Evaluations of Transform-Both-Sides Methods for Nonlinear Mixed Effects Models

• Activity Number: 271
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 3:05 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Noa Molshatzki* and Sandrah P. Eckel
• Companies: University of Southern California and University of Southern California
• Keywords: Biomarkers ; Nonlinear regression ; Mixed models ; Transform both sides

Abstract

Skewed and/or heteroscedastic repeated measures data arising from theoretical models are often encountered in practice. These data violate normality assumptions required for inference on population parameters for nonlinear mixed effects models. A common solution is to transform both the response and the regression function, which preserves the theoretical relationship between response and model parameters. The transformation is commonly chosen a priori (e.g., natural log) but can also be estimated from the data using an extension of the Box-Cox power transformation. Methods for estimating the transformation must overcome the lack of an analytical solution for the marginal likelihood. Existing methods include an approach approximating the likelihood function and an approach estimating the transformation of only the response in a fixed effects model. We have developed implementations of these methods in standard statistical software and use simulation studies to compare performance and limitations. Finally, we apply these methods to data on exhaled nitric oxide measured at multiple exhalation flow rates in >1500 children in the Southern California Children's Health Study.