Modelingand Simulations Relating Overall Survivalto Tumor Growth InhibitioninRenal Cell Carcinoma Patients

Authors:Laurent Claret, PhD1,Francois Mercier, PhD2, Brett E. Houk, PhD3, Peter A. Milligan, PhD4, Rene Bruno, PhD1

1 Pharsight Consulting Services, Pharsight, a CertaraTM Company, Marseille, France

2 Pharsight Consulting Services, Pharsight, a CertaraTM Company, Wintzenheim, France now with Roche, pRED, Basel, Switzerland.

3Pfizer Clinical Pharmacology, La Jolla, CA, USA

4Pfizer Pharmacometrics, Global Clinical Pharmacology, Sandwich, UK

Corresponding author: Rene Bruno

84 Chemin des Grives

13013 Marseille, France

Tel/Fax: 33 (0) 4-91-42-7397

Email:

Key words: Renal cell carcinoma, overall survival, tumor growth inhibition,predictive model

Supplementary Material

Longitudinal Tumor Size Model Equations

The sum of longest diameters (SLD) were modeled using three longitudinal tumor growth inhibition models.

-Stein [21] as implemented in Ref 22

Where y is the sum of longest diameters (SLD) of target lesions; Y0 is the baseline tumor size; D is the rate of tumor shrinkage (1/time unit); G is growth rate (1/time unit).

-Wang model [23]

Where SR is the rate of tumor shrinkage (1/time unit); PR is a zero order growth rate (SLD unit/time unit).

-Simplified TGI model [22]

Where KL is growth rate (1/time unit); KD is the rate of tumor shrinkage (1/time unit) that decreases exponentially at a rate λ (1/time unit).

Supplementary Table 1sTGI model parameter estimates

Parameter / Estimate (CV%) / ?2(Sh%) / ?(KL, KD) (corr)
Y0 (cm) / 10.1 (0.164) / 0.662 (4.33)
KL (week-1) / 3.74x10-3 (6.64) / 1.42 (34.6) / 0.108 (0.103)
KD (week-1) / 2.42x10-2 (4.30) / 0.766 (31.6)
(week-1) / 9.22x10-2 (8.35) / 1.15 (45.6)
s2(cm2) / 0.996 (0.830) / -

CV: coefficient of variation, ?2: inter-individual variance, Sh: shrinkage,

corr: correlation coefficient, Y0: baseline tumor size, KL: growth rate, KD: kill rate,

: resistance appearance rate, s: standard deviation of additive residual error

Supplementary Table 2 Stein model parameter estimates

Parameter / Estimate (CV%) / ?2(Sh%) / ?(D, G) (corr)
Y0 (cm) / 9.80 (0.736) / 0.665 (3.59)
G (week-1) / 6.13x10-3 (0.776) / 0.609 (25.8) / 0.098 (0.150)
D (week-1) / 1.52x10-2 (0.781) / 0.707 (31.7)
s2 / 1.106 (0.566) / -

CV: coefficient of variation, ?2: inter-individual variance, Sh: shrinkage,

corr: correlation coefficient, Y0: baseline tumor size, G:growth rate,

D: shrinkage rate, s: standard deviation of additive residual error

Supplementary Table 3Screening of the potential

covariates using the Cox model

Parameter / Score / p / Sign
Log(TTG*) / 284.9 / < 0.0001 / -
Log(G) / 229.4 / < 0.0001 / +
Baseline hemoglobin / 167.1 / < 0.0001 / -
Log(# metastases) / 150.2 / < 0.0001 / +
Baseline ECOG / 144.7 / < 0.0001 / +
Week 10 ETS / 140.0 / < 0.0001 / +
Week 12 ETS / 138.3 / < 0.0001 / +
Week 8 ETS / 136.4 / < 0.0001 / +
Baseline cor. calcium / 108.7 / < 0.0001 / +
Prior nephrectomy / 46.4 / < 0.0001 / -
Liver metastases / 42.9 / < 0.0001 / +
Time from diagnosis / 42.9 / < 0.0001 / -
Baseline LDH / 33.3 / < 0.0001 / +
Baseline SLD / 17.7 / < 0.0001 / +
Line therapy / 5.1 / 0.001 / -
Lung metastases / 2.1 / 0.038 / -

p by log likelihood ratio test

sign: sign of the parameter estimate. +: increased values prolong OS…increase the risk of death

* shifted by 25.2 days to avoid negative values

Race, age, sex were NS (p 0.05)

Supplementary Table 4Parameter estimates

of the log(TTG) OS model

Parameter / Estimate (SE) / p-value
(Intercept) / 2.81 (0.288) / <0.001
Log(TTG*) / 0.907 (0.045) / <0.001
Hemoglobin (g/L) / 0.124 (0.011) / <0.001
ECOG=1 / -0.386 (0. 046) / <0.001
ECOG=(2, 3) / -0.162 (0.073) / 0.027
Corrected calcium (mg/dL) / -0.100 (0.018) / <0.001
Log(# metastases) / -0.149 (0.030) / <0.001
Time from diagnosis (days) / 6.9E-5 (1.6E-5) / <0.001
Baseline LDH (U/L) / -3.4E-4 (8.8E-5) / <0.001
Lung metastases (yes) / -0.141 (0. 044) / 0.001
Log(scale) / -0.157 (0.0198) / <0.001

SE: standard error, p: wald test (χ2)

+=favorable; -=not favorable

* shifted by 25.2 days to avoid negative values

Supplementary Table 5 Parameter estimate covariance matrix – ETS OS model

(Intercept) / Week 8 ETS / Hemoglobin / ECOG=1 / ECOG=(2,3) / logMET / Calcium / T. diag / LDH / Lung.Met / Log(scale)
(Intercept) / 0.073 / -0.0162 / -0.00184 / -0.00167 / 0.00276 / 3.28E-05 / -0.00337 / -3.34E-07 / -2.40E-06 / -0.00176 / 0.000387
Week 8 ETS / -0.0162 / 0.0182 / 7.96E-05 / -4.87E-05 / -0.00031 / -0.00032 / -4.03E-05 / -1.51E-08 / -5.44E-07 / 0.000183 / -0.00018
Hemoglobin / -0.00184 / 7.96E-05 / 0.000122 / 0.000119 / 0.000114 / 2.92E-05 / 1.66E-05 / -7.28E-09 / 6.30E-08 / -2.74E-05 / 1.28E-05
ECOG=1 / -0.00167 / -4.87E-05 / 0.000119 / 0.00235 / 0.00168 / -7.81E-05 / -9.46E-05 / 4.39E-09 / -2.86E-07 / 0.000141 / -5.37E-05
ECOG=(2,3) / 0.00276 / -0.00031 / 0.000114 / 0.00168 / 0.00587 / -0.00077 / -0.0005 / 4.74E-08 / -9.87E-07 / 0.001 / -6.58E-05
logMET / 3.28E-05 / -0.00032 / 2.92E-05 / -7.81E-05 / -0.00077 / 0.000994 / -0.00012 / 2.98E-08 / -3.68E-07 / -0.00026 / -3.40E-05
Calciun / -0.00337 / -4.03E-05 / 1.66E-05 / -9.46E-05 / -0.0005 / -0.00012 / 0.000346 / 1.46E-08 / 6.57E-08 / 7.52E-05 / -1.44E-05
T. diag / -3.34E-07 / -1.51E-08 / -7.28E-09 / 4.39E-09 / 4.74E-08 / 2.98E-08 / 1.46E-08 / 2.76E-10 / 5.70E-11 / 4.05E-08 / 2.19E-08
LDH / -2.40E-06 / -5.44E-07 / 6.30E-08 / -2.86E-07 / -9.87E-07 / -3.68E-07 / 6.57E-08 / 5.70E-11 / 8.44E-09 / 1.88E-07 / -2.79E-08
Lung.Met / -0.00176 / 0.000183 / -2.74E-05 / 0.000141 / 0.001 / -0.00026 / 7.52E-05 / 4.05E-08 / 1.88E-07 / 0.00207 / -3.30E-05
Log(scale) / 0.000387 / -0.00018 / 1.28E-05 / -5.37E-05 / -6.58E-05 / -3.40E-05 / -1.44E-05 / 2.19E-08 / -2.79E-08 / -3.30E-05 / 0.000398

Supplementary Table 6 Parameter estimate covariance matrix – Log(TTG) OS model

(Intercept) / logTTG / Hemoglobin / ECOG=1 / ECOG=(2,3) / logMET / Calcium / T.Diag / LDH / Lung.Met / Log(scale)
(Intercept) / 0.0829 / -0.0077 / -0.00151 / -0.00161 / 0.0022 / -0.00101 / -0.00316 / -2.96E-07 / -3.44E-06 / -0.00121 / -0.00017
logTTG / -0.0077 / 0.00204 / -3.08E-05 / 2.24E-05 / 3.90E-05 / 0.000201 / 7.23E-06 / -8.76E-09 / 1.75E-07 / -6.85E-05 / 9.92E-05
Hemoglobin / -0.00151 / -3.08E-05 / 0.000112 / 0.000108 / 0.000102 / 2.56E-05 / 1.60E-05 / -5.66E-09 / 5.95E-08 / -2.43E-05 / 1.09E-05
ECOG=1 / -0.00161 / 2.24E-05 / 0.000108 / 0.00215 / 0.00154 / -7.10E-05 / -8.78E-05 / 1.54E-09 / -2.74E-07 / 0.000123 / -4.93E-05
ECOG=(2,3) / 0.0022 / 3.90E-05 / 0.000102 / 0.00154 / 0.00535 / -0.0007 / -0.00046 / 4.07E-08 / -9.35E-07 / 0.000908 / -6.28E-05
logMET / -0.00101 / 0.000201 / 2.56E-05 / -7.10E-05 / -0.0007 / 0.000923 / -0.00011 / 2.81E-08 / -3.21E-07 / -0.00023 / -2.41E-05
Calcium / -0.00316 / 7.23E-06 / 1.60E-05 / -8.78E-05 / -0.00046 / -0.00011 / 0.000316 / 1.31E-08 / 7.05E-08 / 6.86E-05 / -1.32E-05
T.Diag / -2.96E-07 / -8.76E-09 / -5.66E-09 / 1.54E-09 / 4.07E-08 / 2.81E-08 / 1.31E-08 / 2.56E-10 / 5.15E-11 / 3.51E-08 / 1.94E-08
LDH / -3.44E-06 / 1.75E-07 / 5.95E-08 / -2.74E-07 / -9.35E-07 / -3.21E-07 / 7.05E-08 / 5.15E-11 / 7.69E-09 / 1.74E-07 / -2.28E-08
Lung.Met / -0.00121 / -6.85E-05 / -2.43E-05 / 0.000123 / 0.000908 / -0.00023 / 6.86E-05 / 3.51E-08 / 1.74E-07 / 0.00189 / -3.21E-05
Log(scale) / -0.00017 / 9.92E-05 / 1.09E-05 / -4.93E-05 / -6.28E-05 / -2.41E-05 / -1.32E-05 / 1.94E-08 / -2.28E-08 / -3.21E-05 / 0.000394

Supplementary Fig. 1Goodness of fit plots of the sTGI model

Supplementary Fig. 2Goodness of fit plots of the Stein model

Supplementary Fig.3Predictive check of the log(TTG) OS model by tertiles of TTG

solid lines: Kaplan-Meyer plots by tertiles of TTG (days): dark grey: 1st tertile [-25.2,13.5), medium grey: 2nd tertile [13.5, 28.2), light grey: 3rd tertile [28.2,650); areas: 95% prediction intervals by the model

Supplementary Fig. 4 Predictive check of the week 8 ETS OS model by treatments

solid lines: Kaplan-Meyer plots by treatments, areas: 95% prediction intervals by the model. sorafenib (n=313), sunitinib (n=886), temsirolimus + IFN (n=156), axitinib (n=479), temsirolimus (n=182) and IFN (n=475).

Supplementary Fig. 5 Predictive check of the week 8 ETS OS model by treatments and week 8 ETS

solid lines: Kaplan-Meyer plots by treatments and ETS, areas: 95% prediction intervals by the model. sorafenib (n=313), sunitinib (n=886), temsirolimus + IFN (n=156), axitinib (n=479), temsirolimus (n=182) and IFN (n=475). Dark grey: week 8 ETS below median of 0.892, light grey: week 8 ETS at or above median of 0.892

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