Longitudinal Data Analysis

1. Front Matter

   Pages i-x

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2. Longitudinal Data and Linear Mixed Effects Models

   • Ikuko Funatogawa, Takashi Funatogawa

   Pages 1-26

3. Autoregressive Linear Mixed Effects Models

   • Ikuko Funatogawa, Takashi Funatogawa

   Pages 27-58

4. Case Studies of Autoregressive Linear Mixed Effects Models: Missing Data and Time-Dependent Covariates

   • Ikuko Funatogawa, Takashi Funatogawa

   Pages 59-75

5. Multivariate Autoregressive Linear Mixed Effects Models

   • Ikuko Funatogawa, Takashi Funatogawa

   Pages 77-98

6. Nonlinear Mixed Effects Models, Growth Curves, and Autoregressive Linear Mixed Effects Models

   • Ikuko Funatogawa, Takashi Funatogawa

   Pages 99-117

7. State Space Representations of Autoregressive Linear Mixed Effects Models

   • Ikuko Funatogawa, Takashi Funatogawa

   Pages 119-138

8. Back Matter

   Pages 139-141

   PDF

This book provides a new analytical approach for dynamic data repeatedly measured from multiple subjects over time. Random effects account for differences across subjects. Auto-regression in response itself is often used in time series analysis. In longitudinal data analysis, a static mixed effects model is changed into a dynamic one by the introduction of the auto-regression term. Response levels in this model gradually move toward an asymptote or equilibrium which depends on covariates and random effects. The book provides relationships of the autoregressive linear mixed effects models with linear mixed effects models, marginal models, transition models, nonlinear mixed effects models, growth curves, differential equations, and state space representation. State space representation with a modified Kalman filter provides log likelihoods for maximum likelihood estimation, and this representation is suitable for unequally spaced longitudinal data. The extension to multivariate longitudinal data analysis is also provided. Topics in medical fields, such as response-dependent dose modifications, response-dependent dropouts, and randomized controlled trials are discussed. The text is written in plain terms understandable for researchers in other disciplines such as econometrics, sociology, and ecology for the progress of interdisciplinary research.

• Longitudinal
• Mixed Effects
• Autoregressive
• Dynamic
• State Space

• Department of Statistical Data Science, The Institute of Statistical Mathematics, Tachikawa, Japan

  Ikuko Funatogawa

• Clinical Science and Strategy Department, Chugai Pharmaceutical Co. Ltd., Chūō, Japan

  Takashi Funatogawa

Ikuko Funatogawa, The Institute of Statistical Mathematics


Takashi Funatogawa, Chugai Pharmaceutical Co. Ltd.

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