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Analysis of best linear unbiased predictions in the contexts of a linear mixed model and its six correctly-reduced models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2025年

作者： Jiang, Bo Tian, Yongge Shandong Technol & Business Univ Coll Math & Informat Sci Yantai Shandong Peoples R China Yantai Nanshan Univ Coll Technol & Data Yantai Shandong Peoples R China

A parametric regression model can be decomposed into certain partitioned forms, consequently, we are able to construct some small or reduced parametric models that have the same partial unknown parameter vectors with the partitioned model. In this case, predictions/estimations of the same partial unknown parameters in the contexts of the original and reduced models may have different expressions and performances, and thus it would be of interest to consider the relationship for these inference results. This is known to be a tedious task because expressions of prediction/estimation results involve a diverse of complicated matrix calculations. This paper reconsiders this subject in the contexts of a partitioned linear mixed model and its six correctly-reduced linear mixed models (CRLMMs). We shall develop a general theory of establishing connections between the best linear unbiased predictors of the same partial unknown parameters under a partitioned linear mixed model and its correctly-reduced linear mixed models using a series of precise matrix analysis tools. The results obtained in the paper are suitable for other special partitioned linear mixed models, and thus this methodological or theoretical innovation work can serve as general reference on relations research between the predictors under more complicated linear models.

关键词： Block matrix linear mixed model Predictor Range Rank Reduced model

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linear mixed model analysis to evaluate correlations between remdesivir adverse effects with age and gender of patients with mild Covid-19 pneumonia

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JOURNAL OF MEDICAL VIROLOGY 2022年第8期94卷 3783-3790页

作者： Sedighi, Mohsen Amanollahi, Alireza Moghaddam, Omid Moradi Ghafouri, Hamed Basir Hoseini, Seyede Elham Tavakoli, Nader Iran Univ Med Sci Trauma & Injury Res Ctr Tehran Iran Shahid Beheshti Univ Med Sci Sch Publ Hlth & Safety Dept Epidemiol Tehran Iran Islamic Azad Univ Fac Med Tehran Med Sci Tehran Iran

We aimed to assess longitudinal changes in clinical indexes of corona disease 2019 (Covid-19) patients with mild pulmonary infection during 5 days of remdesivir therapy and determine the effect of age and gender on remdesivir adverse effects (AE). Patients' clinical data including inflammatory markers, liver and renal function tests, and heart rate (HR) were extracted from medical records. linear mixed model (LMM) was used to analyze longitudinal changes in patients' clinical indexes. Gender and age were inserted in LMM as covariates to find their correlation with AE and clinical indexes. Of 84 patients, 35 patients met our criteria for the study. There were significant increases in mean levels of white blood cell (WBC;p = 0.005), alanine aminotransferase (ALT;p = 0.001), aspartate aminotransferase (p = 0.001), blood urea nitrogen (BUN;p = 0.001), and creatinine (p = 0.006), whereas mean levels of erythrocyte sedimentation rate (p = 0.005), C-reactive protein (p = 0.001), alkaline phosphatase (p = 0.001), and potassium (p = 0.003) decreased significantly. Estimated glomerular filtration rate (p = 0.001) and HR (p = 0.001) showed a notable decline over the course of treatment. LMM analysis showed that mean changes in WBC (beta = 0.94, p = 0.029), creatinine (beta = 0.12, p = 0.020), and HR (beta = 6.47, p = 0.008) were greater in males than in females. Also, age of patients had a significant effect on the mean changes of WBC (beta = -0.02, p = 0.023), sodium (beta = -0.06, p = 0.010), BUN (beta = 0.23, p = 0.001), and HR (beta = -0.29, p = 0.001). Despite no renal and liver dysfunction, Covid-19 patients with mild pulmonary infection may develop some remdesivir AE and attributed side effects might be affected by gender and age of patients.

关键词： adverse effects Covid-19 linear mixed model remdesivir

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linear mixed model approach to network meta-analysis for continuous outcomes in periodontal research

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JOURNAL OF CLINICAL PERIODONTOLOGY 2015年第2期42卷 204-212页

作者： Tu, Yu-Kang Natl Taiwan Univ Coll Publ Hlth Inst Epidemiol & Prevent Med Taipei 100 Taiwan

AimAnalysing continuous outcomes for network meta-analysis by means of linear mixed models is a great challenge, as it requires statistical software packages to specify special patterns of model error variance and covariance structure. This article demonstrates a non-Bayesian approach to network meta-analysis for continuous outcomes in periodontal research with a special focus on the adjustment of data dependency. DataSeventeen studies on guided tissue regeneration were used to illustrate how the proposed linear mixed models for network meta-analysis of continuous outcomes. Methods & ResultsArm-based network meta-analysis use treatment arms from each study as the unit of analysis;when patients are randomly assigned to each arm, data are deemed independent and therefore no adjustment is required for multi-arm trials. Trial-based network meta-analysis use treatment contrasts as the unit of analysis, and therefore treatment contrasts within a multi-arm trial are not independent. This data dependency occurs also in split-mouth studies, and adjustments for data dependency are therefore required. ConclusionsArm-based analysis is the preferred approach to network meta-analysis, when all included studies use the parallel group design and some compare more than two treatment arms. When included studies used designs that yield dependent data, the trial-based analysis is the preferred approach.

关键词： guided tissue regeneration linear mixed model mixed treatments comparisons network meta-analysis randomized controlled trials

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linear mixed model for heritability estimation that explicitly addresses environmental variation

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2016年第27期113卷 7377-7382页

作者： Heckerman, David Gurdasani, Deepti Kadie, Carl Pomilla, Cristina Carstensen, Tommy Martin, Hilary Ekoru, Kenneth Nsubuga, Rebecca N. Ssenyomo, Gerald Kamali, Anatoli Kaleebu, Pontiano Widmer, Christian Sandhu, Manjinder S. Microsoft Res Los Angeles CA 90024 USA Wellcome Trust Sanger Inst Hinxton CB10 1SA Cambs England Univ Cambridge Dept Med Cambridge CB2 0SP England Microsoft Res Redmond WA 98052 USA MRC UVRI Uganda Res Unit AIDS Entebbe Uganda

The linear mixed model (LMM) is now routinely used to estimate heritability. Unfortunately, as we demonstrate, LMM estimates of heritability can be inflated when using a standard model. To help reduce this inflation, we used a more general LMM with two random effects-one based on genomic variants and one based on easily measured spatial location as a proxy for environmental effects. We investigated this approach with simulated data and with data from a Uganda cohort of 4,778 individuals for 34 phenotypes including anthropometric indices, blood factors, glycemic control, blood pressure, lipid tests, and liver function tests. For the genomic random effect, we used identity-by-descent estimates from accurately phased genome-wide data. For the environmental random effect, we constructed a covariance matrix based on a Gaussian radial basis function. Across the simulated and Ugandan data, narrow-sense heritability estimates were lower using the more general model. Thus, our approach addresses, in part, the issue of "missing heritability" in the sense that much of the heritability previously thought to be missing was fictional. Software is available at https://***/MicrosoftGenomics/FaST-LMM.

关键词： heritability estimation linear mixed model environment Gaussian radial basis function model misspecification

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linear mixed model Selection by Partial Correlation

Linear Mixed Model Selection by Partial Correlation

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作者： Alabiso, Audry Bowling Green State University

学位级别：博士

linear mixed models (LMM) are commonly used when observations are no longer independent of each other, and instead, clustered into two or more groups. In the LMM, the mean response for each subject is modeled by a combination of fixed effects and random effects . The fixed effects are characteristics shared by all individuals in the study; they are analogous to the coefficients of the linear model. The random effects are specific to each group or cluster and help describe the correlation structure of the observations. Because of this, linear mixed models are popular when multiple measurements are made on the same subject or when there is a natural clustering or grouping of observations. Our goal in this dissertation is to perform fixed effect selection in the high-dimensional linear mixed model. We generally define high-dimensional data to be when the number of potential predictors is large relative to the sample size. High-dimensional data is common in genomic and other biological datasets. In the high-dimensional setting, selecting the fixed effect coefficients can be difficult due to the number of potential models to choose from. However, it is important to be able to do so in order to build models that are easy to interpret. Many current techniques for fixed effect selection in the high-dimensional LMM are based on the penalized log likelihood. However, adding a penalized term to the log likelihood results in a non-convex optimization problem which requires numerical methods to solve and a data dependent tuning parameter to select the amount of regularization. In contrast to the penalized likelihood, the partial correlation is based on the marginal measures of association between each predictor and the conditioned response. Techniques based on the partial correlation have two main advantages to those based on penalized likelihoods: no data dependent tuning parameter is required to select the fixed effects and the partial correlation is not influenced by

关键词： Statistics linear mixed model High Dimensional Variable Selection Partial Faithfulness

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Feasible algorithm for linear mixed model for massive data

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2018年第4期47卷 1126-1133页

作者： Zhao, Yanyan Nankai Univ Inst Stat Tianjin 300071 Peoples R China

This article studies computation problem in the context of estimating parameters of linear mixed model for massive data. Our algorithms combine the factored spectrally transformed linear mixed model method with a sequential singular value decomposition calculation algorithm. This combination solves the operation limitation of the method and also makes this algorithm feasible to big dataset, especially when the data has a tall and thin design matrix. Our simulation studies show that our algorithms make the calculation of linear mixed model feasible for massive data on ordinary desktop and have same estimating accuracy with the method based on the whole data.

关键词： linear mixed model Massive data Sequential singular value decomposition

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A variance shift model for detection of outliers in the linear mixed model

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2010年第9期54卷 2128-2144页

作者： Gumedze, Freedom N. Welham, Sue J. Gogel, Beverley J. Thompson, Robin Univ Cape Town Dept Stat Sci ZA-7701 Rondebosch South Africa Rothamsted Res Biomath & Bioinformat Harpenden AL5 2JQ Herts England Univ Adelaide Adelaide SA 5005 Australia Univ London Sch Math Sci London E1 4NS England

A variance shift outlier model (VSOM), previously used for detecting outliers in the linear model, is extended to the variance components model. This VSOM accommodates outliers as observations with inflated variance, with the status of the ith observation as an outlier indicated by the size of the associated shift in the variance. Likelihood ratio and score test statistics are assessed as objective measures for determining whether the ith observation has inflated variance and is therefore an outlier. It is shown that standard asymptotic distributions do not apply to these tests for a VSOM, and a modified distribution is proposed. A parametric bootstrap procedure is proposed to account for multiple testing. The VSOM framework is extended to account for outliers in random effects and is shown to have an advantage over case-deletion approaches. A simulation study is presented to verify the performance of the proposed tests. Challenges associated with computation and extensions of the VSOM to the general linear mixed model with correlated errors are discussed. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Likelihood ratio test linear mixed model Multiple testing Outlier detection REML Score test Variance shift outlier model

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Characterizing relationships between BLUPs under linear mixed model and some associated reduced models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2023年第8期52卷 3438-3451页

作者： Eris Buyukkaya, Melek Karadeniz Tech Univ Dept Stat & Comp Sci Trabzon Turkey

A linear mixed model (LMM) can be given in certain multiple partitioned forms, and there exist reduced linear mixed models (RLMMs) associated with the given partitioned linear mixed model. We consider in this work the best linear unbiased predictors (BLUPs) of LMM and RLMMs. This work aims at establishing some analytical formulas for calculating ranks and inertias of dispersion matrices of BLUPs and using these formulas in the comparison of BLUPs' dispersion matrices under the LMM and RLMMs.

关键词： BLUP Dispersion matrix Inertia linear mixed model Rank Reduced linear mixed model

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A linear mixed model to estimate COVID-19-induced excess mortality

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BIOMETRICS 2023年第1期79卷 417-425页

作者： Verbeeck, Johan Faes, Christel Neyens, Thomas Hens, Niel Verbeke, Geert Deboosere, Patrick Molenberghs, Geert Hasselt Univ Interuniv Inst Biostat & Stat Bioinformat I BioSt Data Sci Inst DSI BE-3500 Hasselt Belgium KULeuven Interuniv Inst Biostat & Stat Bioinformat I BioSt BE-3000 Leuven Belgium Univ Antwerp Ctr Hlth Econ Res & Modelling Infect Dis CHERMID Vaccine & Infect Dis Inst VAXINFECTIO BE-2000 Antwerp Belgium Vrije Univ Brussel Dept Sociol Interface Demog ID BE-1050 Brussels Belgium

The Corona Virus Disease (COVID-19) pandemic has increased mortality in countries worldwide. To evaluate the impact of the pandemic on mortality, the use of excess mortality rather than reported COVID-19 deaths has been suggested. Excess mortality, however, requires estimation of mortality under nonpandemic conditions. Although many methods exist to forecast mortality, they are either complex to apply, require many sources of information, ignore serial correlation, and/or are influenced by historical excess mortality. We propose a linear mixed model that is easy to apply, requires only historical mortality data, allows for serial correlation, and down-weighs the influence of historical excess mortality. Appropriateness of the linear mixed model is evaluated with fit statistics and forecasting accuracy measures for Belgium and the Netherlands. Unlike the commonly used 5-year weekly average, the linear mixed model is forecasting the year-specific mortality, and as a result improves the estimation of excess mortality for Belgium and the Netherlands.

关键词： 5-year weekly average COVID-19 excess mortality linear mixed model

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Estimating Variance Components and Random Effects Using the Box-Cox Transformation in the linear mixed model

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2011年第3期40卷 515-531页

作者： Gurka, Matthew J. Edwards, Lloyd J. W Virginia Univ Sch Med Dept Community Med Morgantown WV 26506 USA Univ N Carolina Dept Biostat Chapel Hill NC USA

The linear mixed model assumes normality of its two sources of randomness: the random effects and the residual error. Recent research demonstrated that a simple transformation of the response targets normality of both sources simultaneously. However, estimating the transformation can lead to biased estimates of the variance components. Here, we provide guidance regarding this potential bias and propose a correction for it when such bias is substantial. This correction allows for accurate estimation of the random effects when using a transformation to achieve normality. The utility of this approach is demonstrated in a study of sleep-wake behavior in preterm infants.

关键词： linear mixed model Longitudinal data Normality Random effects Transformation

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