Yale Univ Sch Med Ctr Child Study New Haven CT USA Boston Childrens Hosp Div Dev Med Lab Cognit Neurosci Boston MA USA Harvard Med Sch Dept Pediat Boston MA USA Duke Univ Duke Ctr Autism & Brain Dev Durham NC USA

Autism spectrum disorder (autism) is a prevalent neurodevelopmental condition characterized by early emerging impairments in social behavior and communication. EEG represents a powerful and non-invasive tool for examining functional brain differences in autism. Recent EEG evidence suggests that greater intra-individual trial-to-trial variability across EEG responses in stimulus-related tasks may characterize brain differences in autism. Traditional analysis of EEG data largely focuses on mean trends of the trial-averaged data, where trial-level analysis is rarely performed due to low neural signal to noise ratio. We propose to use nonlinear (shape-invariant) mixed effects (NLME) models to study intra-individual inter-trial EEG response variability using trial-level EEG data. By providing more precise metrics of response variability, this approach could enrich our understanding of neural disparities in autism and potentially aid the identification of objective markers. The proposed multilevel NLME models quantify variability in the signal's interpretable and widely recognized features (e.g., latency and amplitude) while also regularizing estimation based on noisy trial-level data. Even though NLME models have been studied for more than three decades, existing methods cannot scale up to large data sets. We propose computationally feasible estimation and inference methods via the use of a novel minorization-maximization (MM) algorithm. Extensive simulations are conducted to show the efficacy of the proposed procedures. Applications to data from a large national consortium find that children with autism have larger intra-individual inter-trial variability in P1 latency in a visual evoked potential (VEP) task, compared to their neurotypical peers.

关键词： autism spectrum disorder (autism) electroencephalography intra-individual inter-trial variability minorization-maximization algorithm nonlinear mixed effects models

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The fully visible Boltzmann machine and the Senate of the 45th Australian Parliament in 2016

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JOURNAL OF COMPUTATIONAL SOCIAL SCIENCE 2020年第1期3卷 55-81页

作者： Bagnall, Jessica J. Jones, Andrew T. Karavarsamis, Natalie Nguyen, Hien D. La Trobe Univ Dept Math & Stat Melbourne Vic 3086 Australia Univ Queensland Sch Math & Phys Brisbane Qld 4072 Australia

After the 2016 double dissolution election, the 45th Australian Parliament was formed. At the time of its swearing in, the Senate of the 45th Australian Parliament consisted of nine political parties, the largest number in the history of the Australian Parliament. Due to the breadth of the political spectrum that the Senate represented, the situation presented an interesting opportunity for the study of political interactions in the Australian context. Using publicly available Senate voting data in 2016, we quantitatively analyzed two aspects of the Senate. First, we analyzed the degree to which each of the non-government parties of the Senate is pro- or anti-government. Second, we analyzed the degree to which the votes of each of the non-government Senate parties are in concordance or discordance with one another. We utilized the fully visible Boltzmann machine (FVBM) model to conduct these analyses. The FVBM is an artificial neural network that can be viewed as a multivariate generalization of the Bernoulli distribution. Via a maximum pseudolikelihood estimation approach, we conducted parameter estimation and constructed hypothesis tests that revealed the interaction structures within the Australian Senate. The conclusions that we drew are well supported by external sources of information.

关键词： Australian Parliament Bernoulli distribution Maximum pseudolikelihood estimation minorization-maximization algorithm Neural networks Parametric model

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Transitions in New Technology and Market Structure: Applications and New Methods for Discrete Choice Model Estimation

Transitions in New Technology and Market Structure: Applicat...

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作者： Wang, Shuang Boston University

学位级别：Ph.D., Doctor of Philosophy

My dissertation consists of three chapters that evaluate the social welfare effect of either antitrust policy or industrial transition, all using discrete choice model estimation as the front end for counterfactual analysis. In the first chapter, I investigate the economic impact of the merger that created the world's largest hotel chain, Marriott's acquisition of Starwood, thereby shedding light on the antitrust authorities' performance in protecting competitive markets for the benefit of consumers. Different from traditional merger analysis that focuses on the tradeoff between the upward pricing pressure and the cost synergy among the merging parties while fixing the market structure, I endogenize firms’ entry decisions into an oligopoly price competition model. To tackle the associated multiple equilibria issue, I use moment inequality estimation and propose a novel lower probability bound that reduces the computational burden from being exponential to being linear in the number of players. It also adds to the scant empirical evidence on post-merger cost synergy by showing that every one more affiliated hotel in the local market reduces a hotel's marginal cost by up to 2.3%. Then a comparison between the simulated with-merger and without-merger equilibria indicates that this merger enhances social welfare. In particular, for those markets that are previously not profitable for any firm to enter, because of the post-merger cost saving, Marriott or Starwood would enter 6% - 24% of them, which provides a new perspective for merger reviews. The second chapter, joint with Mingli Chen, Marc Rysman and Krzysztof Wozniak, studies the determinants of the US payment system's shift from paper payment instruments, namely cash and check, to digital instruments, such as debit cards and credit cards. With a 5-year transaction-level panel data, for the first time in the literature, we can distinguish the short-term effects of transaction size from the long-term changes in househ

关键词： Cloud computing Demand estimation Entry game Merger simulation minorization-maximization algorithm Moment inequality

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Mean regression model for the zero-truncated Poisson distribution and its generalization

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2023年 179卷

作者： Li, Xun-Jian Sun, Yuan Tian, Guo-Liang Liang, Jiajuan Shi, Jianhua Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen 518055 Guangdong Peoples R China HKBU United Int Coll Dept Stat & Data Sci Guangdong Prov Key Lab Interdisciplinary Res & App BNU Zhuhai 519087 Guangdong Peoples R China Minnan Normal Univ Sch Math & Stat Zhangzhou 363000 Fujian Peoples R China

Zero-truncated count data (e.g., days of staying in hospital;survival weeks of female patients with breast cancer) often arise in various fields such as medical studies. To model such data, the zero-truncated Poisson (ZTP) distribution is commonly utilized to investigate the relationship between the response counts and a set of covariates. For existing ZTP regression models, it is very hard to explain the regression coefficients beta or it is quite difficult to perform a constrained optimization to calculate the maximum likelihood estimates (MLEs) of beta. This paper aims to introduce a new mean regression model for the ZTP distribution with a clear interpretation about the regression coefficients. Because of challenge that the original Poisson mean parameter lambda i cannot be expressed explicitly the ZTP mean parameter mu i, an embedded Newton-Raphson algorithm is developed calculate the MLEs of regression coefficients. The construction of bootstrap confidence intervals is presented and three hypothesis tests (i.e., the likelihood ratio test, the Wald test and the score test) are considered. Furthermore, the ZTP mean regression model is generalized to the mean regression model for the k-truncated Poisson distribution. Simulation studies are conducted and two real data are analyzed to illustrate the proposed model and methods.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Embedded Newton-Raphson algorithm k-truncated Poisson Mean regression minorization-maximization algorithm Zero-truncated Poisson

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A quadratic upper bound algorithm for regression analysis of credit risk under the proportional hazards model with case-cohort data

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STATISTICS AND COMPUTING 2023年第4期33卷 78-78页

作者： Huang, Chen Ding, Jieli Feng, Yanqin Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China

A case-cohort design is a cost-effective biased-sampling scheme in studies on survival data. We study the regression analysis of credit risk by fitting the proportional hazards model to data collected via the case-cohort design. Using the minorization-maximization principle, we develop a new quadratic upper-bound algorithm for the calculation of estimators and obtain the convergence of the algorithm. The proposed algorithm involves the inversion of the derived upper-bound matrix only one time in the whole process and the upper-bound matrix is independent of parameters. These features make the proposed algorithm have simple update and low per-iterative cost, especially to large-dimensional problems. Rcpp is an R package which enables users to write R extensions with C++. In this paper, we write the program of the proposed algorithm via Rcpp and improve the efficiency of R program execution and realize the fast computing. We conduct simulation studies to illustrate the performance of the proposed algorithm. We analyze a real data example from a mortgage dataset for evaluating credit risk.

关键词： Case-cohort design minorization-maximization algorithm Quadratic upper bound The proportional hazards model

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