# DDMODEL00000113: Russu_2009_dose_escalation_loglog

Short description:
Population approaches to the analysis of dose escalation studies: a log-log model
 Format: PharmML 0.8.x (0.8.1) Related Publication: .hiddenContent {display:none;} Dose escalation studies: a comparison among Bayesian models Russu A., De Nicolao G, Poggesi I, Gomeni R. PAGE. Abstracts of the Annual Meeting of the Population Approach Group in Europe, 6/2009, Volume 10, pages: 1610 Affiliation: (1) Department of Computer Engineering and Systems Science, University of Pavia, Pavia, Italy; (2) GlaxoSmithKline, Clinical Pharmacology/Modelling & Simulation, Verona, Italy Abstract: Objectives: To apply alternative Bayesian models for the population analysis of the dose-exposure 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 [1,2,3]. 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 dose-exposure relationship was explored using a log-linear model (i.e. a linear model in log-log scale), a power model, an Emax model, and a nonparametric model based on population smoothing splines [4]. 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 log-linear 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 cross-check 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 dose-exposure relationships overcoming possible misspecification problems. Moreover, population splines may represent an appealing first-try, especially in early escalation stages, when there is not enough information to support a specific parametric model. Contributors: 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 dose-exposure 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 dose-exposure relationship was explored using a log-linear model (i.e. a linear model in log-log 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 log-linear 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 cross-check 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 dose-exposure relationships overcoming possible misspecification problems. Moreover, population splines may represent an appealing first-try, 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);
 Validation Status: Annotations are correct. Certification Comment: This model is not certified.
• Model owner: Paolo Magni
• Submitted: Dec 13, 2015 10:40:34 PM
##### Revisions
• Version: 11
• Submitted on: Oct 13, 2016 6:46:21 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.
• Version: 8
• Submitted on: Jul 16, 2016 4:09:10 PM
• Submitted by: Paolo Magni
• With comment: Updated model annotations.
• Version: 4
• Submitted on: Dec 13, 2015 10:40:34 PM
• Submitted by: Paolo Magni
• With comment: Edited model metadata online.

### Name

Generated from MDL. MOG ID: russu_log_log_mog

 DOSE

### Function Definitions

 $\mathrm{additiveError}:\mathrm{real}\left(\mathrm{additive}:\mathrm{real}\right)=\mathrm{additive}$

### Covariate Model: $\mathrm{cm}$

#### Continuous Covariates

$\mathrm{DMIN}$

### Parameter Model: $\mathrm{pm}$

#### Random Variables

${\mathrm{ETA_1}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_1}\right)$
${\mathrm{ETA_2}}_{\mathrm{vm_mdl.ID}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=\mathrm{pm.OMEGA_2}\right)$
${\mathrm{EPS_1}}_{\mathrm{vm_err.DV}}~\mathrm{Normal2}\left(\mathrm{mean}=0,\mathrm{var}=1\right)$

#### Population Parameters

$\mathrm{MU_THETA1}=0$
$\mathrm{MU_THETA2}=0$
$\mathrm{VAR_THETA1}=10.0$
$\mathrm{VAR_THETA2}=10.0$
$\mathrm{a_1}=1$
$\mathrm{b_1}=0.1295486$
$\mathrm{a_2}=1$
$\mathrm{b_2}=0.1027284$
$\mathrm{a_sigma}=1$
$\mathrm{b_sigma}=0.001$
${\mathrm{THETA1}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Normal2}\left(\mathrm{mean}=\mathrm{pm.MU_THETA1},\mathrm{var}=\mathrm{pm.VAR_THETA1}\right)$
${\mathrm{THETA2}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Normal2}\left(\mathrm{mean}=\mathrm{pm.MU_THETA2},\mathrm{var}=\mathrm{pm.VAR_THETA2}\right)$
${\mathrm{invOMEGA_1}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Gamma2}\left(\mathrm{shape}=\mathrm{pm.a_1},\mathrm{rate}=\mathrm{pm.b_1}\right)$
${\mathrm{invOMEGA_2}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Gamma2}\left(\mathrm{shape}=\mathrm{pm.a_2},\mathrm{rate}=\mathrm{pm.b_2}\right)$
${\mathrm{invSIGMA2}}_{\mathrm{vm_mdl.MDL__prior}}~\mathrm{Gamma2}\left(\mathrm{shape}=\mathrm{pm.a_sigma},\mathrm{rate}=\mathrm{pm.b_sigma}\right)$
$\mathrm{OMEGA_1}=\frac{1}{\mathrm{pm.invOMEGA_1}}$
$\mathrm{OMEGA_2}=\frac{1}{\mathrm{pm.invOMEGA_2}}$
$\mathrm{SIGMA_1}=\sqrt{\frac{1}{\mathrm{pm.invSIGMA2}}}$

#### 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

$C={e}^{\left(\mathrm{pm.ALPHA}+\mathrm{pm.BETA}\cdot \mathrm{ln}\left(\frac{\mathrm{DOSE}}{\mathrm{cm.DMIN}}\right)\right)}$

### Observation Model: $\mathrm{om1}$

#### Continuous Observation

$\mathrm{ln}\left(Y\right)=\mathrm{ln}\left(\mathrm{sm.C}\right)+\mathrm{additiveError}\left(\mathrm{additive}=\mathrm{pm.SIGMA_1}\right)+\mathrm{pm.EPS_1}$

## External Dataset

 OID $\mathrm{nm_ds}$ Tool Format NONMEM

### File Specification

 Format $\mathrm{csv}$ Delimiter comma File Location Simulated_russu_2009_log_log_data.csv

### Column Definitions

Column ID Position Column Type Value Type
$\mathrm{ID}$
$1$
$\mathrm{id}$
$\mathrm{int}$
$\mathrm{DOSE}$
$2$
$\mathrm{idv}$
$\mathrm{real}$
$\mathrm{DV}$
$3$
$\mathrm{dv}$
$\mathrm{real}$
$\mathrm{DMIN}$
$4$
$\mathrm{covariate}$
$\mathrm{real}$

### Column Mappings

Column Ref Modelling Mapping
$ID$
$\mathrm{vm_mdl.ID}$
$DOSE$
$\mathrm{DOSE}$
$DV$
$\mathrm{om1.Y}$
$DMIN$
$\mathrm{cm.DMIN}$

## 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.invSIGMA2
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
$8000$
niter
$20000$
winbugsgui
$\text{false}$

## Step Dependencies

Step OID Preceding Steps
$\mathrm{estimStep_1}$