Authors

• Mahmoud Torabi ¹
• Alexander R. de Leon ²

¹ Departments of Community Health Sciences and Statistics, University of Manitoba, Winnipeg, Manitoba, CANADA R3E 0W3

² Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CANADA T2N 1N4

Abstract

Mixed models are widely used to analyze longitudinal data. In their conventional formulation as linear mixed models (LMMs) and generalized LMMs (GLMMs), a commonly indispensable assumption in settings involving longitudinal non-Gaussian data is that the longitudinal observations from subjects are conditionally independent, given subject-specific random effects. Although conventional Gaussian LMMs are able to incorporate conditional dependence of longitudinal observations, they require that the data are, or some transformation of them is, Gaussian, a serious limitation in a wide variety of practical applications. Here, we introduce the class of Gaussian copula conditional regression models (GCCRMs) as flexible alternatives to conventional LMMs and GLMMs. One advantage of GCCRMs is that they extend conventional LMMs and GLMMs in a way that reduces to conventional LMMs, when the data are Gaussian, and to conventional GLMMs, when conditional independence is assumed. We implement likelihood analysis of GCCRMs using existing software and statistical packages and evaluate the finite-sample performance of maximum likelihood estimates for GCCRM empirically via simulations vis-a-vis the `naive' likelihood analys is that incorrectly assumes conditionally independent longitudinal data. Our results show that the `naive' analysis yields estimates with possibly severe bias and incorrect standard errors, leading to misleading inferences. We use bolus count data on patients' controlled analgesia comparing dosing regimes and data on serum creatinine from a renal graft study to illustrate the applications of GCCRMs.

Keywords

• Exponential Family
• Gaussian Copula
• Marginal Distribution
• Maximum likelihood estimation
• Random Effects