Bioequivalence and Bioavailability Forum

Dear Mittyri,

I wanted to share some insights on sparse sampling pharmacokinetic (PK) and non-compartmental analysis (NCA) that you might find useful:

1. Standard Error in AUC Calculation: The R package ‘PK’ uses the linear trapezoidal rule based on arithmetic means per time point, properly accounting for standard error (SE). In this case, the area under the curve (AUC) is essentially a weighted mean, where weights are determined by the linear trapezoidal rule and time points. Therefore, the SE can be directly derived because of its linear relationship.
   
2. Geometric Means Usage: When using geometric means instead of arithmetic ones, the standard error formula needs manual adjustment, as it is not supported in the R package 'PK’. I think you can likely use the formula for calculation of the SE for the AUC by replacing the SE for the arithmetic mean by that for the geometric mean and weight it appropriate as indicated by the linear trapezoidal rule and time points (see papers below which gives the formulas for the SE for AUC using arithmetic means and linear trapezoidal rule)
   
3. Linear-Up Log-Linear Down Rule: The SE calculation becomes quite challenging due to the non-linear elements introduced by the log-linear down rule.

The primary challenge in NCA with sparse sampling arises not from the AUC calculation methods but from handling values below the limit of quantification (LLOQ). I recommend the following paper for insights on this:

• Harnett, H. Y., Geys, H., Jacobs, T., & Jaki, T. (2020). Methods for Non-Compartmental Pharmacokinetic Analysis With Observations Below the Limit of Quantification. Statistics in Biopharmaceutical Research, 13(1), 59–70. https://doi.org/10.1080/19466315.2019.1701546

Additionally, here are some papers on NCA with sparse sampling that might interest you. If I recall correctly in the reference section in one of those works refers to a paper which addresses the log-linear rule, though I can’t remember the exact source

Best regards,

Martin

• Jaki T, Pallmann P, Wolfsegger MJ. (2013). Estimation in AB/BA crossover trials with application to bioequivalence studies with incomplete and complete data designs. Statistics in Medicine, 32(30):5469-5483
  
• Jaki T and Wolfsegger MJ (2012). Non-compartmental estimation of pharmacokinetic parameters for fexible sampling designs. Statistics in Medicine, 31(11-12):1059-1073.
  
• Jaki T and Wolfsegger MJ (2011). Estimation of pharmacokinetic parameters with the R package PK. Pharmaceutical Statistics, 10(3):284-288.
  
• Jaki T, Wolfsegger MJ, Lawo J-P (2010). Establishing bioequivalence in complete and incomplete data designs using AUCs. Journal of Biopharmaceutical Statistics, 20(4):803-820.
  
• Wolfsegger MJ and Jaki T (2009). Assessing systemic drug exposure in repeated dose toxicity studies in the case of complete and incomplete sampling. Biometrical Journal, 51(6):1017-1029.
  
• Wolfsegger MJ and Jaki T (2009). Non-compartmental estimation of pharmacokinetic parameters in serial sampling designs. Journal of Pharmacokinetics and Pharmacodynamics, 36(5):479-494.
  
• Jaki T and Wolfsegger MJ (2009). A theoretical framework for estimation of AUCs in complete and incomplete sampling designs. Statistics in Biopharmaceutical Research, 1(2):176-184.
  
• Jaki T, Wolfsegger MJ, Ploner M (2009). Confidence intervals for ratios of AUCs in the case of serial sampling: A comparison of seven methods. Pharmaceutical Statistics, 8(1):12-24.