Analysis of Serially Correlated Data Using Quasi-Least Squares

Abstract

SUMMARY Quasi-least squares (QLS), a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by Chaganty (1997, Journal of Statistical Planning and Inference 63, 39-54), allows for application of a wide range of working correlation structures when analyzing serially correlated data. We extend the application of QLS to serially correlated, unequally spaced, and unbalanced data using three useful working correlation models: the firstorder autoregressive (AR(1)), the Markov, and the generalized Markov structure described by Nuniez-Anton and Woodworth (1994, Biometrics 50, 445-456). We compare QLS and the original formulation of the generalized estimating equation approach (GEE) for these structures, demonstrating that (i) infeasibility of the GEE correlation parameter estimates can be a problem, (ii) it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized Markov structure, and (iii) the use of QLS can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data. To choose between alternative correlation models, we propose a criterion that is based on the principle of generalized least squares. Finally, data for which the generalized Markov structure is appropriate are analyzed to demonstrate the use of QLS in selecting a suitable working correlation structure and identifying In this paper, we apply a statistical method based on the generalized estimating equation approach of Liang and Zeger (1986) to the analysis of longitudinal data that may be difficult to analyze using other established methods. We consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects. Our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject. Accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies. The timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced. The outcome variable may not be normally distributed. The intrasubject correlation may be described using a time-dependent pattern. For example, the correlation between two measurements may decrease as they become more