Assessing Antitumor Activity Assessing Antitumor Activity in Preclinical Tumor Xenograft in Preclinical Tumor Xenograft

Model Model

Department of BiostatisticsSt. Jude Children’s Research Hospital

John(Jianrong) Wu

Tumor Xenograft Model

Tumor xenograft models Tumor xenograft models

Subcutaneous tumor model: tumor xenograft is Subcutaneous tumor model: tumor xenograft is implanted under the skin and typically located on the implanted under the skin and typically located on the flank of the mouse. flank of the mouse.

Orthotopic tumor model: tumor xenograft is either Orthotopic tumor model: tumor xenograft is either implanted into the equivalent organ from which the implanted into the equivalent organ from which the cancer originated, or where metastatsese are found in cancer originated, or where metastatsese are found in patients.patients.

D456-cisplatin tumor xenograft modelD456-cisplatin tumor xenograft model

Challenges Challenges

A relative small number of mice (10/per A relative small number of mice (10/per group) were tested.group) were tested.

Missing data issue: due to mice die of Missing data issue: due to mice die of toxicity or be sacrificed when tumors grow toxicity or be sacrificed when tumors grow to certain size.to certain size.

Skewed distribution of tumor volume dataSkewed distribution of tumor volume data Various of tumor growth patterns. Various of tumor growth patterns.

Tumor Growth Inhibition Tumor Growth Inhibition (T/C ratio)(T/C ratio)

time

Relative Tumor volume

t

Skewed tumor volume dataSkewed tumor volume data

Demidenko, 2010

Anti-tumor activity Anti-tumor activity

Drawback of separate analysis of tumor volume at Drawback of separate analysis of tumor volume at each time pointeach time point

Multiple tests at different time points inflate type I error.Multiple tests at different time points inflate type I error. Excluding animals with missing observation is inefficient Excluding animals with missing observation is inefficient

and could result a biased conclusion. and could result a biased conclusion. T-test may be not valid due to skewed distribution of tumor T-test may be not valid due to skewed distribution of tumor

volume data. volume data. Separate analysis at each time point ignores the intra-Separate analysis at each time point ignores the intra-

subject correlation.subject correlation. Using an arbitrary cut-off point to assess antitumor activity Using an arbitrary cut-off point to assess antitumor activity

and without any formal statistical inference and without any formal statistical inference

Statistical inference for tumor volume Statistical inference for tumor volume data data

Inference T/C ratio and its 95% confidence interval –Inference T/C ratio and its 95% confidence interval –Hothorn (2006), Wu (2009, 2010), Cheng and Wu Hothorn (2006), Wu (2009, 2010), Cheng and Wu (2010)(2010)

Multivariate analysis – Tan et al (2002)Multivariate analysis – Tan et al (2002)

MANOVA – Heitjian et al (1995)MANOVA – Heitjian et al (1995)

Nonparametric multivariate analysis – Koziol et al (1981)Nonparametric multivariate analysis – Koziol et al (1981)

Tumor Growth Delay (T-C)Tumor Growth Delay (T-C)

44

Relative Tumor volume

time

Tumor Growth Delay

Tumor doubling and Tumor doubling and quadrupling timequadrupling time

4

Tumor quadrupling timeTumor quadrupling time

Kaplan-Meier Event-free Survival Kaplan-Meier Event-free Survival Distributions (p<0.0001)Distributions (p<0.0001)

Example: D456-cisplatin tumor Example: D456-cisplatin tumor xenograft modelxenograft model

The medians of tumor quadrupling times are 8.7 The medians of tumor quadrupling times are 8.7 (days) and 24.9 (days) for control and treatment, (days) and 24.9 (days) for control and treatment, respectively. TGD=16.2 days with standard error respectively. TGD=16.2 days with standard error of 1.9 daysof 1.9 days

The 95% confidence bootstrap percentile interval The 95% confidence bootstrap percentile interval of TGD is (10.8, 21.2).of TGD is (10.8, 21.2).

Wu J, Confidence intervals for the difference of median failure times applied to censored tumor growth delay data, Statistics in Biopharmaceutical Research, 3:488-496, 2011

Log10 cell kill (LCK) Log10 cell kill (LCK) Log10 cell kill is defined as the negative log10 fraction of tumor cells Log10 cell kill is defined as the negative log10 fraction of tumor cells

surviving (SF). surviving (SF). We illustrate its quantification with assumptions (a) control tumor We illustrate its quantification with assumptions (a) control tumor

growth follows an exponential growth curve (b) treated tumor growth follows an exponential growth curve (b) treated tumor regrowth after treament approximates untreated controls, then regrowth after treament approximates untreated controls, then

LCK = - log10(SF) = (T – C)/(3.32 DT)LCK = - log10(SF) = (T – C)/(3.32 DT)

where DT is tumor doubling time of control.where DT is tumor doubling time of control.

or -log(SF)=Tumor Growth Delay * Rate of Growth or -log(SF)=Tumor Growth Delay * Rate of Growth

Demidenko, 2010

Log10 cell kill

Anti-tumor activity Anti-tumor activity

SAS macro SAS macro

Macro Macro %long%long: transform the tumor volume : transform the tumor volume data to be a longitudinal form data to be a longitudinal form

Macro Macro %day2event%day2event: calculate tumor : calculate tumor doubling and quadrupling times.doubling and quadrupling times.

Macro Macro %lck%lck: calculate tumor growth delay : calculate tumor growth delay (T-C) and log10 cell kill.(T-C) and log10 cell kill.

References for T/C ratioReferences for T/C ratio Heitjan DF, Manni A, Santen RJ. Statistical analysis of in vivo tumor growth Heitjan DF, Manni A, Santen RJ. Statistical analysis of in vivo tumor growth

experiments. Cancer Research 1993;53:6042–6050experiments. Cancer Research 1993;53:6042–6050 Houghton PJ, Morton CL, et al. (2007). The pediatric preclinical testing program: Houghton PJ, Morton CL, et al. (2007). The pediatric preclinical testing program:

Description of models and early testing results. Description of models and early testing results. Pediatr. Blood Cancer 49:928–940.Pediatr. Blood Cancer 49:928–940. Hothorn L (2006). Statistical analysis of Hothorn L (2006). Statistical analysis of in vivo anticancer experiments: Tumor growth in vivo anticancer experiments: Tumor growth

inhibition. inhibition. Drug Inform. J. 40:229–238.Drug Inform. J. 40:229–238. Wu J (2010), Wu J (2010), Statistical Inference for Tumor Growth Inhibition T/C Ratio, JBS, 20:954-Statistical Inference for Tumor Growth Inhibition T/C Ratio, JBS, 20:954-

964964 Wu J and Houghton PJ (2009),Wu J and Houghton PJ (2009), Interval approach to assessing antitumor activity for Interval approach to assessing antitumor activity for

tumor xenograft studies, Pharmaceutical Statistics, 9:46-54.tumor xenograft studies, Pharmaceutical Statistics, 9:46-54. Tan, M., Fang, H. B., Tian, G. L., Houghton, P. J. (2002). Small-sample inference for Tan, M., Fang, H. B., Tian, G. L., Houghton, P. J. (2002). Small-sample inference for

incomplete longitudinal data with truncation and censoring in tumor xenograft models. incomplete longitudinal data with truncation and censoring in tumor xenograft models. Biometrics 58:612–620.Biometrics 58:612–620.

Koziol et al. (1981). A distribution-free test for tumor-growth curve analyses with Koziol et al. (1981). A distribution-free test for tumor-growth curve analyses with application to an animal tumor immunotherapy experiment. Biometrics, 37:383-390application to an animal tumor immunotherapy experiment. Biometrics, 37:383-390

References for TGDReferences for TGD Wu J, Confidence intervals for the difference of median failure times Wu J, Confidence intervals for the difference of median failure times

applied to censored tumor growth delay data, applied to censored tumor growth delay data, Statistics in Statistics in Biopharmaceutical ResearchBiopharmaceutical Research, 3:488-496, 2011., 3:488-496, 2011.

Wu J, Assessment of antitumor activity for tumor xenograft studies Wu J, Assessment of antitumor activity for tumor xenograft studies using exponential growth models. using exponential growth models. Journal of Biopharmaceutical Journal of Biopharmaceutical StatisticsStatistics, 21:472-483, May, 2011., 21:472-483, May, 2011.

Demidenko E (2010), Three endpoints of in vivo tumor radiobiology Demidenko E (2010), Three endpoints of in vivo tumor radiobiology and their statistical estimation. 86:164-173.and their statistical estimation. 86:164-173.

Corbett, T. H., White, K., Polin, L., Kushner, J., Paluch, J., Shih, C., Corbett, T. H., White, K., Polin, L., Kushner, J., Paluch, J., Shih, C., Grossman, C. S. (2003).Discovery and preclinical antitumor efficacy Grossman, C. S. (2003).Discovery and preclinical antitumor efficacy evaluations of LY32262 and LY33169.evaluations of LY32262 and LY33169.Investigational New Drugs Investigational New Drugs 21:33–45.21:33–45.

References for LCK References for LCK Demidenko E (2010), Three endpoints of in vivo tumor radiology Demidenko E (2010), Three endpoints of in vivo tumor radiology

and their statistical estimation, Int J Radial Biol. 86:164-173and their statistical estimation, Int J Radial Biol. 86:164-173 Lloyd H (1975), Estimation of tumor cell kill from Gompertz growth Lloyd H (1975), Estimation of tumor cell kill from Gompertz growth

curves, Cancer Chemother Rep, 59:267-277.curves, Cancer Chemother Rep, 59:267-277. Corbett TH et al (2003), Discovery and preclinical antitumor efficacy Corbett TH et al (2003), Discovery and preclinical antitumor efficacy

evaluations of LY32262 and LY33169. Invest New Drugs 21:33-45.evaluations of LY32262 and LY33169. Invest New Drugs 21:33-45. Wu J (2011), Assessment of antitumor activity for tumor xenograft Wu J (2011), Assessment of antitumor activity for tumor xenograft

studies using exponential growth models, JBS, 1:472-483studies using exponential growth models, JBS, 1:472-483 Wu J and Houghton PJ (2009), Assessing cytotoxic treatment Wu J and Houghton PJ (2009), Assessing cytotoxic treatment

effects in preclinical tumor xenograft models, JBS,19:755-762effects in preclinical tumor xenograft models, JBS,19:755-762

Thank you !Thank you !