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A Principled Approach to Adjust for Unmeasured Time-Stable Confounding of Supervised Treatment

BIOMETRICAL JOURNAL 2025年第1期67卷 e70026页

作者： Madsen, Jeppe Ekstrand Halkjaer Delvin, Thomas Scheike, Thomas Pipper, Christian Leo Pharma AS Global Clin Dev Ballerup Denmark Univ Copenhagen Dept Publ Hlth Sect Biostat Copenhagen Denmark Novo Nord Biostat OSCD & Outcomes 1 Soborg Denmark Univ Southern Denmark Dept Publ Hlth Epidemiol Biostat & Biodemog Odense Denmark

We propose a novel method to adjust for unmeasured time-stable confounding when the time between consecutive treatment administrations is fixed. We achieve this by focusing on a new-user cohort. Furthermore, we envisage that all time-stable confounding goes through the potential time on treatment as dictated by the disease condition at the initiation of treatment. Following this logic, we may eliminate all unmeasured time-stable confounding by adjusting for the potential time on treatment. A challenge with this approach is that right censoring of the potential time on treatment occurs when treatment is terminated at the time of the event of interest, for example, if the event of interest is death. We show how this challenge may be solved by means of the expectation-maximization algorithm without imposing any further assumptions on the distribution of the potential time on treatment. The usefulness of the methodology is illustrated in a simulation study. We also apply the methodology to investigate the effect of depression/anxiety drugs on subsequent poisoning by other medications in the Danish population by means of national registries. We find a protective effect of treatment with selective serotonin reuptake inhibitors on the risk of poisoning by various medications (1- year risk difference of approximately -3%$-3\%$) and a standard Cox model analysis shows a harming effect (1-year risk difference of approximately 2%$2\%$), which is consistent with what we would expect due to confounding by indication. Unmeasured time-stable confounding can be entirely adjusted for when the time between consecutive treatment administrations is fixed.

关键词： causal inference confounding by indication directed acyclic graph em algorithm unmeasured confounding

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Simultaneous estimation and clustering with finite mixture of nonparanormal graphical models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2025年第3期54卷 709-733页

作者： Aghabozorgi, Hamid Haji Eskandari, Farzad Allameh Tabatabai Univ Dept Stat Tehran Iran

Graphical mixture models provide a powerful tool to visually depict conditional independencies or dependencies between heterogeneous high-dimensional data. When the random variables corresponding to the vertices are continuous, mixture component densities are assumed to be multivariate normal with different covariance matrices, leading to introduction of the Gaussian graphical mixture model (GGMM). The nonparanormal graphical mixture model (NGMM) replaces the restrictive normal assumption with a semiparametric Gaussian copula, which extends the nonparanormal graphical model and mixture models. Such an extension allows us to simultaneously estimate cluster assignments and cluster-specific graphical model structure. To enable such analyses, we propose a regularized estimation scheme with two forms of l1 penalty function (conventional and unconventional) via the expectation-maximization algorithm to learn a finite mixture of nonparanormal graphical models. We illustrate the performance of our method through a simulation study under both ideal and noisy settings. We also apply the proposed methodology to a breast cancer data set to diagnose malignant or benign tumors in patients. The results showed that the combination of NGMM together with unconventional penalty, which was named as NGMM1 during this study, provides the most efficient approach in clustering and estimating the graphical model structure.

关键词： em algorithm Mixture graphical models Model-based clustering Nonparanormal model

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Finite-Mixture Continuous Logit Model: Formulation and Application for Shopping Start Time Choice of Non-Commuters

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TRANSPORTATION RESEARCH RECORD 2024年第1期2678卷 309-320页

作者： Geng, Shuguang Ye, Xin Zhang, Tianran Wang, Ke Tongji Univ Coll Transportat Engn Key Lab Rd & Traff Engn Minist Educ Shanghai Peoples R China Shanghai Urban Planning & Design Res Inst Shanghai Peoples R China Univ Shanghai Sci & Technol Ctr Supernetworks Res Business Sch Shanghai Peoples R China

As a continuous generalization of the multinomial logit (MNL) model, the continuous logit (CL) model can be used for continuous response variables (e.g., departure time and activity duration). However, the existing CL model requires the calculation of numerical integrals to obtain the choice probabilities;it thus takes a long time to estimate the model parameters, particularly when the sample size is large. In this paper, we formulate the finite-mixture CL (FMCL) model as a new continuous choice model by combining the finite-mixture method and the CL model, in which the continuous distributional function of the finite mixture is embedded in the CL model. As a result, the individual choice probability can be obtained directly by computing the probability density of the continuous distribution function;this avoids calculation of the integral but still obeys the random utility maximization (RUM) principle. Simulation experiments are conducted to demonstrate the capability of the model. In an empirical study, the proposed model is applied for non-commuters' shopping activity start time using the expectation-maximization (em) algorithm based on Shanghai Household Travel Survey data. The results show that the FMCL model developed in this paper can greatly reduce the model estimation time (10,048 observations requiring only 3 min) of the CL model, and the model also has a more intuitive interpretation of model coefficients, directly reflecting variable effects on time-of-day choice. These two advantages can greatly enhance the practical value of the proposed modeling method.

关键词： travel behavior modeling continuous logit finite mixture em algorithm time-of-day modeling

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Simple Heterogeneous Step-Stress Accelerated Life Testing Model Under Type II Censoring

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2025年第0期

作者： Lu, Yao Kateri, Maria Rhein Westfal TH Aachen Inst Stat Aachen Germany

Common step-stress accelerated life testing (SSALT) models assume that all testing items are sampled from a homogeneous population. However, this is often not the case in practice. Practitioners observe inhomogeneous aging patterns among items of the same production batch. This work proposes a simple SSALT model with exponentially distributed, Type II censored lifetimes that accounts for underlying heterogeneity in aging. To capture the inhomogeneity, a mixture model is introduced and an expectation-maximization (em) algorithm for censored data is constructed for approximating the maximum likelihood estimates of the model's parameters. The validity of the suggested model and its advantage over the SSALT model in the presence of heterogeneity are demonstrated via simulation studies. Additionally, the log-link function, used to extrapolate the inferential results to normal operating condition (NOC), is adjusted to accommodate the heterogeneous setup. For log-link models, it is demonstrated that in presence of heterogeneity, the common model always overestimates the lifetime under NOC. In contrast, the proposed model, accounting for heterogeneity, reduces the bias in estimation and extrapolation.

关键词： bootstrap cumulative exposure model em algorithm exponential lifetime log-link function mixture model model misspecification

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Estimation and prediction on power Muth distribution with progressive censored data: a Bayesian approach

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第5期53卷 2150-2172页

作者： Kohansal, Akram Bakouch, Hassan S. Imam Khomeini Int Univ Dept Stat Qazvin Iran Tanta Univ Fac Sci Dept Math Tanta Egypt Qassim Univ Coll Sci Dept Math Buraydah Saudi Arabia

In this paper, estimation and prediction inference of power Muth distribution, with the progressive censoring data, are described. The maximum likelihood and Bayesian approaches of the unknown parameters are considered. Several Bayesian estimators are obtained against different symmetric and asymmetric loss functions, such as squared error, linex and general entropy. Also, the asymptotic confidence intervals and highest posterior density credible intervals of them are derived. Most focus of this paper is Bayesian prediction of the removed units in multiple stages of the progressively censored sample, so that, the Gibbs and Metropolis samplers are used, to reach this end. To compare the performance of different methods, Mont Carlo simulation is employed. Moreover, one practical data set is analyzed for illustrative purposes.

关键词： Power Muth distribution Progressive censoring scheme Bayesian prediction em algorithm Monte Carlo simulation

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Additive models with p-order autoregressive skew-normal errors for modeling trend and seasonality in time series

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2025年

作者： Ferreira, Clecio S. Paula, Gilberto A. Oliveira, Rodrigo A. Univ Fed Juiz de Fora Dept Stat Juiz De Fora MG Brazil Univ Sao Paulo Inst Math & Stat Sao Paulo SP Brazil

In this article, we propose an additive model in which the random error follows a skew-normal p-order autoregressive (AR) process where the systematic component is approximated by cubic and cyclic cubic regression splines. The maximum likelihood estimators are calculated through the expectation-maximization (em) algorithm with analytic expressions for the E and M-steps. The effective degrees of freedom concerning the non parametric component are estimated based on a linear smoother. The smoothing parameters are estimated by minimizing the Bayesian information criterion. The conditional quantile residuals are used to construct simulated confidence bands for assessing departures from the error assumptions. Also, we use the same residuals to construct graphs of the autocorrelation and partial autocorrelation functions to verify the AR structure's adequacy for the errors. We then perform local influence analysis based on the conditional expectation of the complete-data log-likelihood function. A simulation study is carried out to evaluate the efficiency of the em algorithm. Finally, the method is illustrated by using a real dataset of the average weekly cardiovascular mortality in Los Angeles.

关键词： Autoregressive models additive models em algorithm penalized smoothing skew-normal distribution

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Adaptive inference for dynamic passenger route usage patterns in a metro network considering time-varying and heavy-tailed travel times

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TRANSPORTATION RESEARCH PART C-emERGING TECHNOLOGIES 2025年 171卷

作者： Shi, Zhuangbin Shen, Wei Schonfeld, Paul Liu, Yang Zhang, Ning Kunming Univ Sci & Technol Fac Transportat Engn Jingming South Rd 727 Kunming 650500 Yunnan Peoples R China Southeast Univ Intelligent Transportat Syst Res Ctr Southeast Univ Rd 2 Nanjing 211189 Jiangsu Peoples R China Univ Maryland Dept Civil & Environm Engn College Pk MD 20742 USA

Due to the dynamic changes in timetables, passenger demand, and passenger composition, the distribution of passengers within a metro system becomes quite complex. Many studies divide a day into intervals to account for the dynamics of travel time. However, the intervals used in these studies are insufficient to capture the gradual and fine-grained changes in passenger travel patterns. This study proposes an adaptive dynamic route inference model (ADRIM) that overcomes these limitations. In the ADRIM, we introduce a constrained Expectation Maximization algorithm (Cem) by confining the parameters of the mixture log-normal distribution model (MLND) within confidence intervals, thereby reducing anomalous estimations. We use the concept of Hidden Markov Models (HMMs) to achieve a parameter-adaptive characterization for the dynamics of route choice and travel time distributions for MLND through an iterative process. For a Nanjing metro case study, the proposed model exhibits superior performance in fitting the actual distribution of travel times and accurately captures the dynamic trends in route travel times. Besides, it is revealed that the maximum difference in expected travel times among multiple valid routes for the same origin-destination (OD) pair primarily falls within the interval [5 min, 15 min], and the distribution range of the maximum ratio is mainly between [1.1, 1.6]. The high consistency in passenger route choice proportions observed for two consecutive weeks, along with an analysis of route choice patterns under dynamic conditions, serves as strong evidence supporting the reliability and practical utility of the dynamic route inference model in understanding and managing metro passenger flows.

关键词： Metro system Route inference em algorithm Adaptive mechanism Travel time

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The Shared Weighted Lindley Frailty Model for Clustered Failure Time Data

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BIOMETRICAL JOURNAL 2025年第2期67卷 e70044页

作者： Gallardo, Diego I. Bourguignon, Marcelo Santibanez, John L. Univ Bio Bio Fac Ciencias Dept Estadist Concepcion Chile Univ Fed Rio Grande do Norte Dept Stat Natal RN Brazil Univ Atacama Fac Ingn Dept Matemat Copiapo Chile

The primary goal of this paper is to introduce a novel frailty model based on the weighted Lindley (WL) distribution for modeling clustered survival data. We study the statistical properties of the proposed model. In particular, the amount of unobserved heterogeneity is directly parameterized by the variance of the frailty distribution such as gamma and inverse Gaussian frailty models. Parametric and semiparametric versions of the WL frailty model are studied. A simple expectation-maximization (em) algorithm is proposed for parameter estimation. Simulation studies are conducted to evaluate its finite sample performance. Finally, we apply the proposed model to a real data set to analyze times after surgery in patients diagnosed with infiltrating ductal carcinoma and compare our results with classical frailty models carried out in this application, which shows the superiority of the proposed model. We implement an R package that includes estimation for fitting the proposed model based on the em algorithm.

关键词： clustered survival data em algorithm frailty models gamma frailty model weighted Lindley distribution

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Dynamic inference for left behind probabilities on congested metro routes

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TRANSPORTATION PLANNING AND TECHNOLOGY 2025年第1期48卷 111-130页

作者： Mu, Weiyan Wang, Xin Xiong, Shifeng Beijing Univ Civil Engn & Architecture Sch Sci Beijing 100044 Peoples R China Chinese Acad Sci Acad Math & Syst Sci NCMIS KLSC Beijing Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

Passengers left behind is an important measure to describe the degree of congestion in metro systems. Note that passengers' left behind probabilities are different for their different tap-in times. This paper proposes a methodology for inferring these dynamic probabilities on congested metro routes using automated data. The em algorithm is used to compute the maximum likelihood estimators of passengers' dynamic boarding probabilities, and then formulas for estimating dynamic left behind probabilities are presented based on the estimated boarding probabilities. Monte Carlo simulations and a real case application show the effectiveness of the proposed method.

关键词： Automated data boarding probabilities left-behind probabilities em algorithm Monte Carlo simulation

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An improvement of FDR for edge detection by applying em method

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INTELLIGENT DATA ANALYSIS 2022年第5期26卷 1161-1184页

作者： Kim, Eun-Gyoung Kim, Sung-Ho Korea Adv Inst Sci & Technol Dept Math Sci Daejeon South Korea

In building a graphical model, accuracy in edge detection for the model structure is crucial for the quality of the model. We explored methods for improvement of false discovery rate(FDR) by devising an estimation procedure which is more data sensitive under some condition. The estimation is made by applying an em method where the parameters include the density function under the null hypothesis (no edge) and the location parameters of the density functions under the alternative hypothesis (presence of edge). Our method is compared favorably with a most popular FDR tool in numerical experiments. We applied our method for analysing gene data of 800 genes and built a network of vector autoregressive model for the data.

关键词： Discrepancy measure edge detection em algorithm error rate graphical Gaussian model mixture distribution Parzen window

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