Jointly Modeling Means and Variances for Nonlinear Mixed Models with Measurement Errors and Outliers

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Qian Ye (1), Lang Wu (1), Viviane Dias Lima (2)

(1) University of British Columbia, Vancouver, British Columbia, (2) Department of Medicine, University of British Columbia, Vancouver, British Columbia

Lang Wu  
University of British Columbia

Viviane Dias Lima  
Department of Medicine, University of British Columbia

Qian Ye  
University of British Columbia

Qian Ye  
N/A

In the longitudinal data analysis, the within-individual repeated measurements often exhibit large variations and these variations appear to change over time. A good understanding the nature of the within-individual systematic and random variations allows us to conduct more efficient statistical inferences and make better predictions. Motivated by HIV viral dynamic studies, we considered a nonlinear mixed effects (NLME) model for modeling the longitudinal means, together with a model for the within-individual variances which also allows us to address outliers in the repeated measurements. Statistical inference was then based on a joint model for the mean and variance, implemented by a computationally efficient approximate method. Extensive simulations evaluated the proposed method. We found that the proposed method produces more efficient estimates than the corresponding method without modeling the variances. Moreover, the proposed method provides robust inference against outliers. The proposed method was applied to a recent HIV-related dataset, with interesting new findings.

h-likelihood|joint model|measurement error|robust| |

SSC (Statistical Society of Canada)

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