Population PK model
The population analysis for oxypurinol PK was conducted using the nonlinear mixed effects modeling program, NONMEM version 7.4 (ICON Development Solutions, LC, Ellicott City, MD) with the first order conditional estimation method with interaction. Exploratory analyses and diagnostic plots were performed with R and Perl-speaks-NONMEM (PsN) version 5.2.6.35 One and two compartmental PK models with linear elimination and first-order absorption models with and without a time lag were explored. Model derived values of the combined absorption and formation rate constant (Kfm ), apparent clearance (CL/fm ) and apparent volume (V/fm ) for oxypurinol were estimated, wherefm represents the fraction of allopurinol dose available as oxypurinol systemically.
The between subject variability (BSV) was assumed to follow a log-normal distribution, described as follow:
\begin{equation} \theta_{\text{ip}}=\theta_{\text{µp}}\exp{(\eta_{\text{ip}})}\nonumber \\ \end{equation}
where \(\theta_{\text{ip}}\) is the \(p^{\text{th}}\) model parameter\(\theta\) for the \(i^{\text{th}}\) individual; \(\theta_{\text{µp}}\)is the population mean of the \(p^{\text{th}}\) model parameter\(\theta\); and \(\eta_{\text{ip}}\) is a random variable that represents the deviation from the mean of the \(p^{\text{th}}\)parameter for the \(i^{\text{th}}\) individual; the collection of\(\eta_{\text{ip}}\) are assumed to have a mean of zero and variance\(\omega^{2}\). The variance \(\omega^{2}\) of BSV was calculated as a percentage of coefficient of variation (%CV) using the following equation:
\begin{equation} \text{CV}\left(\%\right)=\sqrt{\exp\left(\omega^{2}\right)-1}\times 100\%\nonumber \\ \end{equation}
The residual unexplained error (RUV) including additive, proportional, and combined errors were tested.