• Title, Summary, Keyword: GEE

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Small Sample Characteristics of Generalized Estimating Equations for Categorical Repeated Measurements (범주형 반복측정자료를 위한 일반화 추정방정식의 소표본 특성)

  • 김동욱;김재직
    • The Korean Journal of Applied Statistics
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    • v.15 no.2
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    • pp.297-310
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    • 2002
  • Liang and Zeger proposed generalized estimating equations(GEE) for analyzing repeated data which is discrete or continuous. GEE model can be extended to model for repeated categorical data and its estimator has asymptotic multivariate normal distribution in large sample sizes. But GEE is based on large sample asymptotic theory. In this paper, we study the properties of GEE estimators for repeated ordinal data in small sample sizes. We generate ordinal repeated measurements for two groups using two methods. Through Monte Carlo simulation studies we investigate the empirical type 1 error rates, powers, relative efficiencies of the GEE estimators, the effect of unequal sample size of two groups, and the performance of variance estimators for polytomous ordinal response variables, especially in small sample sizes.

반복측정된 포아송 자료의 GEE 분석에서 산포모수의 역할에 관한 연구

  • 박태성;신민웅
    • Communications for Statistical Applications and Methods
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    • v.2 no.2
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    • pp.155-165
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    • 1995
  • 반복측정자료의 분석을 위해 제안된 Liang and Zeger(1986)의 회귀모형은 일반화추정식(generalized estimationg equations, GEE)을 이용하여 모형의 모수를 추정한다. 이 모형은 반복측정된 반응변수와 설명변수들과의 관계를 추정하는 것이 주된 목적이기 때문에 회귀모수는 중요한 모수로 간주되나 산포모수는 중요하지 않은 장애모수(nuisance parameters)로 간주된다. 일반적으로 GEE 분석에서 회귀모수의 추정량은 산포모수에 상관없이 일치적(consistent)으로 얻어진다고 알려져 있다. 그러나 본 논문에서는 포아송분포를 따르는 반복측정자료에 대한 사례연구와 모의 실험을 통해서 일반적으로 믿어져왔던 것과는 달리 GEE 방법이 산포모수에 민감하게 영향을 받고 있음을 보였다. 특히 산포모수의 값이 일정하지 않은 경우에는 GEE 방법이 산포모수에 민감 하게 영향을 받고 있음을 보였다. 특히 산포모수의 값이 일정하지 않은 경우에는 GEE 방법에서 밝혀진 회귀모수 추정량의 일치성에도 문제가 발생할 수 있음을 보였다.

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Bootstrap Estimation for GEE Models (일반화추정방정식(GEE)에 대한 부스트랩의 적용)

  • Park, Chong-Sun;Jeon, Yong-Moon
    • The Korean Journal of Applied Statistics
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    • v.24 no.1
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    • pp.207-216
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    • 2011
  • Bootstrap is a resampling technique to find an estimate of parameters or to evaluate the estimate. This technique has been used in estimating parameters in linear model(LM) and generalized linear model(GLM). In this paper, we explore the possibility of applying Bootstrapping Residuals, Pairs, and an Estimating Equation that are most widely used in LM and GLM to the generalized estimating equation(GEE) algorithm for modelling repeatedly measured regression data sets. We compared three bootstrapping methods with coefficient and standard error estimates of GEE models from one simulated and one real data set. Overall, the estimates obtained from bootstrap methods are quite comparable, except that estimates from bootstrapping pairs are somewhat different from others. We conjecture that the strange behavior of estimates from bootstrapping pairs comes from the inconsistency of those estimates. However, we need a more thorough simulation study to generalize it since those results are coming from only two small data sets.

Analysis of Repeated Measured VAS in a Clinical Trial for Evaluating a New NSAID with GEE Method (퇴행성 관절염 환자를 대상으로 새로운 진통제 평가를 위한 임상시험자료의 GEE 분석)

  • Lim, Hoi-Jeong;Kim, Yoon-I;Jung, Young-Bok;Seong, Sang-Cheol;Ahn, Jin-Hwan;Roh, Kwon-Jae;Kim, Jung-Man;Park, Byung-Joo
    • Journal of Preventive Medicine and Public Health
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    • v.37 no.4
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    • pp.381-389
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    • 2004
  • Objective : To compare the efficacy between SKI306X and Diclofenac by using generalized estimating equations (GEE) methodology in the analysis of correlated bivariate binary outcome data in Osteoarthritis (OA) diseases. Methods : A randomized, double-blind, active comparator-controlled, non-inferiority clinical trial was conducted at 5 institutions in Korea with the random assignment of 248 patients aged 35 to 75 years old with OA of the knee and clinical evidence of OA. Patients were enrolled in this study if they had at least moderate pain in the affected knee joint and a score larger than 35mm as assessed by VAS (Visual Analog Scale). The main exposure variable was treatment (SKI 306X vs. Diclofenac) and other covariates were age, sex, BMI, baseline VAS, center, operation history (Yes/No), NSAIDS (Y/N), acupuncture (Y/N), herbal medicine (Y/N), past history of musculoskeletal disease (Y/N), and previous therapy related with OA (Y/N). The main study outcome was the change of VAS pain scores from baseline to the 2nd and 4th weeks after treatment. Pain scores were obtained as baseline, 2nd and 4th weeks after treatment. We applied GEE approach with empirical covariance matrix and independent(or exchangeable) working correlation matrix to evaluate the relation of several risk factors to the change of VAS pain scores with correlated binary bivariate outcomes. Results : While baseline VAS, age, and acupuncture variables had protective effects for reducing the OA pain, its treatment (Joins/Diclofenac) was not statistically significant through GEE methodology (ITT:aOR=1.37, 95% CI=(0.8200, 2.26), PP:aOR=1.47, 95% CI=(0.73, 2.95)). The goodness-of-fit statistic for GEE (6.55, p=0.68) was computed to assess the adequacy of the fitted final model. Conclusions : Both ANCOVA and GEE methods yielded non statistical significance in the evaluation of non-inferiority of the efficacy between SKI306X and Diclofenac. While VAS outcome for each visit was applied in GEE, only VAS outcome for the fourth visit was applied in ANCOVA. So the GEE methodology is more accurate for the analysis of correlated outcomes.

Note on Working Correlation in the GEE of Longitudinal Counts Data

  • Jeong, Kwang-Mo
    • Communications for Statistical Applications and Methods
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    • v.18 no.6
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    • pp.751-759
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    • 2011
  • The method of generalized estimating equations(GEE) is widely used in the analysis of a correlated dataset that consists of repeatedly observed responses within subjects. The GEE uses a quasi-likelihood equations to find the parameter estimates without assuming a specific distribution for the correlated responses. In this paper we study the importance of specifying the working correlation structure appropriately in fitting GEE for correlated counts data. We investigate the empirical coverages of confidence intervals for the regression coefficients according to four kinds of working correlations where one structure should be specified by the users. The confidence intervals are computed based on the asymptotic normality and the sandwich variance estimator.

van McGee's Counterexample, Probability, and Equivocation (반 멕기의 반례, 확률, 그리고 애매성)

  • Choi, Wonbae
    • Korean Journal of Logic
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    • v.19 no.2
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    • pp.233-251
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    • 2016
  • In their recent paper published in this journal Shin Kim and Jinyong Lee have attacked some previous studies on the counterexample to modus ponens. Among their arguments I would like to discuss the following two; first, those attempts to explain van McGee's example by reference to conditional probability do not accord with van McGee's position, second, van McGee'e example is to be best seen as an argument containing the fallacy of equivocation. I show that the first argument is not correct, the second one is not so persuasive as it seemed first.

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Upgraded quadratic inference functions for longitudinal data with type II time-dependent covariates

  • Cho, Gyo-Young;Dashnyam, Oyunchimeg
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.1
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    • pp.211-218
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    • 2014
  • Qu et. al. (2000) proposed the quadratic inference functions (QIF) method to marginal model analysis of longitudinal data to improve the generalized estimating equations (GEE). It yields a substantial improvement in efficiency for the estimators of regression parameters when the working correlation is misspecified. But for the longitudinal data with time-dependent covariates, when the implicit full covariates conditional mean (FCCM) assumption is violated, the QIF can not provide more consistent and efficient estimator than GEE (Cho and Dashnyam, 2013). Lai and Small (2007) divided time-dependent covariates into three types and proposed generalized method of moment (GMM) for longitudinal data with time-dependent covariates. They showed that their GMM type II and GMM moment selection methods can be more ecient than GEE with independence working correlation (GEE-ind) in the case of type II time-dependent covariates. We develop upgraded QIF method for type II time-dependent covariates. We show that this upgraded QIF method can provide substantial gains in efficiency over QIF and GEE-ind in the case of type II time-dependent covariates.

Quadratic inference functions in marginal models for longitudinal data with time-varying stochastic covariates

  • Cho, Gyo-Young;Dashnyam, Oyunchimeg
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.3
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    • pp.651-658
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    • 2013
  • For the marginal model and generalized estimating equations (GEE) method there is important full covariates conditional mean (FCCM) assumption which is pointed out by Pepe and Anderson (1994). With longitudinal data with time-varying stochastic covariates, this assumption may not necessarily hold. If this assumption is violated, the biased estimates of regression coefficients may result. But if a diagonal working correlation matrix is used, irrespective of whether the assumption is violated, the resulting estimates are (nearly) unbiased (Pan et al., 2000).The quadratic inference functions (QIF) method proposed by Qu et al. (2000) is the method based on generalized method of moment (GMM) using GEE. The QIF yields a substantial improvement in efficiency for the estimator of ${\beta}$ when the working correlation is misspecified, and equal efficiency to the GEE when the working correlation is correct (Qu et al., 2000).In this paper, we interest in whether the QIF can improve the results of the GEE method in the case of FCCM is violated. We show that the QIF with exchangeable and AR(1) working correlation matrix cannot be consistent and asymptotically normal in this case. Also it may not be efficient than GEE with independence working correlation. Our simulation studies verify the result.

Induction of Apoptosis in AGS Human Gastric Cancer Cell by Ethanol Extract of Ganoderma lucidum (영지 약침액이 인체 위암 세포 성장억제 및 세포사멸 유발에 미치는 영향)

  • Lee, Byung-Hoon;Kim, Hong-Gi;Kim, Cheol-Hong;Youn, Hyoun-Min;Song, Choon-Ho;Jang, Kyung-Jeon
    • Korean Journal of Acupuncture
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    • v.29 no.2
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    • pp.271-289
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    • 2012
  • Objectives : Ganoderma lucidum(Ganoderma or lingzhi, 靈芝) is a well-known oriental medical mushroom containing many bioactive compounds. The possible mechanisms involved in its effects on cancer cells remain to be elucidated. In the present study, the anti-proliferative and apoptotic activities of the G. lucidum ethanol extract(GEE), in AGS human gastric cancer cells were investigated. Methods : It was found that exposure of AGS cells to GEE resulted in the growth inhibition in a dose and time dependent manner as measured by trypan blue count and MTT assay. The anti-proliferative effect of GEE treatment in AGS cells was associated with morphological changes and formation of apoptotic bodies, and the flow cytometry analysis confirmed that GEE treatment increased the populations of apoptotic-sub G1 phase. Growth inhibition and apoptosis of AGS cells by GEE were connected with a concentration and time-dependent up-regulation of tumour necrosis factor-related apoptosis-inducing ligand(TRAIL) expression. Results : The levels of XIAP and survivin expression, members of IAP family proteins, were gradually down-regulated by GEE treatment. However other members of IAP family proteins such as cIAP-1 and cIAP-2 remained unchanged in GEE-treated AGS cells. GEE treatment also induced the proteolytic activation of caspase-3, caspase-8 and caspase-9 and a concomitant degradation of poly(ADP-ribose) polymerase(PARP) protein, a caspase-3 substrate protein. Additionally, GEE-induced apoptosis was associated with the inhibition of Akt activation in a concentration and time-dependent manner, and pre-treatment with LY294002, a phosphoinositide 3-kinase(PI3K)/Akt inhibitor, significantly increased GEE-induced growth inhibition and apoptosis. Conclusions : Therefore, G. lucidum has a strong potential as a therapeutic agent for preventing cancers such as gastric cancer cells.

Comparison of GEE Estimators Using Imputation Methods (대체방법별 GEE추정량 비교)

  • 김동욱;노영화
    • The Korean Journal of Applied Statistics
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    • v.16 no.2
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    • pp.407-426
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    • 2003
  • We consider the missing covariates problem in generalized estimating equations(GEE) model. If the covariate is partially missing, GEE can not be calculated. In this paper, we study the performance of 7 imputation methods to handle missing covariates in GEE models, and the properties of GEE estimators are investigated after missing covariates are imputed for ordinal data of repeated measurements. The 7 imputation methods include i) Naive Deletion ii) Sample Average Imputation iii) Row Average Imputation iv) Cross-wave Regression Imputation v) Carry-over Imputation vi) Bayesian Bootstrap vii) Approximate Bayesian Bootstrap. A Monte-Carlo simulation is used to compare the performance of these methods. For the missing mechanism generating the missing data, we assume ignorable nonresponse. Furthermore, we generate missing covariates with or without considering wave nonresp onse patterns.