Transcript Diapositive 1

Modeling of Longitudinal Tumor Size Data
in Clinical Oncology Studies of Drugs in Combination
#1355
N. Frances1, L. Claret2, F. Schaedeli Stark3, R. Bruno2, A. Iliadis1
1School of Pharmacy, University Méditerranée, Marseille, France;
2Pharsight Corp., Mountain View, USA; 3Hoffman-La Roche, Basel, Switzerland
Data presentation
ABSTRACT
Retrospective analysis :
 2 drugs in metastatic breast cancer
 Elaborate the best model (parsimonious principle) fitting
the longitudinal tumor size data on :
 Single agent data
 Combination data
• Docetaxel (D)
• Capecitabine (C)
 PD-data : observed tumor burden
• sum of the longest diameter of metastatic sites measured
(dependent variable in NONMEM)
 3 studies [1, 2, 3] :
 # 14697 : phase II data on C ( n  112 )
 # 15542 : phase II data on C ( n  56 )
 # 14999 : phase III data on C+D ( n  222 ) vs. D ( n  223 )
 Data already treated by a different growth model [4, 5]
KL
KEC
KED
R
 Is this model able to describe the contribution of each
drug in the combination data ?
 Can a drug interaction term be estimated ?
 What is the minimum number of patients in a study to
obtain a good enough estimation of the model parameters ?
 e.g. in a prospective Phase Ib or Phase II study
n0
0.008
0.008
0.008
0.008
0.002
0.002
0.002
0.002
KL
100
40
50
60
0
Patient ID n° 30
Patient ID n° 74
50
50
0.0012
0.0012
0.0012
35
60
0.0012
30
30
40
20
0.0004
0.0004
0
2
2
30
0
10
20
120
30
40
0
0.5
0.5
Tumor
size
(mm)
0.12
0.12
100
60
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80
40
60
R
0.04
15
5
0
5
10
15
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25
0
10
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0
Patient ID n° 122
40
100
40
30
80
20
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50
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100
0.002
0.008
100
0.0004
0.0012
100
0.5
2
10
0.04
0
0.12
120
Patient ID n° 147
50
60
300
n0
1. Choose a model
• Proliferation Gompertz vs. exponential
• Resistance term
• Dynamical dose model
• Estimation of the initial condition
• Residual variability
• Define bounds in the parameters
300
0
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0.04
100
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Patient ID n° 91
20
80
300
15
10
50
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25
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5
30
Patient ID n° 88
70
0
0.12
20
Patient ID n° 87
0.5
0.12
10
80
2
100
0.5
20
25
0.0004
0
KED
2
0.0004
Patient ID n° 85
80
40
KEC
Introduction : The analysis of tumor size measurements, obtained in clinical
studies involving combination chemotherapy, remains an open modeling
problem. We used retrospective clinical data in metastatic breast cancer in
order to investigate whether the contribution to the anti-tumor effect of each
compound in a combination setting can be estimated 1) from single agent data
and combination data with or without single agent data, and 2) from datasets
with a limited number of patients .
Methods : Data concerning tumor size measurements and treatments
characteristics were available for docetaxel (D, n=223), capecitabine (C,
n=168) [1, 2] given as single agents and their combination (D+C, n=222) [3].
The developed model is an extension of already presented disturbed growth
models [4, 5] and it is based on the following hypotheses: 1) Tumor growth is
exponential or Gompertz; 2) K-PD model describes administration protocols; 3)
Resistance is materialized by exponential decline of cell-kill rate; 4) Drugs are
combined either in a linear, or Emax, or Weibull model involving a drug
interaction term. Population analyses were performed using NONMEM Version
6 within a MATLAB environment. The models were validated using posterior
predictive checks.
Results : In the developed models, over-parameterization was the most
frequent problem. K-PD models involve only one parameter expressing the
dynamics of drug amounts in the cell-kill rate formulation. This parameter was
obtained for D and C from the single agent studies and was fixed in the
analysis using the combination data only. When using the combination data
only, the contribution of each drug to the anti-tumor effect was accurately
estimated and the estimates were consistent with those obtained using singleagent data. The effect of the 2 drugs was found to be additive with no drug
interaction term. Situation #2 is still under investigation.
Conclusion : Using combination data, the tumor size dynamic model
parameters were successfully estimated. Further investigations are in progress
for assessing the minimum required extent and type of clinical data for
evaluating drug combinations in oncology. This model will be part of a modeling
framework to simulate expected clinical response of new compounds and to
support end-of-phase II decisions and design of phase III studies [6].
Objectives
100 200 300
0
5
10
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Patient ID n° 153
60
0
Figure 1. Dispersion plots and histograms
10
20
30
40
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Time (weeks)
Figure 2. Individual fits
For 9 patients from the phase III combination study (C+D),
observed tumor size data (o) and model predictions vs. time :
Final model
Non
usable
models
• population ( - - - ),
dy1 t 
  KBC  y1 t   u1 t 
dt
dy2 t 
  KBD  y2 t   u2 t 
dt

dnt  
  
  KL  exp  R  t   ln 
  KEC  y1 t   KED  y2 t   nt 
dt
 nt  


2. Define the KB values in the dose model
• Studies on single agent data
Phase II-C (14697+15542)
Phase III-D (14999)
• Validation on the combination (C+D) data
• individual (
Remove the variability
added by individual designs
Model explanations
 y1 t  , y2 t  g 

: “Effective dose” for C and D respectively
 u1 t  , u 2 t  g .w
mm 
 nt 
• Covariance matrix of estimates
• Parameter variability (Omega)
• Residual error (Sigma)
Actual data
(drug combination)
 : Administration protocols for C and D respectively
« Posterior Predictive Check » on
( at the first visit t1 )
ratio  nt1  n0
: Tumor size
w 
 KB _
3. Modeling tests : Phase III-(C+D) 14999
1
-1
)
-1
: K-PD elimination constants (already evaluated on single agent data)
NONMEM
Intra- and inter-patient variability
Posthoc estimated
parameters n=222
Random drawn
parameters n=1000
Reference design
Reference design
« Observed » ratio
(from actual data)
Predicted ratio
 Estimated parameters :
w  : Proliferation parameter (max tumor size :   1000 mm, fixed)
w  : Resistance parameter, common to both drugs
g .w  : Constant cell kill rate (efficacy parameter), distinct for each drug
• KL
-1
-1
•R
1
-1
• KE _
mm 
• n0
: Initial tumor size
Numerical results
pdf(ratio)
Fixed effects :
Validate
d
models
KL
KEC
KED
R
n0
1.69 E  3 1.69 E  3 1.82 E  1 4.51E  2 5.54e  1
s.e.m. 7.38E  4 3.15E  4 3.58E  2 1.14 E  2
Figure 3a. Flow chart for Posterior Predictive Check
2.52
Random effects are log-normal distributed :
KL
KEC
KED
R
n0
5
5.09 E  1 9.51E  1 6.75E  1 1.77 E  1 4.19 E  1
Residual error is proportional :
4. Comparison between retained models
Objective function :
• Objective function
• Residual error
pdf
6.64 %
(>100 models tested)
6334.56
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KEC
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Final model
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Design ID n° 333
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Tumor size ratio
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Tumor size ratio
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For 4 typical designs, predicted ratio from :
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0.03
Flow chart for model development
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Design ID n° 425
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Probability density functions of the ratio : nt1  n0
R
5
Dispersion plots and histograms (Figure 1)
Individual fits (Figure 2)
“Posterior Predictive Check” (Figure 3a, b)
Minimum number of patients (Figure 4)
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Figure 3b. Posterior Predictive Check
0.001 0.002 0.003
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•
•
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•
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0.06
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5. Ultimate validation
1.5
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Design ID n° 487
0.08
pdf
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Design ID n° 172
• posthoc estimated parameters (
• randomly drawn parameters (
0.02
n  222 ) and
, n  1000 )
,
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Conclusion
Figure 4. Minimum number of patients
• The model is built from Phase III data :
(Probability density functions of model parameters)
• two drugs (D+C) in combination,
Samples were obtained from 100 random permutations of the 222
patients data in the phase III combination study.
• 50-patients tailed samples (
) and
• 70-patients tailed samples (
).
Covariance matrix obtained : 26/100 with 50 patients and 38/100 with
70 patients.
• resistance parameter common to both drugs and acting by
increasing proliferation term (selection of resistant cells by the
treatment),
• interaction term not estimated (assumes additive effects).
• This model can be used to predict therapy efficacy in a future
clinical trial [6] :
References:
[1] Blum JL, Jones SE, Buzdar AU, et al: Multicenter Phase II Study of Capecitabine in Paclitaxel-Refractory Metastatic Breast Cancer. J. Clin. Oncol. 17: 485-493, 1999.
[2] Blum JL, Dieras V, Mucci Lo Russo P, et al: Multicenter, phase II study of capecitabine in taxane pretreated metastatic breast carcinoma patients, Cancer 92:1759-1768, 2001.
[3] O’Shaughnessy J, Miles D, Vukelja S et al. Superior survival with capecitabine plus docetaxel combination therapy in anthracycline-pretreated patients with advanced breast cancer:
Phase III trial results. J. Clin. Oncol. 12: 2812-2823, 2002.
[4] Iliadis A, Barbolosi D: Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Comput. Biomed. Res. 33:211-226, 2000.
[5] Claret L, Girard P, Zuideveld KP, et al: A longitudinal model for tumor size measurements in clinical oncology studies. PAGE 15 (abstract 1004), 2006a [www.pagemeeting.org/?abstract=1004].
[6] Claret L, Girard P, O'Shaughnessy J et al: Model-based predictions of expected anti-tumor response and survival in phase III studies based on phase II data of an investigational
agent. Proc. Am. Soc. Clin. Oncol, 24, 307s (abstract 6025), 2006b.
• using Bayesian approach,
• a minimum number of patient seems to be necessary, but
small sample sizes typical to those in early clinical studies (e.g.
50 patients) may be enough,
• instead of K-PD, a PK-PD model would supply consistent
information.