Model description
In this Expo, we will fit models to the percent FXa inhibition as a direct effect of drug concentration. The models will differ with respect to the random effects distribution (uncorrelated and correlated), parameterization (centered and non-centered), and whether additional covariates are included to explain interindividual variability in the model parameters.
The basic statistical model will be:
\[\begin{align*} Y_{ij} &\sim N(\mu_{ij}, \sigma) \\ \mu_{ij} &= \text{e0}_i + \frac{(\text{Emax}-e0_i) \cdot C_{ij}^\gamma}{\text{EC50}_i^\gamma + C_{ij}^\gamma} \end{align*}\]
where \(i=1, \dots, n\) indexes individuals and \(j\) indexes observation within an individual.
The parameters are subject specific and (possibly conditional on covariates) are assumed to follow a normal distribution in the population:
\[\begin{align*} \{\text{e0}_i, \log \text{EC50}_i \}^T & \sim N(\{ \text{tv\_e0},\text{tv\_log\_ec50} \}^T, \boldsymbol{\Omega}) \end{align*}\]
where \(\boldsymbol{\Omega}\) is the variance-covariance matrix of the parameters.
The primary way the models differ will be in the structure of \(\boldsymbol{\Omega}\) and how the models for the inter-subject parameters are coded.