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

Peto Trend Test: Investigating
The Impact Of Tumor
Misclassification
FDA/Industry Workshop
Amrik Shah
Melody Goodman
- Schering-Plough
- Harvard University
Outline
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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
Long-term Oncogenicity Study Design
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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
STUDY DESIGN/OBJECTIVES
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To test if exposure to increasing dose levels of
compound leads to increase in tumor rates.
Design Criteria based on:
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Dose levels
Randomization
Data collection/readings
Sample size
Study Duration
DATA STRUCTURE
 Animal ID
 Organ and Tumor
 Binary response indicator
 1 -> tumor found at given organ site
 Time at which the tumor response
was observed or death time.
 Indicator defining Incidental or Fatal
tumor.
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
Statistical Methods
Complication:
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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
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Peto mortality–prevalence 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.
Issue Of Misclassification
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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
How to Assess Impact ?
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Simulating/bootstrapping the data with
Varying percentage of misclassification
 Apply Peto trend test in all data sets
[THIS APPROACH IS NOT EFFICIENT]
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Permuting data sets
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Create datasets with varying Peto p-values
Permute the membership of tumors in I or F
 Apply Peto trend test for each permutation
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[USED THIS TECHNIQUE]
Implementation
Generated datasets with Peto trend test pvalues close to 0.005, 0.025 and 0.1.
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250 animals
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100 controls and 50 each in 3 dose groups
X number of incidental tumors
Y number of fatal tumors
Death time (for each animal)
Permuting the Tumors
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Find all combinations of
1.
Changing incidental to fatal
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2.
Changing fatal to incidental
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3.
One, two and three tumors at a time
One, two and three tumors at a time
Simultaneous misclassification (I
F)
Compute the Peto trend test p-values for all
permuted data sets.
RESULTS
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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
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
Data 1 - Tumor Incidence
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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
1
1
2
3
fatal
Data 1: All Combinations Of Two Tumors
Changing From Incidental To Fatal
ID
41
41
41
ID
116
185
210
P-value
0.0280
0.0256
0.0254
41
116
224
185
0.0231
0.0275
116
116
185
210
224
210
0.0270
0.0245
0.0251
185
210
224
224
0.0227
0.0222
Results - Data 1
Misclassification
N
Min p-value
Max p-value
1
I

F
5
0.0226
0.0274
2
I
 F
10
0.0222
0.0280
3
I
 F
10
0.0224
0.0278
1
F

I
7
0.0225
0.0292
2
F

I
21
0.0204
0.0330
3
F

I
2
I

F
35
0.0187
0.0368
70
0.0182
0.0357
I
 F
105
0.0197
0.0322
I
 F
350
0.0165
0.0402
1
1
2
3
3
Graphical Results
Original p-value = 0.0253
Graphical Results
Original p-value = 0.0253
Graphical Results
Original p-value = 0.0253
Original p-value = 0.0253
Data 2 - Tumor Incidence
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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
1
1
3
4
fatal
Results- Data 2
Misclassification
N
Min p-value
Max p-value
4
0.0055
0.0062
2
I
 F
6
0.0054
0.0061
3
I
 F
4
0.0055
0.0060
1
F

I
9
0.0052
0.0073
2
F

I
36
0.0047
0.0086
3
F

I
2
I

F
84
0.0043
0.0100
54
0.0047
0.0074
I
 F
144
0.0043
0.0089
I
 F
336
0.0039
0.0100
1
I

F
1
1
2
3
3
Data 3 - Tumor Incidence
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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
2
2
1
1
fatal
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
Survival – Data 3
•p-value=0.1038
•8 incidental, 6 fatal tumors
Results- Data 3
Misclassification
N
Min p-value
Max p-value
1
I

F
8
0.0941
0.1075
28
0.0888
0.1083
3
I
 F
56
0.0867
0.1086
1
F

I
6
0.0982
0.1129
2
F

I
15
0.0911
0.1154
3
F

I
2
I

F
20
0.0846
0.1146
168
0.0838
0.1177
I
 F
120
0.0823
0.1194
I
 F
1120
0.0701
0.1162
I
 F
2
1
1
2
3
3
Data 3 - Animal death times
Conclusions & Work in Progress
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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.