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The analytical solution for multi-compartment models with a non-zero initial condition is complex because of the inter-compartmental transfer. An elegant solution and its implementation in the ‘wnl' R package can be useful in solving examples of textbooks and developing software of therapeutic drug monitoring, pharmacokinetic simulation, and parameter estimation. This solution uses Laplace transformation, convolution, matrix inversion, and the fact that the general solution of an inhomogeneous ordinary differential equation is the sum of a homogenous and a particular solution, together.
Drug Monitoring

The first-order conditional estimation (FOCE) method is more complex than the first-order (FO) approximation method because it estimates the empirical Bayes estimate (EBE) for each iteration. By contrast, it is a further approximation of the Laplacian (LAPL) method, which uses second-order expansion terms. FOCE without INTERACTION can only be used for an additive error model, while FOCE with INTERACTION (FOCEI) can be used for any error model. The formula for FOCE without INTERACTION can be derived directly from the extension of the FO method, while the FOCE with INTERACTION method is a slight simplification of the LAPL method. Detailed formulas and R scripts are presented here for the reproduction of objective function values by NONMEM.
Bays ; Methods ; Reproduction*

SAS® is commonly used for bioequivalence (BE) data analysis. R is a free and open software for general purpose data analysis, and is less frequently used than SAS® for BE data analysis. This tutorial explains how R can be used for BE data analysis to generate comparable results with SAS® . The main SAS® procedures for BE data analysis are PROC GLM and PROC MIXED, and the corresponding R main packages are “sasLM” and “nlme” respectively. For fixed effects only or balanced data, the SAS® PROC GLM and R “sasLM” provide good estimates; however, for a mixed-effects model with unbalanced data, the SAS® PROC MIXED and R “nlme” are better for providing estimates without bias. The SAS® and R scripts are provided for convenience.

SAS® is commonly used for bioequivalence (BE) data analysis. R is a free and open software for general purpose data analysis, and is less frequently used than SAS® for BE data analysis. This tutorial explains how R can be used for BE data analysis to generate comparable results with SAS® . The main SAS® procedures for BE data analysis are PROC GLM and PROC MIXED, and the corresponding R main packages are “sasLM” and “nlme” respectively. For fixed effects only or balanced data, the SAS® PROC GLM and R “sasLM” provide good estimates; however, for a mixed-effects model with unbalanced data, the SAS® PROC MIXED and R “nlme” are better for providing estimates without bias. The SAS® and R scripts are provided for convenience.

In healthcare situations, time-to-event (TTE) data are common outcomes. A parametric approach is often employed to handle TTE data because it is possible to easily visualize different scenarios via simulation. Not all pharmacometricians are familiar with the use of non-linear mixed effects models (NONMEMs) to deal with TTE data. Therefore, this tutorial simply explains how to analyze TTE data using NONMEM. We show how to write the code and evaluate the model. We also provide an example of a hands-on model for training.

Analysis of a 2 × 2 table for clinical data involves computing the point estimate and confidence interval for risk difference, relative risk, or odds ratio. While point estimates of these comparative parameters are uniquely defined, several statistical methods have been proposed to estimate the confidence interval for each parameter. The Miettinen-Nurminen (MN) score method is expected to be used increasingly over traditional interval estimation methods. The MN score method has not been previously implemented in R software for data with stratification. There is a need for a comprehensive software implementation of the MN score method. This article describes the implementation of the MN score method in the sasLM R software package. To demonstrate the usage of the sasLM functions introduced, recently published clinical data are provided as examples.

BACKGROUND: Aquafol(R) is a microemulsion formulation of propofol. This study was designed to investigate the population pharmacokinetic and pharmacodynamic modeling in beagle dogs sedated by Aquafol(R). METHODS: Electroencephalogram was recorded and venous blood was sampled at preset times in 15 beagle dogs during 3 hours of infusion of Aquafol(R) and subsequently during 3 hours of recovery. Venous blood was sampled at 0, 2, 10, 30, 60, 120, 180, 190, 240 and 360 minutes after infusion. We evaluated the effect of propofol on electroencephalogram by calculating SEF(90). In the preliminary analysis, two compartment model best described all data from all subjects. The pharmacodynamics were best described using an effect compartment model and k(e0), a first-order elimination rate constant characterizing the effect-site equivalent to estimate the apparent effect-site concentrations. The relationship between propofol effect-site concentration and SEF90 was analyzed using an inhibitory sigmoid E(max) model. RESULTS: The final pharmacokinetic model was best described with the followings: V(1) = 18.5e(0.114*BWT), k(10) = 1.86 min(-1), k(12) = 0.6 min(-1), k(21) = 0.684 min(-1). The final pharmacodynamic model was best described with the followings: t(1/2)k(e0) = 0.62 min, C(e50) = 32.2 ng/ml, E(o) = 31.3 Hz, E(max) = 20.9 Hz, gamma = 1.28. CONCLUSIONS: The propofol microemulsion shows different pharmacokinetics and pharmacodynamics compared with the propofol lipid emulsion.
Animals ; Colon, Sigmoid ; Dogs* ; Electroencephalography ; Pharmacokinetics ; Propofol*

Drunk driving is a serious social problem. We estimated the blood alcohol concentration of a defendant on the request of local prosecutor's office in Korea. Based on the defendant's history, and a previously constructed pharmacokinetic model for alcohol, we estimated the possible alcohol concentration over time during his driving using a Bayesian method implemented in NONMEM®. To ensure generalizability and to take the parameter uncertainty of the alcohol pharmacokinetic models into account, a non-parametric bootstrap with 1,000 replicates was applied to the Bayesian estimations. The current analysis enabled the prediction of the defendant's possible blood alcohol concentrations over time with a 95% prediction interval. The results showed a high probability that the alcohol concentration was ≥ 0.05% during driving. The current estimation of the alcohol concentration during driving by the Bayesian method could be used as scientific evidence during court trials.
Bayes Theorem ; Blood Alcohol Content ; Driving Under the Influence ; Forensic Sciences* ; Korea ; Pharmacology, Clinical* ; Social Problems ; Uncertainty