Estimation of dynamical model parameters taking into account undetectable marker values.

Area of Science:

• Mathematical modeling
• Virology
• Pharmacokinetics

Background:

• Mathematical models are essential for studying infectious agent dynamics, like hepatitis C virus (HCV).
• Estimating model parameters often uses standard least-squares, but left-censored data (undetectable viral load) pose challenges.
• Hierarchical models and methods addressing left-censoring are needed for accurate parameter estimation.

Purpose of the Study:

• To propose and validate a method for estimating parameters in nonlinear mixed-effects models with left-censored data.
• To assess the impact of this method on parameter estimation in hepatitis C virus (HCV) dynamics.
• To compare the proposed method with traditional approaches using simulations and a clinical trial.

Main Methods:

• A full likelihood approach was employed, differentiating between observed and left-censored measurements.
• A lognormal distribution was assumed for the outcome variable (viral load).
• Parameters were estimated using standard statistical software for the analytical solution of differential equations.

Main Results:

• Ignoring left-censoring led to significant parameter bias (up to 133%) in simulations.
• The proposed method reduced relative bias on fixed effects to ≤2%.
• Clinical trial data showed significant differences in parameter estimates, particularly for infected cell death rates, impacting treatment efficacy assessment.

Conclusions:

• The proposed method provides unbiased parameter estimates when the assumed distribution (e.g., lognormal) is correct.
• This approach is practical and can be implemented using standard statistical software.
• Accurate estimation, especially with left-censored data, is vital for reliable interpretation of anti-HCV drug clinical trials.