Peto Trend Test: Investigating The Impact Of Tumor Misclassification

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Peto Trend Test Investigating The Impact Of
Tumor Misclassification

• FDA/Industry Workshop

Amrik Shah - Schering-Plough Melody Goodman - Harvard University Amrik Shah - Schering-Plough Melody Goodman - Harvard University


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Outline

• Study design
• Data structure
• Statistical methodology
• Misclassification of Tumors
• Methods Assessment of misclassification
• Data and Permutation of Tumors
• Results 3 Data sets
• Conclusions and Work in progress

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Long-term Oncogenicity Study Design

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

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STUDY DESIGN/OBJECTIVES

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

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DATA STRUCTURE

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

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Data Structure
ID Dose Tumor Tumor Type Time
41 0 1 I 104
50 0 1 F 84
116 1 1 I 89
141 1 0 - 104
142 1 1 F 88
155 2 1 F 93
176 2 0 - 82
185 2 1 I 104
193 2 1 F 76
210 3 1 I 104
215 3 1 F 96
224 3 1 I 79
230 3 1 F 78
235 3 1 F 75
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Statistical Methods

• Complication
• 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

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Peto Test

• Peto mortalityprevalence test
• Modified Cochran-Armitage test
• Computed like two Cochran-Armitage Z-score
  approximations
• One for prevalence
• One for mortality
• Assume The two statistics are independent.

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Issue Of Misclassification

• Analyses is biased if tumor lethality and cause
  of death is not valid/accurate
• Pathologist are stressed about classifying
  tumors as incidental or fatal

OBJECTIVE To assess the impact of
misclassification on the Peto Trend test
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How to Assess Impact ?

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

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Implementation

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

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Permuting the Tumors

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

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RESULTS

• Dataset 1 Original Peto p-value 0.0253
• Dataset 2 Original Peto p-value 0.006
• Dataset 3 Original Peto p-value 0.1038
• Additional
• Dataset 4 Original Peto p-value 0.0031
• Dataset 5 Original Peto p-value 0.1067

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Survival in Data 1
Time C T1 T2 T3
0-75 weeks 18 14 8 7
76-88 weeks 15 7 18 11
89-103 weeks 29 8 9 11
104 weeks 38 21 15 21
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Data 1 - Tumor Incidence

• Data 1 has 5 incidental and 7 fatal tumors
• Initial Peto test p-value of 0.0253

Tumor type C T1 T2 T3
no tumor 98 48 47 45
incidental 1 1 1 2
fatal 1 1 2 3
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Data 1 All Combinations Of Two Tumors Changing
From Incidental To Fatal
ID ID P-value
41 116 0.0280
41 185 0.0256
41 210 0.0254
41 224 0.0231
116 185 0.0275
116 210 0.0270
116 224 0.0245
185 210 0.0251
185 224 0.0227
210 224 0.0222
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Results - Data 1
Misclassification N Min p-value Max p-value
5 0.0226 0.0274
10 0.0222 0.0280
10 0.0224 0.0278
7 0.0225 0.0292
21 0.0204 0.0330
35 0.0187 0.0368
70 0.0182 0.0357
105 0.0197 0.0322
350 0.0165 0.0402
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Graphical Results
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Graphical Results
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Graphical Results
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Data 2 - Tumor Incidence

• Data 2 has 4 incidental and 9 fatal tumors
• Initial Peto test p-value of 0.0060

Tumor type C T1 T2 T3
no tumor 98 49 46 44
incidental 1 0 1 2
fatal 1 1 3 4
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Results- Data 2
Misclassification N Min p-value Max p-value
4 0.0055 0.0062
6 0.0054 0.0061
4 0.0055 0.0060
9 0.0052 0.0073
36 0.0047 0.0086
84 0.0043 0.0100
54 0.0047 0.0074
144 0.0043 0.0089
336 0.0039 0.0100
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Data 3 - Tumor Incidence

• Data 3 has 8 incidental and 6 fatal tumors
• Original Peto test p-value of 0.1038

Tumor type C T1 T2 T3
no tumor 97 47 46 46
incidental 1 1 3 3
fatal 2 2 1 1
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Data 3 - Survival
Time C T1 T2 T3
0-75 weeks 19 8 13 9
76-88 weeks 24 13 10 10
89-103 weeks 14 13 9 12
104 weeks 43 16 18 19
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Survival Data 3

• p-value0.1038
• 8 incidental, 6 fatal tumors

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Results- Data 3
Misclassification N Min p-value Max p-value
8 0.0941 0.1075
28 0.0888 0.1083
56 0.0867 0.1086
6 0.0982 0.1129
15 0.0911 0.1154
20 0.0846 0.1146
168 0.0838 0.1177
120 0.0823 0.1194
1120 0.0701 0.1162
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Data 3 - Animal death times
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Conclusions Work in Progress

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