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   Paris, France

Transformations and Variance Functions in Nonlinear Mixed-Effects Models

Jose Pinheiro

Biostatistics, Novartis Pharmaceuticals

Population pharmacokinetics (PK) studies consist of longitudinal concentration measurements in a sample of individuals, with the concentration profiles typically being represented by nonlinear functions of PK parameters and covariates. Nonlinear mixed-effects (NLME) models flexibly describe nonlinear relationships between a response variable and parameters and covariates in correlated, longitudinal data, being the primary modeling tool for fitting and analyzing population PK models.

In its simplest form, NLME models assume additive Gaussian within-subject errors with constant variance and Gaussian random effects. However, when real data are analyzed, departures from these assumptions are frequently observed. Some of the most common departures are non-normality of within-subject errors and/or random effects and non-constant within-subject variance (heteroscedasticity). In classical regression analysis with independent data, non-normality has been typically dealt with by transforming the response (and sometimes also the model, as in the "transform both sides" approach) and heteroscedasticy has been addressed through either data transformation or the use of variance functions (leading to weighted
regression methods).

This talk discusses the use of transformations and variance functions in the context of NLME models, for the purpose of correcting suspected departures from the model assumptions. Transform both sides strategies for NLME models are described and compared to the use of variance functions, in the context of heteroscedastic data. Parameter transformation to allow unconstrained optimization and to address non-normality in the random effects are also discussed. Real and simulated data from population PK models are used to illustrate the methods described.