Taesung Park

A test of missing completely at random for longitudinal data with missing observations.

Liang and Zeger proposed a generalized estimating equations approach to the analysis of longitudinal data. Their models assume that missing observations are missing completely at random in the sense of Rubin. However, when this assumption does not hold, their analysis may yield biased results. In this paper, we develop a simple and practical procedure for testing this assumption. The proposed procedure is related to that of Park and Davis.

A generalized estimating equations approach for testing ordered group effects with repeated measurements.

In repeated measures studies, we are often interested in comparing group effects in which groups are associated with a certain order relation. We propose testing procedures for ordered group effects using the generalized estimating equations (GEE) approach of Liang and Zeger (1986, Biometrika 73, 13-22). The order-constrained GEE estimators of group effects are approximated by the isotonic regression of the unconstrained GEE estimators. Based on these constrained estimators, we construct test statistics for detecting ordered group effects. The limiting distributions of the test statistics are mixtures of chi-square distributions. A Monte Carlo experiment shows improved performances of the proposed tests over the usual chi-square tests in detecting ordered group effects. The proposed test procedures are illustrated by familial polyposis supplementation trial data.

Generalized multivariate models for longitudinal data

A general class of multivariate models is proposed for unbalanced and incomplete longitudinal data. The proposed model is an extension of the seemingly unrelated regression model (Zellner, 1962). The advantage of this model is discussed regarding its applicability to a larger class of problems and the ease of estimation. The application of the model includes the model for the time varying covariates proposed by Patel (1988) and growth curve models. Two estimation methods are considered; one method is the generalized least squares method based on Zellners noniterative two-stage estimation and the other is the iterative maximum likelihood estimation method using the EM algorithm (Dempster,Laird,and Rubin,1977). Simulation studies are conducted to compare the small sample properties of the two estimators.

A test of the missing data mechanism for repeated measures data

The occurrence of missing data is an often unavoidable consequence of repeated measures studies. Fortunately, multivariate general linear models such as growth curve models and linear mixed models with random effects have been well developed to analyze incomplete normally-distributed repeated measures data. Most statistical methods have assumed that the missing data occur at random. This assumption may include two types of missing data mechanism: missing completely at random (MCAR) and missing at random (MAR) in the sense of Rubin (1976). In this paper, we develop a test procedure for distinguishing these two types of missing data mechanism for incomplete normally-distributed repeated measures data. The proposed test is similar in spiril to the test of Park and Davis (1992). We derive the test for incomplete normally-distribrlted repeated measures data using linear mixed models. while Park and Davis (1992) cleirved thr test for incomplete repeatctl categorical data in the framework of Grizzle Starmer. and...

Multivariate regression models for discrete and continuous repeated measurements

A general class of multivariate regression models is considered for repeated measurements with discrete and continuous outcome variables. The proposed model is based on the seemingly unrelated regression model (Zellner, 1962) and an extension of the model of Park and Woolson(1992). The regression parameters of the model are consistently estimated using the two-stage least squares method. When the out come variables are multivariate normal, the two-stage estimator reduces to Zellner’s two-stage estimator. As a special case, we consider the marginal distribution described by Liang and Zeger (1986). Under this this distributional assumption, we show that the two-stage estimator has similar asymptotic properties and comparable small sample properties to Liang and Zegers estimator. Since the proposed approach is based on the least squares method, however, any distributional assumption is not required for variables outcome variables. As a result, the proposed estimator is more robust to the marginal distributi...

A practical extension of the generalized estimating equation approach for longitudinal data

Liang and Zeger (1986) proposed an extension of generalized linear models to the analysis of longitudinal data. In their formulation, a common dispersion parameter assumption across observation times is required. However, this assumption is not expected to hold in most situations. Park (1993) proposed a simple extension of Liang and Zegers formulation to allow for different dispersion parameters for each time point. The proposed model is easy to apply without heavy computations and useful to handle the cases when variations in over-dispersion over time exist. In this paper, we focus on evaluating the effect of additional dispersion parameters on the estimators of model parameters. Through a Monte Carlo simulation study, efficiency of Parks method is compared with the Liang and Zegers method.

Analysis of ordered covariate effects among groups with repeated measurements

Testing procedures for ordered covariate effects are developed in the repeated measures experiment. The maximum likelihood estimators of covariate effects under the ordered hypothesis are approximated by the isotonic regression of their unconstrained estimators. The asymptotic null distributions of the test statistics are chi-bar-square distributions which are mixtures of chi-square distributions. A Monte-Carlo simulation reveals that the proposed test for ordered covariate effects is seriously more powerful than the usual chi-square test that neglects the information on the order restriction. These testing methods are applied for analyzing the effect of vitamin E diet supplement on growth rate of animals.