Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses

Area of Science:

• Biostatistics
• Statistical modeling
• Longitudinal data analysis

Background:

• Nonlinear mixed effects models (NLME) are crucial in biological, agricultural, and environmental sciences.
• Estimating parameters in NLME models is challenging due to random effects distribution and left-censored data.
• Accurate modeling of human immunodeficiency virus (HIV) RNA viral load trajectories is essential.

Purpose of the Study:

• To develop a flexible statistical approach for fitting NLME models with left-censored data.
• To address the complexities of random effects distribution and correlation in modeling biological data.
• To accurately characterize nonlinear HIV RNA viral load trajectories after antiretroviral therapy interruption.

Main Methods:

• A smoothed simulated pseudo-maximum likelihood estimation (SSPMLE) approach is proposed.
• The method handles left-censored observations in nonlinear mixed effects models.
• Consistency and asymptotic normality of estimators are established, with testing procedures for random effects.

Main Results:

• The proposed SSPMLE method provides consistent and asymptotically normal estimators.
• New testing procedures are developed for random effects correlation and distributional assumptions.
• The approach offers greater flexibility in random effects distribution specification compared to EM variants.

Conclusions:

• The developed statistical methods effectively handle left-censored data in NLME models.
• The approach enhances the analysis of complex biological data, including HIV viral load dynamics.
• Simulation studies and real-world data analysis validate the proposed methods' performance.