DDMODEL00000114: Russu_2009_dose_escalation_Emax
Short description:
Population approaches to the analysis of dose escalation studies: Emax model
PharmML 0.8.x (0.8.1) 



Paolo Magni

Context of model development:  Dose & Schedule Selection and Label Recommendation; 
Model compliance with original publication:  Yes; 
Model implementation requiring submitter’s additional knowledge:  No; 
Modelling context description:  Objectives: To apply alternative Bayesian models for the population analysis of the doseexposure relationship in dose escalation Phase I studies. In these studies, subjects receive increasing dose levels and, at each dose escalation, a decision is made on the next dose level to be administered, based on safety/tolerability constraints. In recent years there has been a growing interest in Bayesian methods applied to such experiments In the present work, the performance of four alternative Bayesian models was evaluated on real and simulated datasets and a model comparison procedure was developed for the identification of the most appropriate model. Methods: The doseexposure relationship was explored using a loglinear model (i.e. a linear model in loglog scale), a power model, an Emax model, and a nonparametric model based on population smoothing splines . In all cases, a Bayesian population approach was adopted. The parametric models were estimated using WinBUGS 1.4.3. Sum of squared residuals, predictive root mean square error, AIC and BIC were used as model comparison criteria. Results: Ten phase I dose escalation studies and 60 simulated datasets (generated with the three parametric models) were analyzed. In the experimental datasets, the power and loglinear models provided comparable results in terms of point estimates and credibility intervals, whereas the Emax model proved inadequate when data showed upward curvature. The population spline approach provided good results for both experimental and simulated datasets. In the former case, the goodness of fit was comparable to parametric models. In the simulated benchmark, population splines performed comparably to the true models used to generate the data. The proposed comparison approach correctly identified the true parametric model in most cases. Conclusions: A thorough model comparison procedure was developed, based on model complexity criteria and crossvalidatory techniques. Applying several criteria represents a useful crosscheck when one is faced with the problem of finding the most adequate model. It has been shown that the parallel estimation of four models (three parametric, one nonparametric), complemented with model comparison criteria, can robustly handle a variety of doseexposure relationships overcoming possible misspecification problems. Moreover, population splines may represent an appealing firsttry, especially in early escalation stages, when there is not enough information to support a specific parametric model.; 
Modelling task in scope:  estimation; 
Nature of research:  Early clinical development (Phases I and II); 
Annotations are correct. 

This model is not certified. 
 Model owner: Paolo Magni
 Submitted: Dec 13, 2015 10:44:47 PM
 Last Modified: Oct 13, 2016 7:05:32 PM
Revisions

Version: 10
 Submitted on: Oct 13, 2016 7:05:32 PM
 Submitted by: Paolo Magni
 With comment: Edited model metadata online.

Version: 7
 Submitted on: Jul 16, 2016 3:59:51 PM
 Submitted by: Paolo Magni
 With comment: Updated model annotations.

Version: 4
 Submitted on: Dec 13, 2015 10:44:47 PM
 Submitted by: Paolo Magni
 With comment: Edited model metadata online.
Name
Generated from MDL. MOG ID: russu_Emax_mog
Independent Variables

Function Definitions
$\mathrm{proportionalError}:\mathrm{real}\left(\mathrm{proportional}:\mathrm{real},f:\mathrm{real}\right)=\mathrm{proportional}\cdot f$

Parameter Model: $\mathrm{pm}$
Random Variables
${\mathrm{ETA\_1}}_{\mathrm{vm\_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA\_1}\right)$
${\mathrm{ETA\_2}}_{\mathrm{vm\_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA\_2}\right)$
${\mathrm{EPS}}_{\mathrm{vm\_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=1\right)$
Population Parameters
$\mathrm{MU\_THETA1}=4.481375$
$\mathrm{MU\_THETA2}=1.54563$
$\mathrm{VAR\_THETA1}={2.148283}^{2}$
$\mathrm{VAR\_THETA2}={2.148283}^{2}$
$\mathrm{a\_1}=1$
$\mathrm{b\_1}=0.0262989$
$\mathrm{a\_2}=1$
$\mathrm{b\_2}=0.1021269$
$\mathrm{a\_cv}=1$
$\mathrm{b\_cv}=1$
${\mathrm{THETA1}}_{\mathrm{vm\_mdl.MDL\_\_prior}}~\mathrm{Normal2}\left(\mathrm{mean}=\mathrm{pm.MU\_THETA1},\mathrm{var}=\mathrm{pm.VAR\_THETA1}\right)$
${\mathrm{THETA2}}_{\mathrm{vm\_mdl.MDL\_\_prior}}~\mathrm{Normal2}\left(\mathrm{mean}=\mathrm{pm.MU\_THETA2},\mathrm{var}=\mathrm{pm.VAR\_THETA2}\right)$
${\mathrm{invOMEGA\_1}}_{\mathrm{vm\_mdl.MDL\_\_prior}}~\mathrm{Gamma2}\left(\mathrm{shape}=\mathrm{pm.a\_1},\mathrm{rate}=\mathrm{pm.b\_1}\right)$
${\mathrm{invOMEGA\_2}}_{\mathrm{vm\_mdl.MDL\_\_prior}}~\mathrm{Gamma2}\left(\mathrm{shape}=\mathrm{pm.a\_2},\mathrm{rate}=\mathrm{pm.b\_2}\right)$
${\mathrm{invCV2}}_{\mathrm{vm\_mdl.MDL\_\_prior}}~\mathrm{Gamma2}\left(\mathrm{shape}=\mathrm{pm.a\_cv},\mathrm{rate}=\mathrm{pm.b\_cv}\right)$
$\mathrm{OMEGA\_1}=\frac{1}{\mathrm{pm.invOMEGA\_1}}$
$\mathrm{OMEGA\_2}=\frac{1}{\mathrm{pm.invOMEGA\_2}}$
$\mathrm{CV}=\sqrt{\frac{1}{\mathrm{pm.invCV2}}}$
Individual Parameters
$\mathrm{ALPHA}=\mathrm{pm.THETA1}+\mathrm{pm.ETA\_1}$
$\mathrm{BETA}=\mathrm{pm.THETA2}+\mathrm{pm.ETA\_2}$
Structural Model: $\mathrm{sm}$
Variables
$C=\frac{{e}^{\mathrm{pm.ALPHA}}\cdot T}{\left({e}^{\mathrm{pm.BETA}}+T\right)}$
Observation Model: $\mathrm{om1}$
Continuous Observation
$Y=\mathrm{sm.C}+\mathrm{proportionalError}\left(\mathrm{proportional}=\mathrm{pm.CV},f=\mathrm{sm.C}\right)+\mathrm{pm.EPS}$
External Dataset
OID

$\mathrm{nm\_ds}$

Tool Format

NONMEM

File Specification
Format

$\mathrm{csv}$

Delimiter

comma

File Location

Simulated_russu_2009_emax_data.csv

Column Definitions
Column ID  Position  Column Type  Value Type 

$\mathrm{ID}$ 
$1$

$\mathrm{id}$

$\mathrm{int}$

$\mathrm{DOSE}$ 
$2$

$\mathrm{idv}$

$\mathrm{real}$

$\mathrm{DV}$ 
$3$

$\mathrm{dv}$

$\mathrm{real}$

Column Mappings
Column Ref  Modelling Mapping 

$\mathrm{ID}$ 
$\mathrm{vm\_mdl.ID}$ 
$\mathrm{DOSE}$ 
$T$ 
$\mathrm{DV}$ 
$\mathrm{om1.Y}$ 
Estimation Step
OID

$\mathrm{estimStep\_1}$

Dataset Reference

$\mathrm{nm\_ds}$

Parameters To Estimate
Parameter  Initial Value  Fixed?  Limits 

pm.THETA1 
false

$\left(,\right)$


pm.THETA2 
false

$\left(,\right)$


pm.invOMEGA_1 
false

$\left(,\right)$


pm.invOMEGA_2 
false

$\left(,\right)$


pm.invCV2 
false

$\left(,\right)$

Operations
Operation: $1$
Op Type

generic

Operation Properties
Name  Value 

algo

$\text{mcmc}$

Operation: $2$
Op Type

BUGS

Operation Properties
Name  Value 

nchains

$1$

burnin

$1000$

niter

$5000$

winbugsgui

$\text{false}$

Step Dependencies
Step OID  Preceding Steps 

$\mathrm{estimStep\_1}$
