Handling data below the limit of quantification in mixed effect models.

Area of Science:

• Pharmacometrics
• Statistical Modeling
• Drug Development

Background:

• Observations below the limit of quantification (BQL) present challenges in pharmacokinetic (PK) and pharmacodynamic (PD) modeling.
• Standard methods for handling BQL data can introduce bias in parameter estimates.
• Visual predictive checks (VPCs) are essential for assessing model fit but require careful interpretation with censored data.

Purpose of the Study:

• To investigate the impact of BQL observations on parameter estimates and model fit.
• To compare different methods for handling BQL data in PK/PD models.
• To propose an improved standard for VPCs to better evaluate model performance.

Main Methods:

• Simulations were performed using three distinct models (A, B, C) representing different scenarios of BQL data occurrence.
• One hundred datasets were generated for each model at various limits of quantification (LOQ) levels.
• Approaches including data omission, LOQ/2 substitution, and incorporating the likelihood of being below LOQ were compared.

Main Results:

• Omitting BQL data led to substantial bias in parameter estimates across all tested models.
• Substituting BQL data with LOQ/2 introduced bias and was suboptimal.
• Incorporating the likelihood of being below LOQ into the model yielded unbiased parameter estimates.
• Improved VPCs clearly identified model misfit for data both above and below LOQ.

Conclusions:

• The method of incorporating the likelihood of being below LOQ is the most effective for handling BQL data, preventing bias in parameter estimates.
• Data omission and LOQ/2 substitution are suboptimal and can lead to biased results.
• Enhanced VPCs provide a more robust assessment of model fit, especially when dealing with BQL data.