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generalized linear mixed model for binary outcomes when covariates are subject to measurement errors and detection limits

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STATISTICS IN MEDICINE 2018年第1期37卷 119-136页

作者： Xie, Xianhong Xue, Xiaonan Strickler, Howard D. Albert Einstein Coll Med Dept Epidemiol & Populat Hlth 1300 Morris Pk AveBelfer Bldg 1312D Bronx NY 10461 USA

Longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease. However, biomarkers are subject to measurement error, and some are also subject to left-censoring due to a lower limit of detection. Statistical methods to address these issues are few. We herein propose a generalized linear mixed model and estimate the model parameters using the Monte Carlo Newton-Raphson (MCNR) method. Inferences regarding the parameters are made by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCNR method with existing methods including the maximum likelihood (ML) method and the ad hoc approach of replacing the left-censored values with half of the detection limit (HDL). The results showed that the performance of the MCNR method is superior to ML and HDL with respect to the empirical standard error, as well as the coverage probability for the 95% confidence interval. The HDL method uses an incorrect imputation method, and the computation is constrained by the number of quadrature points;while the ML method also suffers from the constrain for the number of quadrature points, the MCNR method does not have this limitation and approximates the likelihood function better than the other methods. The improvement of the MCNR method is further illustrated with real-world data from a longitudinal study of local cervicovaginal HIV viral load and its effects on oncogenic HPV detection in HIV-positive women.

关键词： detection limit generalized linear mixed model longitudinal data measurement error Monte Carlo Newton-Raphson

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Predicting deadwood densities of Cryptomeria japonica and Chamaecyparis obtusa forests using a generalized linear mixed model with a national-scale dataset

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FOREST ECOLOGY AND MANAGEMENT 2013年 295卷 228-238页

作者： Sakai, Yoshimi Ishizuka, Shigehiro Takenaka, Chisato Forestry & Forest Prod Res Inst Dept Forest Site Environm Tsukuba Ibaraki 3058687 Japan Forestry & Forest Prod Res Inst Kyushu Res Ctr Chuo Ku Kumamoto 8600862 Japan Nagoya Univ Grad Sch Bioagr Sci Dept Biosphere Resources Sci Chikusa Ku Nagoya Aichi 4648601 Japan

Predicting the stocks of deadwood in planted stands is important for controlling biodiversity, carbon content, and nutrient cycling in forest ecosystems and for managing deadwood accumulation because of conservation activities for biodiversity and economic reasons. To calculate the carbon stock in deadwood, the volume, carbon content, and appropriate wood density for the decomposition state must be known. To develop a predictive model for estimating deadwood density, we used a generalized linear mixed model and a national-scale dataset with large variations in different deadwood factors related to wood properties and climatic conditions. Our samples of fallen logs were obtained by noncommercial thinning of Cryptomeria japonica D. Don (C. japonica) and Chamaecyparis obtusa (Sieb. et Zucc.) Endl. (C. obtusa) planted forests throughout Japan, covering various climatic conditions. The wood density model for C. japonica was D-w = 0.342 - 0.010y - 0.001d + 0.001Sa + 0.012C - 0.028F(c1) - 0.006 F-c2 + re and that for C. obtusa was D-w = 0.431 - 0.015y - 0.001d + re, where d is the diameter, Sa is the stand age, C is contact with the forest floor, F-c1 and F-c2 are the climatic factors, and y is the years since death with random site effect re. F-c1 and F-c2 are the principal component scores showing Japanese climatic characteristics that were calculated through principal component analysis using temperature, precipitation, and snow depth data. The negligible variance in the random site effect for both tree species suggested that the models could be applied to other sites. In this study, our models showed accurate predictions of deadwood densities comparable to single exponential decay models, as shown by values for root-mean-square error and root-mean-square relative error. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Carbon pool Deadwood generalized linear mixed model Principal component analysis Initial wood density Noncommercial thinning

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An R² statistic for fixed effects in the generalized linear mixed model

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JOURNAL OF APPLIED STATISTICS 2017年第6期44卷 1086-1105页

作者： Jaeger, Byron C. Edwards, Lloyd J. Das, Kalyan Sen, Pranab K. Univ N Carolina Dept Biostat Chapel Hill NC 27599 USA Univ Calcutta Dept Stat Kolkata India

Measuring the proportion of variance explained (R2) by a statistical model and the relative importance of specific predictors (semi-partial R2) can be essential considerations when building a parsimonious statistical model. The R2 statistic is a familiar summary of goodnessof- fit for normal linear models and has been extended in various ways to more general models. In particular, the generalized linear mixed model (GLMM) extends the normal linear model and is used to analyze correlated (hierarchical), non-normal data structures. Although various R2 statistics have been proposed, there is no consensus in statistical literature for the most sensible definition of R2 in this context. This research aims to build upon existing knowledge and definitions of R2 and to concisely define the statistic for the GLMM. Here, we derive a model and semi-partial R2 statistic for fixed (population) effects in the GLMM by utilizing the penalized quasi-likelihood estimation method based on linearization. We show that our proposed R2 statistic generalizes the widely used marginal R2 statistic introduced by Nakagawa and Schielzeth, demonstrate our statistics capability in model selection, show the utility of semi-partial R2 statistics in longitudinal data analysis, and provide software that computes the proposed R2 statistic along with semi-partial R2 for individual fixed effects. The software provided is adapted for both SAS and R programming languages.

关键词： Blood pressure CD4(+) cell counts generalized linear mixed model clustered data R-squared statistical software 62-07 62Fxx 62Hxx 62Pxx

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Variant-set association test for generalized linear mixed model

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GENETIC EPIDEMIOLOGY 2021年第4期45卷 402-412页

作者： Zhan, Xiang Banerjee, Kalins Chen, Jun Penn State Univ Dept Publ Hlth Sci Hershey PA USA Mayo Clin Div Biomed Stat & Informat Rochester MN 55905 USA

Advances in high-throughput biotechnologies have culminated in a wide range of omics (such as genomics, epigenomics, transcriptomics, metabolomics, and metagenomics) studies, and increasing evidence in these studies indicates that the biological architecture of complex traits involves a large number of omics variants each with minor effects but collectively accounting for the full phenotypic variability. Thus, a major challenge in many "ome-wide" association analyses is to achieve adequate statistical power to identify multiple variants of small effect sizes, which is notoriously difficult for studies with relatively small-sample sizes. A small-sample adjustment incorporated in the kernel machine regression framework was proposed to solve this for association studies under various settings. However, such an adjustment in the generalized linear mixed model (GLMM) framework, which accounts for both sample relatedness and non-Gaussian outcomes, has not yet been attempted. In this study, we fill this gap by extending small-sample adjustment in kernel machine association test to GLMM. We propose a new Variant-Set Association Test (VSAT), a powerful and efficient analysis tool in GLMM, to examine the association between a set of omics variants and correlated phenotypes. The usefulness of VSAT is demonstrated using both numerical simulation studies and applications to data collected from multiple association studies. The software for implementing the proposed method in R is available at .

关键词： generalized linear mixed model kernel machine regression omics variants small sample variant‐ set association test

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The effect of travel time variability on route choice decision: a generalized linear mixed model based analysis

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TRANSPORTATION 2014年第2期41卷 339-350页

作者： Gan, Hongcheng Bai, Yang Univ Shanghai Sci & Technol Dept Transportat Engn Shanghai Peoples R China Shanghai Univ Finance & Econ Sch Stat & Management Shanghai Peoples R China

The effect of travel time variability (TTV) on route choice behavior is explored in this study. A stated preference survey is conducted to collect behavioral data on Shanghai drivers' choice between a slow but stable route and a fast but unreliable route. Travel time and TTV are respectively measured by mean and standard deviation of random travel time. The generalized linear mixed model (GLMM) is applied to quantify trade-offs between travel time and TTV. The GLMM based route choice model effectively accounts for correlations among repeated observations from the same respondent, and captures heterogeneity in drivers' values of TTV. model estimation results show that, female drivers and drivers with rich driving experience are less likely to choose a route with high TTV;smaller expected travel time of a route increase the probability of its being chosen;all drivers have intrinsic preference for a route with smaller expected travel time, but the degree of preference may vary within the population;TTV on average has negative effects on route choice decision, but a small portion of drivers are risk-prone to choose a fast but unreliable route despite high TTV.

关键词： Travel time variability Route choice generalized linear mixed model Stated preference Repeated observations Heterogeneity

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Computation and application of generalized linear mixed model derivatives using lme4

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PSYCHOMETRIKA 2022年第3期87卷 1173-1193页

作者： Wang, Ting Graves, Benjamin Rosseel, Yves Merkle, Edgar C. Amer Board Family Med Lexington KY 40511 USA Univ Missouri Columbia MO 65211 USA Univ Ghent Ghent Belgium

Maximum likelihood estimation of generalized linear mixed models (GLMMs) is difficult due to marginalization of the random effects. Derivative computations of a fitted GLMM's likelihood are also difficult, especially because the derivatives are not by-products of popular estimation algorithms. In this paper, we first describe theoretical results related to GLMM derivatives along with a quadrature method to efficiently compute the derivatives, focusing on fitted lme4 models with a single clustering variable. We describe how psychometric results related to item response models are helpful for obtaining the derivatives, as well as for verifying the derivatives' accuracies. We then provide a tutorial on the many possible uses of these derivatives, including robust standard errors, score tests of fixed effect parameters, and likelihood ratio tests of non-nested models. The derivative computation methods and applications described in the paper are all available in easily obtained R packages.

关键词： generalized linear mixed model score test lme4 derivatives merDeriv

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Estimation of a generalized linear mixed model for response-adaptive designs in multi-centre clinical trials

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2017年第3期45卷 310-325页

作者： Selvaratnam, Selvakkadunko Oyet, Alwell J. Yi, Yanqing Gadag, Veeresh Mem Univ Dept Math & Stat St John NF ALC 5S7 Canada Mem Univ Dept Community Hlth & Humanities St John NF A1B 3V6 Canada

Response-adaptive designs are important alternatives to equal allocation in clinical trials because equal treatment allocation has been found to have ethical issues. In this article we discuss the implementation of response-adaptive designs in multi-centre clinical trials. We develop a generalized linear mixed model (GLMM) for analyzing data obtained from multi-centre clinical trials and use the maximum likelihood (ML) approach to estimate the model parameters. We apply influence function techniques to derive the asymptotic properties of our estimators. The advantage of using the influence function approach is that it leads to a closed form expression for the asymptotic covariance of the estimated parameters. To our knowledge such a closed form expression does not currently exist in the literature. The performance of the ML estimator under various response-adaptive designs is examined through simulation studies. We use our simulation studies to compare the asymptotic covariance matrix, based on the influence function to that based on the inverse of the Hessian matrix obtained from the likelihood function of the observations. The techniques are applied to real data obtained from a multi-centre clinical trial designed to compare two cream preparations (active drug/control) for treating an infection. The Canadian Journal of Statistics 45: 310-325;2017 (c) 2017 Statistical Society of Canada

关键词： Asymptotic properties Clinical trials generalized linear mixed model influence function maximum likelihood response-adaptive designs MSC 2010: Primary 62F12 secondary 62L05

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dPQL: a lossless distributed algorithm for generalized linear mixed model with application to privacy-preserving hospital profiling

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JOURNAL OF THE AMERICAN MEDICAL INFORMATICS ASSOCIATION 2022年第8期29卷 1366-1371页

作者： Luo, Chongliang Islam, Md Nazmul Sheils, Natalie E. Buresh, John Schuemie, Martijn J. Doshi, Jalpa A. Werner, Rachel M. Asch, David A. Chen, Yong Univ Penn Dept Biostat Epidemiol & Informat 602 Blockley Hall423 Guardian Dr Philadelphia PA 19104 USA Washington Univ Div Publ Hlth Sci Sch Med St Louis St Louis MO USA OptumLabs Minnetonka MN USA Janssen Res & Dev LLC Titusville NJ USA Univ Penn Div Gen Internal Med Philadelphia PA 19104 USA Leonard Davis Inst Hlth Econ Philadelphia PA USA Cpl Michael J Crescenz VA Med Ctr Philadelphia PA USA

Objective To develop a lossless distributed algorithm for generalized linear mixed model (GLMM) with application to privacy-preserving hospital profiling. Materials and Methods The GLMM is often fitted to implement hospital profiling, using clinical or administrative claims data. Due to individual patient data (IPD) privacy regulations and the computational complexity of GLMM, a distributed algorithm for hospital profiling is needed. We develop a novel distributed penalized quasi-likelihood (dPQL) algorithm to fit GLMM when only aggregated data, rather than IPD, can be shared across hospitals. We also show that the standardized mortality rates, which are often reported as the results of hospital profiling, can also be calculated distributively without sharing IPD. We demonstrate the applicability of the proposed dPQL algorithm by ranking 929 hospitals for coronavirus disease 2019 (COVID-19) mortality or referral to hospice that have been previously studied. Results The proposed dPQL algorithm is mathematically proven to be lossless, that is, it obtains identical results as if IPD were pooled from all hospitals. In the example of hospital profiling regarding COVID-19 mortality, the dPQL algorithm reached convergence with only 5 iterations, and the estimation of fixed effects, random effects, and mortality rates were identical to that of the PQL from pooled data. Conclusion The dPQL algorithm is lossless, privacy-preserving and fast-converging for fitting GLMM. It provides an extremely suitable and convenient distributed approach for hospital profiling.

关键词： distributed penalized quasi-likelihood algorithm federated learning generalized linear mixed model hospital profiling privacy-preserving

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HANDLING MISSING RESPONSES IN generalized linear mixed model WITHOUT SPECIFYING MISSING MECHANISM

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JOURNAL OF BIOPHARMACEUTICAL STATISTICS 2009年第6期19卷 1001-1017页

作者： Zhang, Hui Paik, Myunghee Cho Columbia Univ Dept Biostat New York NY 10032 USA Pfizer China Res & Dev Ctr Dept Stat Shanghai Peoples R China

In longitudinal studies, missingness of data is often unavoidable. Valid estimators from the generalized linear mixed model usually rely on the correct specification of the missing data mechanism. An incorrectly specified missing mechanism may lead to a biased estimator. In this article, we propose a class of unbiased estimating equations using pairwise conditional technique to deal with the generalized linear mixed model under benign non-ignorable missingness where specification of the missing model is not needed. We show that the proposed estimator is consistent and asymptotically normal under certain conditions. Simulation results and an example using longitudinal course of neuropsychological data are also shown.

关键词： generalized linear mixed model Missing responses Non-ignorable missing Pairwise conditional method

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Selecting traits that explain species-environment relationships: a generalized linear mixed model approach

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JOURNAL OF VEGETATION SCIENCE 2013年第6期24卷 988-1000页

作者： Jamil, Tahira Ozinga, Wim A. Kleyer, Michael ter Braak, Cajo J. F. Univ Wageningen & Res Ctr NL-6700 AC Wageningen Netherlands COMSATS Inst Informat Technol Dept Math Islamabad Pakistan Wageningen Univ & Res Ctr Alterra NL-6700 AA Wageningen Netherlands Radboud Univ Nijmegen NL-6525 ED Nijmegen Netherlands Carl von Ossietzky Univ Oldenburg Landscape Ecol Grp D-26111 Oldenburg Germany

QuestionQuantification of the effect of species traits on the assembly of communities is challenging from a statistical point of view. A key question is how species occurrence and abundance can be explained by the trait values of the species and the environmental values at the sites. MethodsUsing a sitesxspecies abundance table, a sitexenvironment data table and a speciesxtrait data table, we address the above question using a novel generalized linear mixed model (GLMM) approach. The GLMM overcomes problems of pseudo-replication and heteroscedastic variance by including sites and species as random factors. The method is equally applicable to presence-absence data as to count and multinomial data. We present a tiered forward selection approach for obtaining a parsimonious model and compare the results with alternative methods (the fourth corner method and RLQ ordination). ResultsWe illustrate the approach on a presence-absence version on two data sets. In the Dune Meadow data, species presence is parsimoniously explained by moisture and manure on the meadows in combination with seed mass and specific leaf area (SLA). In the Grazed Grassland data, species presence is parsimoniously explained by the grazing intensity and soil phosphorus in combination with the C:N ratio and flowering mode. ConclusionsOur GLMM approach can be used to identify which species traits and environmental variables best explain the species distribution, and which traits are significantly correlated with environmental variables. We argue that the method is better suited for providing an interpretable and predictive model than the fourth corner method and RLQ.

关键词： Community assembly Environmental gradient Fourth corner Functional ecology generalized linear mixed model RLQ Species traits Trait-environment relationship

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