Fast inference for robust nonlinear mixed-effects models

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Nonlinear mixed-effects models (NLME) are crucial in pharmacokinetics, growth curves, and HIV dynamics.
• Standard NLME models face challenges with random effects, estimation, and sensitivity to non-normal data.
• Scale mixture of normal distributions offer heavy-tailed alternatives for robust estimation against outliers.

Purpose of the Study:

• Compare two estimation methods for NLME models with multivariate scale mixture of normal distributions.
• Evaluate the performance and robustness of Monte Carlo Expectation-Maximization (MCEM) and an approximate likelihood-based method.
• Assess the trade-offs between computational speed and estimation accuracy.

Main Methods:

• Development of a Monte Carlo Expectation-Maximization (MCEM) algorithm.
• Development of an efficient likelihood-based approximate estimation method.
• Comparison through simulation studies and analysis of real nonlinear applications.

Main Results:

• The approximate method significantly outperforms MCEM in terms of speed.
• Both methods achieve efficient likelihood maximization, with the approximate method showing slightly higher bias in fixed-effects parameters.
• Scale mixture models demonstrate robustness against outlying observations.

Conclusions:

• The approximate method provides a computationally efficient alternative for estimating NLME models with scale mixtures of normal distributions.
• Careful consideration of potential bias is necessary when using the approximate method.
• The proposed scale mixture models enhance the robustness of NLME analyses in various scientific fields.