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Linear Models and Regression

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Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Abstract

A model is said to be linear if the partial derivatives with respect to any of the model parameters are independent of the other parameters. This chapter introduces linear models and regression, both simple linear and multiple regression, within the framework of ordinary least squares and maximum likelihood. Influence diagnostics, conditional models, error in variables, and smoothers and splines are discussed. How to appropriately handle missing data in both the dependent and independent variables is discussed.

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Notes

  1. 1.

    More formally, leverage is defined as the partial derivative of the predicted value with respect to the corresponding dependent variable, i.e., \( {h_i} = \partial {\hat Y_i}/\partial {Y_i} \), which reduces to the HAT matrix for linear models.

  2. 2.

    The intent to treat principle essentially states that all patients are analyzed according to the treatment they were randomized to, irrespective of the treatment they actually received. Hence, a patient is included in the analysis even if that patient never received the treatment.

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Authors and Affiliations

  1. Astellas Pharma Global Development Pharmacokinetics, Modeling, and Simulation, Deerfield, IL, USA

    Peter L. Bonate Ph.D.

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  1. Peter L. Bonate Ph.D.
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Bonate, P.L. (2011). Linear Models and Regression. In: Pharmacokinetic-Pharmacodynamic Modeling and Simulation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9485-1_2

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