POWRE: Methods for the Analysis of Data with Multiple Levels of Correlation and a Comparison of Several Fundamental Statistical Approaches

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

We will develop improved statistical approaches for the analysis of potentially non-Gaussian data with multiple levels of correlation, as might be encountered when repeated observations collected on siblings within families are correlated due to within subject, or within family, similarities. Our first objective is to fulfill the need in the literature for a relatively straightforward approach for analysis of multi-level correlated data by extending the method of quasi-least squares (QLS) [Chaganty (1997), Shults and Chaganty (1998), and Chaganty and Shults (1999)]. We will implement QLS using a correlation model discussed in Shults (2000) that is a generalization of a structure proposed by Lefkopolou, Moore, and Ryan (1989). Motivational examples for our research include an international trial to promote exclusive breast-feeding (Morrow, Guerrero, Shults, et. al., 1999) and an ongoing study of Interstitial Cystitis at the University of Pennsylvania (Mazurick, Landis, et. al., 2000). Our next objective is to explore issues related to the benefits and implementation of approaches that use patterned correlation matrices to model association among outcomes. We will examine the impact of failure to specify an appropriate model for the correlation structure of our data, by considering several study designs and examining the loss of efficiency when the correlation structure has been incorrectly specified. Of particular interest will be the effect of ignoring one or more levels of correlation for data with multiple levels of association. Simulations will also be conducted to explore the effect of misspecification on the mean square error of the estimates of the regression and correlation parameters for small samples. We will then explore the development of improved guidelines for selection of an appropriate correlation structure when several plausible models are available. Our final objective is to explore the theoretical underpinnings of QLS and contrast QLS with pseudo-likelihood (PL, Carroll and Ruppert, 1998) and several other fundamental approaches that have been described in the statistical literature. We will then describe a modified PL approach that is closely related to QLS and will explore the development of this approach for several models for the correlation structure of our data. This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).