Analyzing Multivariate Longitudinal Data Using SAS ®

Multivariate longitudinal data provides a unique opportunity in studying the joint evolution of multiple response variables over time. Comparing to the traditional univariate longitudinal data, the analysis of multivariate longitudinal data can be challenging because a) the variances of errors are likely to be different for different markers, b) the errors are likely to be correlated for the same marker measured at different occasions, and c) the errors are also likely to be correlated among markers measured at the same time. In this paper, with application to a real-world study to evaluate the joint evolution of the biomarkers for renal structure and function, we illustrate and compare 3 different approaches provided by SAS to analyze multivariate longitudinal data: the multivariate repeated measurement model with a Kronecker product covariance (PROC MIXED), the random coefficient mixed model (PROC MIXED) and the structural equation modeling approach (PROC CALIS). INTRODUCTION In many epidemiological studies and clinical trials, subjects are measured on several occasions with regarding to a collection of response variables. Multivariate longitudinal data of this kind would be useful to study the joint evolution of these response variables over time. Consider, as an example, the Consortium for Radiologic Imaging Studies of Polycystic Kidney Disease (CRISP) (Chapman et al 2003). CRISP is an observational study using imaging techniques to track the progress of patients with polycystic kidney disease where the biomarkers for kidney structure and function are simultaneously measured in each subject over the time course. Similar examples include the joint modeling of CD4 and CD8 lymphocyte counts in the process of HIV infection (Thiebaut et al 2002) as well as the couple-level growth curve analysis in social sciences (Newsom 2002). However, the analysis of such a multivariate longitudinal data can be challenging because a) the variances of errors are likely to be different for different markers, b) the errors are likely to be correlated for the same marker measured at different occasions, and c) the errors are also likely to be correlated among markers measured at the same time. In the SAS software, 3 different approaches have been provided to analyze multivariate longitudinal data: multivariate repeated measurement models with a Kronecker product covariance structure (Galecki 1994), random coefficient mixed models (Littell et al 1996) and structural equation modeling (Hatcher 1998). In this paper, we first present the CRISP data that motivates our study. Then we illustrate and compare these 3 approaches in studying the joint evolution of the renal structure and function for patients at an early stage of autosomal dominant polycystic kidney disease (ADPKD). Consortium for Radiologic Imaging Studies of Polycystic Kidney Disease (CRISP) Autosomal dominant polycystic kidney disease (ADPKD) is the most common genetically-caused renal disease that is characterized by gradual renal enlargement and cyst growth prior to loss of renal function. The CRISP study is a multi-center prospective observational study on subjects in early course of ADPKD. It is designed to develop innovative imaging techniques using magnetic resonance imaging (MRI) to accurately monitor the progression of cyst and renal volume. A total of 241 individuals from 211 families were enrolled in CRISP and followed up to 3 Table 1: Measurements of log-transformed KVS, CVS and GFR in CRISP KVS (X) CVS (Y) GFR (Z) VISIT -----------------------------------------------------N mean SD N mean SD N mean SD 0 241 6.81 0.56 240 5.74 1.16 236 4.55 0.25 1 228 6.85 0.57 223 5.89 1.14 227 4.55 0.28 2 214 6.94 0.58 205 5.99 1.18 217 4.51 0.33 3 203 6.98 0.60 199 6.11 1.15 210 4.48 0.34 years, using MRI to prospectively monitor the change of the renal structure. The study population was described elsewhere (Chapman et al 2003). In this paper, we only considered two markers for renal structure, kidney volume (KVS) and cyst volume (CVS), as well as one marker for renal function -glomerular filtration rate (GFR) as estimated by observed iothalamate clearance. Our primary interest is to assess the interrelationships among these markers. Table 1 shows the log-transformed values for each variable. For an easy notation, throughout this paper we let X, Y, and Z represent KVS, CVS and GFR respectively. We note that, as ubiquitous in longitudinal studies, not all markers Statistics and Data Analysis SUGI 31