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

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

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

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

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.

Data Structure IDDoseTumor Tumor Type Time 4101I F I F F I F I F I F F75

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

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.

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

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]

Implementation Implementation Generated datasets with Peto trend test p- values close to 0.005, and 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)

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.

RESULTS Dataset 1: Original Peto p-value = Dataset 1: Original Peto p-value = Dataset 2: Original Peto p-value = Dataset 2: Original Peto p-value = Dataset 3: Original Peto p-value = Dataset 3: Original Peto p-value = Additional: Dataset 4: Original Peto p-value = Dataset 4: Original Peto p-value = Dataset 5: Original Peto p-value = Dataset 5: Original Peto p-value =

Survival in Data 1 TimeCT1T2T weeks weeks weeks weeks

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 Initial Peto test p-value of Tumor type CT1T2T3 no tumor incidental1112 fatal1123

Data 1: All Combinations Of Two Tumors Changing From Incidental To Fatal IDIDP-value

Results - Data 1 MisclassificationNMin p-valueMax p-value

Graphical Results Original p-value =

Graphical Results Original p-value =

Graphical Results Original p-value =

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 Initial Peto test p-value of Tumor type CT1T2T3 no tumor incidental1012 fatal1134

Results- Data 2 MisclassificationNMin p-valueMax p-value

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 Original Peto test p-value of Tumor type CT1T2T3 no tumor incidental1133 fatal2211

Data 3 - Survival Data 3 - Survival TimeCT1T2T weeks weeks weeks weeks

Survival – Data 3 p-value= incidental, 6 fatal tumors

Results- Data 3 MisclassificationN Min p-value Max p-value

Data 3 - Animal death times Data 3 - Animal death times

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.