関: GEE

WordNet

draw from specific cases for more general cases (同)generalise, extrapolate, infer
become systemic and spread throughout the body; "this kind of infection generalizes throughout the immune system" (同)generalise
speak or write in generalities (同)generalise
the act of regarding as equal (同)equating
a mathematical statement that two expressions are equal
not biologically differentiated or adapted to a specific function or environment; "the hedgehog is a primitive and generalized mammal" (同)generalised

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等式; 方程式

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/10/05 13:07:25」(JST)

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In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unknown correlation between outcomes. ^[1] ^[2]

Parameter estimates from the GEE are consistent even when the covariance structure is misspecified, under mild regularity conditions. The focus of the GEE is on estimating the average response over the population ("population-averaged" effects) rather than the regression parameters that would enable prediction of the effect of changing one or more covariates on a given individual. GEEs are usually used in conjunction with Huber-White standard error estimates, also known as "robust standard error" or "sandwich variance" estimates. In the case of a linear model with a working independence variance structure, these are known as "heteroskedasticity consistent standard error" estimators. Indeed, the GEE unified several independent formulations of these standard error estimators in a general framework.

GEEs belong to a class of semiparametric regression techniques because they rely on specification of only the first two moments. Under correct model specification and mild regularity conditions, parameter estimates from GEEs are consistent. They are a popular alternative to the likelihood–based generalized linear mixed model which is more sensitive to variance structure specification. They are commonly used in large epidemiological studies, especially multi-site cohort studies because they can handle many types of unmeasured dependence between outcomes.

Formulation[edit]

Given a mean model, , and variance structure, , the estimating equation is formed via:^[3]

The parameter estimates solve U(β)=0 and are typically obtained via the Newton-Raphson algorithm. The variance structure is chosen to improve the efficiency of the parameter estimates. The Hessian of the solution to the GEEs in the parameter space can be used to calculate robust standard error estimates. The term "variance structure" refers to the algebraic form of the covariance matrix between outcomes, Y, in the sample. Examples of variance structure specifications include independence, exchangeable, autoregressive, stationary m-dependent, and unstructured. The most popular form of inference on GEE regression parameters is the Wald test using naive or robust standard errors, though the Score test is also valid and preferable when it is difficult to obtain estimates of information under the alternative hypothesis. The likelihood ratio test is not valid in this setting because the estimating equations are not necessarily likelihood equations. Model selection can be performed with the GEE equivalent of the Akaike Information Criterion (AIC) the Quasi-AIC (QIC).

Computation[edit]

Software for solving generalized estimating equations is available in MATLAB,^[4] SAS (proc genmod^[5]), SPSS (the gee procedure^[6]), Stata (the xtgee command^[7]) and R (packages gee^[8] and geepack^[9]).

References[edit]

^ Kung-Yee Liang and Scott Zeger (1986). "Longitudinal data analysis using generalized linear models". Biometrika 73 (1): 13–22.
^ Hardin, James; Hilbe, Joseph (2003). Generalized Estimating Equations. London: Chapman and Hall/CRC. ISBN 978-1-58488-307-4.
^ Diggle, Peter J.; Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger (2002). Analysis of Longitudinal Data. Oxford Statistical Science Series. ISBN 978-0-19-852484-7.
^ Sarah J. Ratcliffe and Justine Shults (2008). "GEEQBOX: A MATLAB Toolbox for Generalized Estimating Equations and Quasi-Least Squares". Journal of Statistical Software 25 (14): 1–14.
^ "The GENMOD Procedure". The SAS Institute.
^ "IBM SPSS Advanced Statistics". IBM SPSS website.
^ "Stata’s implementation of GEE". Stata website.
^ "gee: Generalized Estimation Equation solver". CRAN.
^ geepack: Generalized Estimating Equation Package, CRAN

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Quantitative CT: technique dependence of volume estimation on pulmonary nodules.

Chen B, Barnhart H, Richard S, Colsher J, Amurao M, Samei E.SourceMedical Physics Graduate Program, Duke University, Durham, NC 27705, USA. Carl E Ravin Advanced Imaging Laboratories, Duke University, Durham, NC 27705, USA.
Physics in medicine and biology.Phys Med Biol.2012 Mar 7;57(5):1335-48. Epub 2012 Feb 21.
Current estimation of lung nodule size typically relies on uni- or bi-dimensional techniques. While new three-dimensional volume estimation techniques using MDCT have improved size estimation of nodules with irregular shapes, the effect of acquisition and reconstruction parameters on accuracy (bias)
PMID 22349265

Factors predicting the outcome of conservatively treated adenocarcinoma in situ of the uterine cervix: An analysis of 166 cases.

Costa S, Venturoli S, Negri G, Sideri M, Preti M, Pesaresi M, Falasca A, Barbieri D, Zerbini M, Santini D, Sandri MT, Ghiringhello B, Caroppo Venturini N, Syrjänen S, Syrjänen K.SourceDepartment of Obstetrics and Gynecology, S.Orsola-Malpighi University Hospital, Bologna, Italy.
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OBJECTIVE: The present study assessed the clinical outcome of patients conservatively treated for cervical adenocarcinoma in situ (AIS) and their predictive factors using univariate and multivariate population averaged (PA) generalized estimating equation (GEE) model in a longitudinal setting.METHOD
PMID 22188786

Japanese Journal

Humphrey自動視野計のvisual field indexとmean deviationの比較検討

木村聡,木村泰朗,小野浩一 [他]
日本眼科学会雑誌 115(8), 686-692, 2011-08
NAID 40018953755

Modifications of QIC and CIC for Selecting a Working Correlation Structure in the Generalized Estimating Equation Method

Gosho Masahiko,Hamada Chikuma,Yoshimura Isao
計量生物学 32(1), 1-12, 2011
… The generalized estimating equation (GEE) method is a popular method for analyzing longitudinal data. …
NAID 130000999548

ESTIMATION OF GROWTH CURVE MODELS WITH STRUCTURED ERROR COVARIANCES BY GENERALIZED ESTIMATING EQUATIONS

Hwang Heungsun,Takane Yoshio
Behaviormetrika 32(2), 155-163, 2005-07
… In this paper, the generalized estimating equation method is adopted to estimate parameters of the growth curve model. …
NAID 110004045820