A Surprising Bias in Functional Data Analysis and Its Solution

• Activity Number: 688
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Junshui Ma*+ and Vladmir Svetnik
• Companies: Merck & Co., Inc. and Merck & Co., Inc.
• Keywords: Functional Data Analysis ; Longitudinal Data Analysis ; Generalized Least Square ; complex covariance structure ; covariance matrix estimation ; Cholesky factorization

Abstract

Functional data acquired via image and bio-signal modalities are increasingly frequent in pre-clinical experiments and clinical trials. Statistical methods to analyze this complex data type have been proposed in the areas of both functional data analysis (FDA) and longitudinal data analysis (LDA). A surprising bias in the fixed factors was observed when an approach combining ideas from both areas was implemented using popular statistical software. The bias was first demonstrated with a real dataset. The observation reveals that statistical packages, e.g. the R package of Nonlinear Mixed Effect Model (NLME) , can produce biased fixed effects when relatively complex covariance matrix structures are used. Further investigation suggests that the optimization procedure used in those statistical packages fails to properly address the interaction between an under-specified mean and a complex variance. After it is shown that a simple solution can leads to potential over-fitting, a more sophisticated method is proposed. The proposed method is based on unconstrained parameterization of covariance matrix with Cholesky factorization, which has been presented in the literature.