Assessing Antitumor Activity in Preclinical Tumor Xenograft Model Department of Biostatistics St. Jude Children’s Research Hospital John(Jianrong) Wu

Tumor Xenograft Model

Tumor xenograft models Subcutaneous tumor model: tumor xenograft is implanted under the skin and typically located on the flank of the mouse. Orthotopic tumor model: tumor xenograft is either implanted into the equivalent organ from which the cancer originated, or where metastatsese are found in patients.

D456-cisplatin tumor xenograft model

Challenges A relative small number of mice (10/per group) were tested. Missing data issue: due to mice die of toxicity or be sacrificed when tumors grow to certain size. Skewed distribution of tumor volume data Various of tumor growth patterns.

Tumor Growth Inhibition (T/C ratio) Relative Tumor volume time t

Skewed tumor volume data Demidenko, 2010

Anti-tumor activity

Drawback of separate analysis of tumor volume at each time point Multiple tests at different time points inflate type I error. Excluding animals with missing observation is inefficient and could result a biased conclusion. T-test may be not valid due to skewed distribution of tumor volume data. Separate analysis at each time point ignores the intra-subject correlation. Using an arbitrary cut-off point to assess antitumor activity and without any formal statistical inference

Statistical inference for tumor volume data Inference T/C ratio and its 95% confidence interval –Hothorn (2006), Wu (2009, 2010), Cheng and Wu (2010) Multivariate analysis – Tan et al (2002) MANOVA – Heitjian et al (1995) Nonparametric multivariate analysis – Koziol et al (1981)

Tumor Growth Delay (T-C) 4 Relative Tumor volume time

Tumor Growth Delay

Tumor doubling and quadrupling time 4

Tumor quadrupling time

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

Example: D456-cisplatin tumor xenograft model The medians of tumor quadrupling times are 8.7 (days) and 24.9 (days) for control and treatment, respectively. TGD=16.2 days with standard error of 1.9 days The 95% confidence bootstrap percentile interval 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) or -log(SF)=Tumor Growth Delay * Rate of Growth Log10 cell kill is defined as the negative log10 fraction of tumor cells surviving (SF). We illustrate its quantification with assumptions (a) control tumor growth follows an exponential growth curve (b) treated tumor regrowth after treament approximates untreated controls, then LCK = - log10(SF) = (T – C)/(3.32 DT) where DT is tumor doubling time of control. or -log(SF)=Tumor Growth Delay * Rate of Growth

Demidenko, 2010

Log10 cell kill

Anti-tumor activity

SAS macro Macro %long: transform the tumor volume data to be a longitudinal form Macro %day2event: calculate tumor doubling and quadrupling times. Macro %lck: calculate tumor growth delay (T-C) and log10 cell kill.

References for T/C ratio Heitjan DF, Manni A, Santen RJ. Statistical analysis of in vivo tumor growth experiments. Cancer Research 1993;53:6042–6050 Houghton PJ, Morton CL, et al. (2007). The pediatric preclinical testing program: Description of models and early testing results. Pediatr. Blood Cancer 49:928–940. Hothorn L (2006). Statistical analysis of in vivo anticancer experiments: Tumor growth inhibition. Drug Inform. J. 40:229–238. Wu J (2010), Statistical Inference for Tumor Growth Inhibition T/C Ratio, JBS, 20:954-964 Wu J and Houghton PJ (2009), Interval approach to assessing antitumor activity for tumor xenograft studies, Pharmaceutical Statistics, 9:46-54. 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. Biometrics 58:612–620. Koziol et al. (1981). A distribution-free test for tumor-growth curve analyses with application to an animal tumor immunotherapy experiment. Biometrics, 37:383-390

References for TGD 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. Wu J, Assessment of antitumor activity for tumor xenograft studies using exponential growth models. Journal of Biopharmaceutical Statistics, 21:472-483, May, 2011. Demidenko E (2010), Three endpoints of in vivo tumor radiobiology and their statistical estimation. 86:164-173. Corbett, T. H., White, K., Polin, L., Kushner, J., Paluch, J., Shih, C., Grossman, C. S. (2003).Discovery and preclinical antitumor efficacy evaluations of LY32262 and LY33169.Investigational New Drugs 21:33–45.

References for LCK Demidenko E (2010), Three endpoints of in vivo tumor radiology and their statistical estimation, Int J Radial Biol. 86:164-173 Lloyd H (1975), Estimation of tumor cell kill from Gompertz growth curves, Cancer Chemother Rep, 59:267-277. Corbett TH et al (2003), Discovery and preclinical antitumor efficacy evaluations of LY32262 and LY33169. Invest New Drugs 21:33-45. Wu J (2011), Assessment of antitumor activity for tumor xenograft studies using exponential growth models, JBS, 1:472-483 Wu J and Houghton PJ (2009), Assessing cytotoxic treatment effects in preclinical tumor xenograft models, JBS,19:755-762

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