1. Evaluation of Live Phase Results from Carcinogenicity Studies Wherly Hoffman, Ph.D. Statistics and Information Sciences Lilly Research Laboratories

2. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 2 Outline

3. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 3 Background The objectives of carcinogenicity studies are to identify a tumorigenic potential in animals and to understand the potential for such risk in humans. Federal Register, Vol 61, No. 42. March 1996 Required for most pharmaceuticals for global submissions

4. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 4 Background Some Design factors –Duration –Species/strain –Sample size –Dose selection –Allocation of animals to dose groups …. Guidance for industry statistical aspects of the design,analysis, and interpretation of chronic rodent carcinogenicity studies of pharmaceuticals (draft guidance online) by Lin, K. K. (2001). http://www.fda.gov/cder/guidance/815dft.pdf. Accessed: 2003 May 27

5. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 5 Statistical Considerations Design –2 years –Control + 3 to 4 doses –Body weight stratification (groups) –60 animals/group/sex –Column randomization (location) Key response variables analyzed –Survival –Tumor incidence –Body weight and food consumption

6. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 6 Growth Parameters Measured/Derived Body weight Body weight gain (current-initial) Relative daily food consumption (daily food consumption/day/avg wt)

7. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 7 Statistical Analyses on Growth Parameters Primary Purpose: examine compound-related effects –Is there a treatment effect? monotonic or not? => Evaluation of dose-response relationship without time consideration will be illustrated prior to the repeated measures analysis –Is the treatment effect consistent across time? => Evaluate dose-response relationship with time consideration

8. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 8 Examples of Dose-response Curves

9. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 9 Evaluation of Dose-response Relationship Without Time Considerations Is there a monotonic dose-response relationship? Want to identify the highest no-effect dose Reference: Tukey JW, Ciminera JL, Heyse JF. 1985. Testing the statistical certainty of a response to increasing doses of a drug. Biometrics 41:295-301.

10. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 10 Sequential Trend Test with ANOVA: Hypotheses Notation: d 1, d 2,...d k - dose levels of a compound. response of the i th subject in the i th dose group Model: Y ij = i + ij ij ~ iid N(0, ), i = 1 to k, j= 1 to n i Hypotheses: Ho: i = for all i, Ha: 1 < 2 <... i... < k, at least one inequality Test for trends: test if the contrast is 0, i.e. where i may be on the log scale c i determines different types of trends

11. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 11 Sequential Trend Test with ANOVA: Test Statistic Under the null hypothesis of no trend, the t-statistic is distributed as t(N-k). N= total # of subjects, k= # of dose levels

12. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 12 Sequential Trend Test with ANOVA: Decision Process Start at the high dose. Is the p <.05 (= for the high dose trend? No- Stop. No monotonic trend at the high dose. Yes- Continue to the next lower dose. Test for trend at the next lower dose with 0 coefficient for the high dose.Is the trend p-value <.05? No- Stop. No monotonic trend at this dose. Yes- Continue…

13. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 13 Sequential Trend Test with ANOVA: Illustration with Body Weight Data Trend test up to the highest dose (4th) p<0.05 Trend up to the next lower dose (3rd) p<0.05 Trend up to the next lower dose (2nd) p>0.05 Stop and conclude 2nd dose is a no effect dose level

14. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 14 Sequential Trend Test with ANOVA: Approach to Non-monotonicity What if there is no monotonic dose-response relationship at the high dose (p>.05)? Need to look for a nonmonotonic trend in the treatment means F-test ( =.01) Dunnett's t-test comparing each treated group to control ( =.05) Reference: Dunnett CW. 1964. New tables for multiple comparisons with a control. Biometrics 20:482-491.

15. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 15 No Perform linear trend test ( =.05) & trt F-test ( =.01) STP Yes 1-Factor ANOVA with Trend Test & Dunnetts Test 1 Perform Dunnetts t-test ( =.05) No Yes SOP STOP Was trend significant? p<.05 Was trt F-test significant? p<.01

16. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 16 Evaluation of Dose-response Relationship With Time Considerations Is there a monotonic dose-response relationship? How is the effect changing with time? - identify the highest no-effect dose - test for a monotonic effect in treatment means - evaluate the time effect - evaluate the interaction between time and dose Same for non-monotonic effects

17. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 17 Sequential Trend Test with One-Factor Repeated Measures Analysis: Data N animals in total, k dose levels (including control), M time intervals Test both compound and time effects Dose LevelAnimal Time 1Time 2 Time 3 …... Control 0001 x x x Control 0002 x x x... Low 1001 x x x Low 1002 x x x …... High 4001 x x x High 4002 x x x …..

18. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 18 Sequential Trend Test with One-Factor Repeated Measures Analysis: Model Linear Mixed Effects Model Fixed: dose, time. Random: animal, error. y = X + Z + y = (y ijk ) y ijk = body weight of i th dose, j th time, k th animal = fixed effects- dose, time, dose*time, (covariates) = random effects- animal = errors N(0, G), N(0 R) and are independent

19. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 19 Sequential Trend Test with One-Factor Repeated Measures Analysis: SAS code PROC MIXED DATA=ONE; CLASS DOSE TIME ANIMAL; MODEL Y= DOSE TIME DOSE*TIME COVARIATE/ DDFM=KNEWARDROGER; {RANDOM INT/ SUBJECT=ANIMAL(DOSE);} {{REPEATED TIME/TYPE=XXX SUBJECT=ANIMAL(DOSE);}} ESTIMATE "LINEAR TREND in DOSE AT TIME 1" DOSE -3 -1 1 3 DOSE*TIME -3 0 0 0.. -1 0 0 0.. 1 0 0 0.. 3 0 0 0..; CONTRAST ….. Note:This works on long data (transpose time). Either { } or {{ }} is included for different covariance structures.

20. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 20 Sequential Trend Test with One-Factor Repeated Measures ANOVA: Monotonicity Look for a monotonic effect in treatment means Linear trend test on treatment means ( =.05) - at each time point if at least one of the following is significant (1) linear treatment trend by linear time trend ( =.05) (2) linear treatment trend by quadratic time trend ( =.05) (3) linear treatment trend by time ( =.01) - on means pooled across all time points otherwise

21. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 21 Sequential Trend Test with One-Factor Repeated Measures ANOVA: non-monotonicity What if there is no monotonic dose-response relationship? Look for a nonmonotonic effect in treatment means Bonferroni adjusted t-test comparing each treated group to control ( =.05) - at each time point if treatment by time interaction F-test p<.01 - on means pooled across all time points if main treatment F-test p<.01 Reference: Miller RG, Jr. 1981. Simultaneous statistical inference. 2nd ed. New York: Springer-Verlag. p 67-69.

22. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 22 No Perform Interaction Tests: LinTrt*LinTime( =.05) LinTrt*QrdTime( =.05) LinTrt*Time( =.01) Perform LinTrt ( =.05) pooled across time NoYes STO STP Yes 1-Factor Repeated Measures Yes 1 Perform Bonferroni-adjusted pair-wise t-tests Pooled across time STOP No Yes SOP No Yes STOP 1 Perform LinTrt ( =.05) at each time point Any p < Was trend significant? P<.05 STOP Perform Bonferroni-adjusted pair-wise t-tests at each time point Was Trt*Time p<.01? 1 WasTrt F-test significant? P<.01 STOP Perform Trt*Time F-test (.01) & Trt F-test(.01) pooled across time Was any trend significant? p<.05 Go To 1

23. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 23 Rodent Growth Data Two rodent growth parameters are statistically analyzed – Interval body weight adjusted for baseline weight – Interval daily relative food consumption (Interval food consumption/day/avg wt) Body weight gains: descriptive statistics and %change relative to control (ICH, 1995)

24. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 24 Analysis Phases Statistical Analysis Phases Growth Phase up to 3 months ( 9 time intervals) Maintenance Phase the rest ( 9 time intervals)

25. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 25 Data Preparation Consolidate time intervals First Month: take all or weekly (t=2 to 4) Months 2-3: every 2 wks (t=4,5) Months 4-6: every 4 wks (t=3) Months 7-12: every 3 mos (t=2) Months 13-24: every 3 mos (t=4) t: number of time points

26. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 26 Example: Mouse Body Weights

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30. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 30 Analysis summary Body weight – Key time intervals (interval body weight) – Include all non-missing interval data – Baseline weight as a covariate – Two analysis phases – Covariance structure (historical control/current data) – Report %change of body weight gain relative to control (ICH, 1995) Food consumption – Key time intervals (interval daily food consumption) – Relative not absolute food consumption – Include all non-missing interval data – Two analysis phases – Covariance structure (historical control/current data)

31. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 31 General Strategy No change proposed for body weight and food consumption collection schedule Analyze key parameters: body weight and relative food consumption Identify key time points/intervals Perform appropriate/efficient statistical analyses Benefits – fewer statistical tests – fewer false positives – Succinct yet comprehensive interpretation of treatment effects

32. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 32 Summary Perform repeated measures analysis on growth data measured across time in two analysis phases Implementation tools-one step at a time Regulatory acceptance Reference Analysis of Rodent Growth Data in Toxicology Studies by Wherly P. Hoffman, Daniel Ness, and Robert van Lier Toxicological sciences 66, 313-319 (2002)

33. 2003 FDA/Industry Statistics Workshop Wherly Hoffman Company Confidential Copyright © 2003 Eli Lilly and Company 33 Daniel NessBob van Lier Cindy LeeKathy Piroozi Karl LinRay Carroll Wendell SmithMike Dorato Gerald LongMary Jeanne Kallman Judy HoytPatrick Cocke Susan Christopher For questions W.Hoffman@Lilly.com Acknowledgements