The Estimation And Testing In GEE Method Without PA Condition

In clinic medical research, epidemiology, health care management, biology, ecology, longitudinal studies are more and more popular. The advantage of longitudinal studies is its capacity to seperate what in the contex of population studies are called cohort and time effects. Marginal regression model and its associated generalized estimating equation (GEE) are becoming increasingly being used in longitudinal studies. But Pepe and Anderson (1994) pointed out that there is an important assumption called PA condition behind GEE method. If the assumption is violated and nondiagonal working correlation matrix is used in GEE, the statistical inference may be defficient. This paper mainly discussed PA condition's infulence on the GEE estimators and tests based on the GEE method.The first chapter introduced the theories and ideas of the longitudinal data and the generalized estimating equations . In the second chapter, we discussed the properties of the GEE estimators. The AR(1) model with different covariate structures was used to get the properties of the bias and sandwich variance estimaors of the GEE estimators. Irrespective of whether the PA condition is violated, the resulting estimator (OLS estimator in this paper) from the independent estimating equations with the independent correlation structure is compared with the estimators (GLS estimators in this paper)from the generalized estimating equations.The third chapter fucoused on PA condition's infulence on hyposesis and testing of regression coefficients in GEE method. Two commmon statisticses: Wald statistics and Score statistics were chosen to analysize the their distributions and efficiency. Due to the violation of the PA condition, the distributions of Wald statistics and Score statistics based on GLS estimators are noncentral x~2 distributions. The efficiency of test based on the GEE mothod is infulenced.The innovations of this paper lie in the second and the third chapter. Furthermore, some numeric simulations were made in the fourth chapter to insight how the PA condition influnces the estimation and testing in GEE method. In addition, it can be seen that the efficeincy of the statistical inference is infulunced by some other factors including the working correlation structures, covariate structures, size of true treatment effects.