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τ-Inflated Beta Regression Model for Estimating τ-Restricted Means and Event-Free Probabilities for Censored Time-to-Event Data

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BIOMETRICAL JOURNAL 2024年第8期66卷

作者： Wang, Yizhuo Murray, Susan Univ Michigan Dept Biostat Ann Arbor MI 48109 USA

In this research, we propose analysis of tau-restricted censored time-to-event data via a tau-inflated beta regression (tau-IBR) model. The outcome of interest is min(tau,T), where T and tau are the time-to-event and follow-up duration, respectively. Our analysis goals include estimation and inference related to tau-restricted mean survival time (tau-RMST) values and event-free probabilities at tau that address the censored nature of the data. In this setting, it is common to observe many individuals with min(tau,T)=tau, a point mass that is typically overlooked in tau-restricted event-time analyses. Our proposed tau-IBR model is based on a decomposition of min(tau,T) into tau[I(T >=tau)+(T/tau)I(Texpectation-maximization algorithm. An alternative multiple imputation (MI) algorithm for fitting the tau-IBR model has the additional advantage of producing uncensored datasets for analysis. Simulations indicate excellent performance of the tau-IBR model(s), and corresponding tau-RMST estimates, in independent and dependent censoring settings. We apply our method to the Azithromycin for Prevention of Chronic Obstructive Pulmonary Disease (COPD) Exacerbations Trial. In addition to tau-IBR model results providing a nuanced understanding of the treatment effect, visually appealing heatmaps of the tau-restricted event times based on our MI datasets are given, a visualization not typically available for censored time-to-event data.

关键词： expectation-maximization algorithm inflated beta regression multiple imputation of censored times-to-event restricted mean survival time

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An algorithm for maximum likelihood estimation of hidden Markov models with unknown state-tying

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 1998年第1期6卷 61-70页

作者： Cappe, O Mokbel, CE Jouvet, D Moulines, E ENST Dept Signal CNRS URA 820 F-75634 Paris 13 France

For speech recognition based on hidden Markov modeling, parameter-tying, which consists in constraining some of the parameters of the model to share the same value, has emerged as a standard practice. In this paper, an original algorithm is proposed that makes it possible to jointly estimate both the shared model parameters and the tying characteristics;using the maximum likelihood criterion, The proposed algorithm is based on a recently introduced extension of the classic expectation-maximization (EM) framework. The convergence properties of this class of algorithms are analyzed in detail. The method is evaluated on an isolated word recognition task using hidden Markov models (HMM's) with Gaussian observation densities and tying at the state level. Finally, the extension of this method to the case of mixture observation densities with tying at the mixture component level is discussed.

关键词： expectation-maximization algorithm hidden Markov models maximum likelihood estimation speech recognition

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Unsupervised restoration of hidden nonstationary Markov chains using evidential priors

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2005年第8期53卷 3091-3098页

作者： Lanchantin, P Pieczynski, W Inst Natl Telecommun GET INT Dept CITI CNRS UMR 5157 F-91011 Evry France

This paper addresses the problem of unsupervised Bayesian hidden Markov chain restoration. When the hidden chain is stationary, the classical "Hidden Markov Chain" (HMC) model is quite efficient, and associated unsupervised Bayesian restoration methods using the "expectation-maximization" (EM) algorithm work well. When the hidden chain is non stationary, on the other hand, the unsupervised restoration results using the HMC model can be poor, due to a bad match between the real and estimated models. The novelty of this paper is to offer a more appropriate model for hidden nonstationary Markov chains, via the theory of evidence. Using recent results relating to Triplet Markov Chains (TMCs), we show, via simulations, that the classical restoration results can be improved by the use of the theory of evidence and Dempster-Shafer fusion. The latter improvement is performed in an entirely unsupervised way using an original parameter estimation method. Some application examples to unsupervised image segmentation are also provided.

关键词： Bayesian restoration Dempster-Shafer fusion expectation-maximization algorithm Hidden Markov chains nonstationary Markov chain restoration parameter estimation theory of evidence

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A Multi-Rate Probabilistic Slow Feature Regression Model for Dynamic Feature Learning and Industrial Soft Sensor Development

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IEEE ACCESS 2022年 10卷 128994-129003页

作者： Zhang, Miao Wen, Zhiwei Zhou, Le Zhejiang Univ Sci & Technol Sch Automat & Elect Engn Hangzhou 310023 Peoples R China Zhejiang Huashi Technol Co Ltd Hangzhou 310023 Peoples R China

In practical process industries, the measurements coming from different sources are collected at different sampling rates, thereby soft sensors developed using uniformly sampled measurements may result in poor prediction performance. Besides, industrial processes are inherently stochastic and most of them present dynamic characteristic. To cope with these issues, a multi-rate probabilistic slow feature regression (MR-PSFR) model is proposed in this paper for dynamic feature learning and soft sensor development in industrial processes. In the MR-PSFR, both input and output observation datasets with different sampling rates are used to extract the slow features, which can separate slowly and fast changing features and have a better interpretation of the outputs. Then, the expectation-maximization algorithm is modified to derive the model parameters of MR-PSFR and the quality prediction strategy for multi-rate processes is constructed. Finally, the proposed method is investigated through a numerical example and a real industrial process. The simulation results show that the extracted slow features better represent the intrinsic characteristics of the processes and the proposed model has better prediction performance for multi-rate dynamic processes than other methods.

关键词： Soft sensor feature learning multi-rate probabilistic slow feature regression expectation-maximization algorithm multi-rate dynamic process

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Latent variable modeling and state estimation of non-stationary processes driven by monotonic trends

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JOURNAL OF PROCESS CONTROL 2021年 108卷 40-54页

作者： Chiplunkar, Ranjith Huang, Biao Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 1H9 Canada

In certain non-stationary processes, the non-stationary dynamics is caused by degradation or wearing of certain process components. Such dynamics can be characterized by a latent monotonic signal. Meanwhile, there also exist stationary dynamics characterizing the regular process variables. It hence becomes pertinent to distinguish these two sets of latent variables for the monitoring of the process from both the stationary and non-stationary aspects. In this regard, we propose a methodology to achieve such a goal by modeling the latent monotonic trend as a closed skew-normal random walk model. The other stationary relations are characterized by a state-space model with Gaussian noises. The problem is solved as a simultaneous state and parameter estimation problem using the expectation-maximization algorithm. As a result of the closed skew-normal random walk model for the monotonic trend, the state estimation problem becomes a skew-normal filtering and smoothing problem. The effectiveness of the proposed method is verified through a numerical simulation, and the algorithm is applied to solve a Hot Lime Softener fouling predictive monitoring problem. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Monotonic trends Closed skew-normal distribution expectation-maximization algorithm Dynamic latent variables Fouling monitoring

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Semiparametric model for bivariate survival data subject to biased sampling

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2019年第2期81卷 409-429页

作者： Piao, Jin Ning, Jing Shen, Yu Univ Southern Calif Los Angeles CA USA Univ Texas MD Anderson Canc Ctr Houston TX 77030 USA

To understand better the relationship between patient characteristics and their residual survival after an intermediate event such as the local recurrence of cancer, it is of interest to identify patients with the intermediate event and then to analyse their residual survival data. One challenge in analysing such data is that the observed residual survival times tend to be longer than those in the target population, since patients who die before experiencing the intermediate event are excluded from the cohort identified. We propose to model jointly the ordered bivariate survival data by using a copula model and appropriately adjusting for the sampling bias. We develop an estimating procedure to estimate simultaneously the parameters for the marginal survival functions and the association parameter in the copula model, and we use a two-stage expectation-maximization algorithm. Using empirical process theory, we prove that the estimators have strong consistency and asymptotic normality. We conduct simulation studies to evaluate the finite sample performance of the method proposed. We apply the method to two cohort studies to evaluate the association between patient characteristics and residual survival.

关键词： Bivariate survival outcomes Copula model expectation-maximization algorithm Prevalent cohort Sampling bias Two-stage estimation

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The beta-binomial convolution model for 2x2 tables with missing cell counts

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STATISTICA NEERLANDICA 2009年第1期63卷 24-42页

作者： Eisinga, Rob Radboud Univ Nijmegen Dept Social Sci Res Methods NL-6500 HE Nijmegen Netherlands

This paper considers the beta-binomial convolution model for the analysis of 2x2 tables with missing cell counts. We discuss maximum-likelihood (ML) parameter estimation using the expectation-maximization algorithm and study information loss relative to complete data estimators. We also examine bias of the ML estimators of the beta-binomial convolution. The results are illustrated by two example applications.

关键词： ecological inference beta-binomial distribution convolution likelihood expectation-maximization algorithm missing information principle Fisher information loss bias correction 2x2 table

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Semiparametric Efficient Estimation for a Class of Generalized Proportional Odds Cure Models

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2010年第489期105卷 302-311页

作者： Mao, Meng Wang, Jane-Ling Univ Calif Davis Dept Stat Davis CA 95616 USA

We present a mixture cure model with the survival time of the "uncured" group coming from a class of linear transformation models, which is an extension of the proportional odds model This class of model. first proposed by Dabrowska and Doksum ( 988). which we term "generalized proportional odds model," is well suited for the mixture cure model setting due to a clear separation between long-term and short-term effects A standard expectation-maximization algorithm can he employed to locate the nonparametric likelihood estimators which are shown to he consistent and semiparametric efficient However. there are difficulties in the M-step due to the nonparametric component We overcome these difficulties by proposing two different algorithms The first is to employ an majorize-minimize (MM) algorithm in the M-step instead of the usual Newton-Raphson method, and the other is based on an alternative form to express the model as a proportional hazards frailty model The two new algorithms are compared in a simulation study with an existing estimating equation approach by DJ and Ying (2004) The MM algorithm provides both computational stability and efficiency A case study of leukemia dam is conducted to illustrate the proposed procedures

关键词： expectation-maximization algorithm Logistic regression Majorize-minimize algorithm Newton-Raphson algorithm Nonparametric maximum likelihood estimator Transformation model

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A shared-parameter continuous-time hidden Markov and survival model for longitudinal data with informative dropout

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STATISTICS IN MEDICINE 2019年第6期38卷 1056-1073页

作者： Bartolucci, Francesco Farcomeni, Alessio Univ Perugia Fac Econ Perugia Italy Sapienza Univ Rome Dept Publ Hlth & Infect Dis Piazzale Aldo Moro 5 I-00186 Rome Italy

A shared-parameter approach for jointly modeling longitudinal and survival data is proposed. With respect to available approaches, it allows for time-varying random effects that affect both the longitudinal and the survival processes. The distribution of these random effects is modeled according to a continuous-time hidden Markov chain so that transitions may occur at any time point. For maximum likelihood estimation, we propose an algorithm based on a discretization of time until censoring in an arbitrary number of time windows. The observed information matrix is used to obtain standard errors. We illustrate the approach by simulation, even with respect to the effect of the number of time windows on the precision of the estimates, and by an application to data about patients suffering from mildly dilated cardiomyopathy.

关键词： Baum-Welch recursions expectation-maximization algorithm latent class model mildly dilated cardiomyopathy

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Type II combination questionnaire model: A new survey design for a totally sensitive binary variable correlated with another nonsensitive binary variable

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2015年第3期44卷 432-447页

作者： Huang, Xifen Tian, Guo-Liang Liu, Yin Yu, Jun-Wu Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Hong Kong Peoples R China Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan Hunan Peoples R China

Recently, Yu, Lu, and Tian (2013) introduced a combination questionnaire model to investigate the association between one sensitive binary variable and another non-sensitive binary variable. However, in practice, we sometimes need to assess the association between one totally sensitive binary variable (e.g., the number of sex partners being <= 3 or >3, the annual income being <=$25,000 or >$25,000, and so on) and one non-sensitive binary variable (e.g., good or poor health status, with or without cervical cancer, and so on). Although we could directly adopt the four-category parallel model (Liu & Tian, 2013), the information contained in the non-sensitive binary variable cannot be utilized in the design. Intuitively, such information can be used to enhance the degree of privacy protection so that more respondents will not face the sensitive question. The objective of this paper is to propose a new survey design (called Type II combination questionnaire model, which consists of a four-category parallel questionnaire and a supplemental direct questionnaire) and to develop corresponding statistical methods for analyzing sensitive data collected by this technique. Likelihood-based methods including maximum likelihood estimates, asymptotic and bootstrap confidence intervals of parameters of interest are derived. A likelihood ratio test is provided to test the association between the two binary random variables. Bayesian methods are also presented. Simulation studies are performed and a cervical cancer data set in Atlanta is used to illustrate the proposed methods. (C) 2015 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Bayesian methods expectation-maximization algorithm Non-randomized response technique The combination questionnaire model Type II combination questionnaire model

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