1. Peto Trend Test: Investigating The Impact Of Tumor Misclassification FDA/Industry Workshop Amrik Shah - Schering-Plough Melody Goodman - Harvard University

2. Outline Study design Study design Data structure Data structure Statistical methodology Statistical methodology Misclassification of Tumors Misclassification of Tumors Methods: Assessment of misclassification Methods: Assessment of misclassification Data and Permutation of Tumors Data and Permutation of Tumors Results – 3 Data sets Results – 3 Data sets Conclusions and Work in progress Conclusions and Work in progress

3. Long-term Oncogenicity Study Design Studies involve both sexes of 2 rodent species Studies involve both sexes of 2 rodent species Exposure starts at 6-8 weeks of age Exposure starts at 6-8 weeks of age One control group + 3 dose groups One control group + 3 dose groups Exposure through various routes Exposure through various routes (Food, water, gavage, inhalation etc) (Food, water, gavage, inhalation etc) Some interim sacrifices, controls are untreated or vehicle control

4. STUDY DESIGN/OBJECTIVES To test if exposure to increasing dose levels of compound leads to increase in tumor rates. To test if exposure to increasing dose levels of compound leads to increase in tumor rates. Design Criteria based on: Design Criteria based on: Dose levels Dose levels Randomization Randomization Data collection/readings Data collection/readings Sample size Sample size Study Duration Study Duration

5. DATA STRUCTURE Animal ID Animal ID Organ and Tumor Organ and Tumor Binary response indicator Binary response indicator 1 -> tumor found at given organ site 1 -> tumor found at given organ site Time at which the tumor response was observed or death time. Time at which the tumor response was observed or death time. Indicator defining Incidental or Fatal tumor. Indicator defining Incidental or Fatal tumor.

6. Data Structure IDDoseTumor Tumor Type Time 4101I104 5001F84 11611I89 14110-104 14211F88 15521F93 17620-82 18521I104 19321F76 21031I104 21531F96 22431I79 23031F78 23531F75

7. Statistical Methods Complication: Drug may affect the mortality of different groups Drug may affect the mortality of different groups Adjusting for differences in mortality is complex due to non-observable onset time of tumors. Assume: Death time is onset time for FATAL tumors

8. Peto Test Peto mortality–prevalence test Peto mortality–prevalence test Modified Cochran-Armitage test Modified Cochran-Armitage test Computed like two Cochran-Armitage Z-score approximations Computed like two Cochran-Armitage Z-score approximations One for prevalence One for prevalence One for mortality One for mortality Assume: The two statistics are independent.

9. Issue Of Misclassification Analyses is biased if tumor lethality and cause of death is not valid/accurate Analyses is biased if tumor lethality and cause of death is not valid/accurate Pathologist are stressed about classifying tumors as incidental or fatal Pathologist are stressed about classifying tumors as incidental or fatal OBJECTIVE: To assess the impact of misclassification on the Peto Trend test

10. How to Assess Impact ? Simulating/bootstrapping the data with Simulating/bootstrapping the data with Varying percentage of misclassification Varying percentage of misclassification Apply Peto trend test in all data sets Apply Peto trend test in all data sets [THIS APPROACH IS NOT EFFICIENT] Permuting data sets Permuting data sets Create datasets with varying Peto p-values Create datasets with varying Peto p-values Permute the membership of tumors in I or F Permute the membership of tumors in I or F Apply Peto trend test for each permutation Apply Peto trend test for each permutation [USED THIS TECHNIQUE]

11. Implementation Implementation Generated datasets with Peto trend test p- values close to 0.005, 0.025 and 0.1. 250 animals 250 animals 100 controls and 50 each in 3 dose groups 100 controls and 50 each in 3 dose groups X number of incidental tumors X number of incidental tumors Y number of fatal tumors Y number of fatal tumors Death time (for each animal) Death time (for each animal)

12. Permuting the Tumors Find all combinations of Find all combinations of 1. Changing incidental to fatal One, two and three tumors at a time One, two and three tumors at a time 2. Changing fatal to incidental One, two and three tumors at a time One, two and three tumors at a time 3. Simultaneous misclassification (I F) Compute the Peto trend test p-values for all permuted data sets.

13. RESULTS Dataset 1: Original Peto p-value = 0.0253 Dataset 1: Original Peto p-value = 0.0253 Dataset 2: Original Peto p-value = 0.006 Dataset 2: Original Peto p-value = 0.006 Dataset 3: Original Peto p-value = 0.1038 Dataset 3: Original Peto p-value = 0.1038Additional: Dataset 4: Original Peto p-value = 0.0031 Dataset 4: Original Peto p-value = 0.0031 Dataset 5: Original Peto p-value = 0.1067 Dataset 5: Original Peto p-value = 0.1067

14. Survival in Data 1 TimeCT1T2T3 0-75 weeks 181487 76-88 weeks 1571811 89-103 weeks 298911 104 weeks 38211521

15. Data 1 - Tumor Incidence Data 1 has 5 incidental and 7 fatal tumors Data 1 has 5 incidental and 7 fatal tumors Initial Peto test p-value of 0.0253 Initial Peto test p-value of 0.0253 Tumor type CT1T2T3 no tumor 98484745 incidental1112 fatal1123

16. Data 1: All Combinations Of Two Tumors Changing From Incidental To Fatal IDIDP-value 411160.0280 411850.0256 412100.0254 412240.0231 1161850.0275 1162100.0270 1162240.0245 1852100.0251 1852240.0227 2102240.0222

17. Results - Data 1 MisclassificationNMin p-valueMax p-value 50.02260.0274 100.02220.0280 100.02240.0278 70.02250.0292 210.02040.0330 350.01870.0368 700.01820.0357 1050.01970.0322 3500.01650.0402

18. Graphical Results Original p-value = 0.0253

19. Graphical Results Original p-value = 0.0253

20. Graphical Results Original p-value = 0.0253

21. Data 2 - Tumor Incidence Data 2 has 4 incidental and 9 fatal tumors Data 2 has 4 incidental and 9 fatal tumors Initial Peto test p-value of 0.0060 Initial Peto test p-value of 0.0060 Tumor type CT1T2T3 no tumor 98494644 incidental1012 fatal1134

22. Results- Data 2 MisclassificationNMin p-valueMax p-value 40.00550.0062 60.00540.0061 40.00550.0060 90.00520.0073 360.00470.0086 840.00430.0100 540.00470.0074 1440.00430.0089 3360.00390.0100

23. Data 3 - Tumor Incidence Data 3 has 8 incidental and 6 fatal tumors Data 3 has 8 incidental and 6 fatal tumors Original Peto test p-value of 0.1038 Original Peto test p-value of 0.1038 Tumor type CT1T2T3 no tumor 97474646 incidental1133 fatal2211

24. Data 3 - Survival Data 3 - Survival TimeCT1T2T3 0-75 weeks 198139 76-88 weeks 24131010 89-103 weeks 1413912 104 weeks 43161819

25. Survival – Data 3 p-value=0.1038 8 incidental, 6 fatal tumors

26. Results- Data 3 MisclassificationN Min p-value Max p-value 80.09410.1075 280.08880.1083 560.08670.1086 60.09820.1129 150.09110.1154 200.08460.1146 1680.08380.1177 1200.08230.1194 11200.07010.1162

27. Data 3 - Animal death times Data 3 - Animal death times

28. Conclusions & Work in Progress Mis-classification does not impact the original data findings. Mis-classification does not impact the original data findings. Fatal to incidental seems to have (relatively) more of an effect – why? Fatal to incidental seems to have (relatively) more of an effect – why? In Progress: Early deaths in High dose group. Early deaths in High dose group. Opposing incidence trends for fatal and incidental tumors. Opposing incidence trends for fatal and incidental tumors.