Difference between revisions of "Overview"

Revision as of 17:19, 25 January 2013

Data: concentrations at times $0, 1, \ldots 15$, from 6 patients who received each 100 mg at time $t=0$ (bolus intravenous):

Goal of modelling: describe the variability of the data (structural, intra $\&$ inter variabilities) using a statistical model.

Classical individual approach: derive a model for a unique individual:

\href{intro2}{More details} %\href{run:/individualModel.pdf}{More details}

\begin{itemize} * Predicted concentration at time '"`UNIQ-MathJax4-QINU`"': \begin{equation} f(t ; V,k) = \frac{D}{V} \ e^{-k \, t} \end{equation}

\begin{equation} y_j = f(t_j ; V,k) + \varepsilon_j \end{equation}

Observed concentrations from individual 1 and predicted concentration profile obtained with $V=10.5$ and $k=0.279$:

@@ Line 5: / Line 5: @@
-Goal of modelling: describe the variability of the data (structural, intra \& inter variabilities) using a {\it statistical model}.
+Goal of modelling: describe the variability of the data (structural, intra $\&$ inter variabilities) using a ''statistical model''.
-Classical {\it individual approach}:  derive a model for a unique individual:
+Classical ''individual approach'':  derive a model for a unique individual:
 \href{intro2}{More details}
@@ Line 14: / Line 14: @@
 \begin{itemize}
-\item Predicted concentration at time $t$:
+* Predicted concentration at time $t$:
-$$f(t ; V,k) = \frac{D}{V} \ e^{-k \, t}$$
+\begin{equation}
-\item Observed concentration at time $t_j$, $j=1, 2, \ldots, 15$:
+f(t ; V,k) = \frac{D}{V} \ e^{-k \, t}
-$$ y_j = f(t_j ; V,k) + \varepsilon_j $$
+\end{equation}
-\end{itemize}
+* Observed concentration at time $t_j$, $j=1, 2, \ldots, 15$:
+\begin{equation}
+y_j = f(t_j ; V,k) + \varepsilon_j
+\end{equation}
 Observed concentrations from individual 1 and predicted concentration profile obtained with $V=10.5$ and $k=0.279$:
-\begin{figure}[!ht]
-\begin{centering}
+[[Image:intro2.png]]
- \includegraphics[width=15cm]{introduction/intro2.png}
-\label{fig:intro2}
-\end{centering}
-\end{figure}