Peto Trend Test: Investigating The Impact Of Tumor Misclassification FDA/Industry Workshop Amrik...
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Peto Trend Test: Investigating Peto Trend Test: Investigating The Impact Of Tumor The Impact Of Tumor
MisclassificationMisclassification
FDA/Industry WorkshopFDA/Industry Workshop
Amrik Shah - Schering-PloughAmrik Shah - Schering-Plough
Melody Goodman - Harvard UniversityMelody Goodman - Harvard University
OutlineOutline
Study designStudy design Data structureData structure Statistical methodologyStatistical methodology Misclassification of TumorsMisclassification of Tumors Methods: Assessment of misclassificationMethods: Assessment of misclassification Data and Permutation of TumorsData and Permutation of Tumors Results – 3 Data setsResults – 3 Data sets Conclusions and Work in progressConclusions and Work in progress
Long-term Oncogenicity Study Long-term Oncogenicity Study DesignDesign
Studies involve both sexes of 2 rodent Studies involve both sexes of 2 rodent speciesspecies
Exposure starts at 6-8 weeks of ageExposure starts at 6-8 weeks of age One control group + 3 dose groupsOne control group + 3 dose groups Exposure through various routesExposure through various routes
(Food, water, gavage, inhalation etc)(Food, water, gavage, inhalation etc)
Some interim sacrifices, controls are untreated Some interim sacrifices, controls are untreated or ‘vehicle’ controlor ‘vehicle’ control
STUDY DESIGN/OBJECTIVESSTUDY DESIGN/OBJECTIVES ToTo test if exposure to increasing dose test if exposure to increasing dose
levels of compound leads to increase in levels of compound leads to increase in tumor rates.tumor rates.
Design Criteria based on:Design Criteria based on: Dose levelsDose levels RandomizationRandomization Data collection/readingsData collection/readings Sample sizeSample size Study DurationStudy Duration
DATA STRUCTUREDATA STRUCTURE
Animal ID Animal ID Organ and TumorOrgan and Tumor Binary response indicatorBinary response indicator
1 -> tumor found at given organ site1 -> tumor found at given organ site Time at which the tumor response Time at which the tumor response
was observed or death time.was observed or death time. Indicator defining Incidental or Fatal Indicator defining Incidental or Fatal
tumor.tumor.
Data StructureData StructureIDID DoseDose TumorTumor Tumor TypeTumor Type TimeTime
4141 00 11 II 104104
5050 00 11 FF 8484
116116 11 11 II 8989
141141 11 00 -- 104104
142142 11 11 FF 8888
155155 22 11 FF 9393
176176 22 00 -- 8282
185185 22 11 II 104104
193193 22 11 FF 7676
210210 33 11 II 104104
215215 33 11 FF 9696
224224 33 11 II 7979
230230 33 11 FF 7878
235235 33 11 FF 7575
Statistical MethodsStatistical Methods Complication:Complication:
Drug may affect the mortality of different groupsDrug may affect the mortality of different groups
Adjusting for differences in mortality is Adjusting for differences in mortality is complex due to non-observable onset time complex due to non-observable onset time of tumors.of tumors.
Assume: Death time is onset time for FATAL Assume: Death time is onset time for FATAL tumorstumors
Peto TestPeto Test
Peto mortality–prevalence testPeto mortality–prevalence test Modified Cochran-Armitage testModified Cochran-Armitage test Computed like two Cochran-Armitage Z-Computed like two Cochran-Armitage Z-
score approximationsscore approximations One for prevalenceOne for prevalence One for mortalityOne for mortality
Assume: The two statistics are Assume: The two statistics are independent.independent.
Issue Of MisclassificationIssue Of Misclassification Analyses is biased if tumor lethality and Analyses is biased if tumor lethality and
cause of death is not valid/accuratecause of death is not valid/accurate
Pathologist are “stressed” about Pathologist are “stressed” about classifying tumors as incidental or fatal classifying tumors as incidental or fatal
OBJECTIVE: To assess the impact of misclassification on the Peto Trend test
How to Assess Impact ?How to Assess Impact ? Simulating/bootstrapping the data withSimulating/bootstrapping the data with
Varying percentage of misclassificationVarying percentage of misclassification Apply Peto trend test in all data setsApply Peto trend test in all data sets
[THIS APPROACH IS NOT EFFICIENT][THIS APPROACH IS NOT EFFICIENT]
Permuting data setsPermuting data sets Create datasets with varying Peto p-values Create datasets with varying Peto p-values
Permute the membership of tumors in I or FPermute the membership of tumors in I or F Apply Peto trend test for each permutationApply Peto trend test for each permutation
[USED THIS TECHNIQUE][USED THIS TECHNIQUE]
ImplementationImplementationGeneratedGenerated datasets with Peto trend test datasets with Peto trend test
p-values close to 0.005, 0.025 and 0.1.p-values close to 0.005, 0.025 and 0.1.
250 animals 250 animals 100 controls and 50 each in 3 dose groups100 controls and 50 each in 3 dose groups
X number of incidental tumorsX number of incidental tumors Y number of fatal tumorsY number of fatal tumors Death time (for each animal)Death time (for each animal)
Permuting the TumorsPermuting the Tumors Find all combinations ofFind all combinations of
1.1. Changing incidental to fatalChanging incidental to fatal One, two and three tumors at a timeOne, two and three tumors at a time
2.2. Changing fatal to incidentalChanging fatal to incidental One, two and three tumors at a timeOne, two and three tumors at a time
3.3. Simultaneous misclassification (ISimultaneous misclassification (I F) F)
Compute the Peto trend test p-values Compute the Peto trend test p-values for all permuted data sets.for all permuted data sets.
RESULTSRESULTS
Dataset 1: Original Peto p-value = 0.0253Dataset 1: Original Peto p-value = 0.0253 Dataset 2: Original Peto p-value = 0.006Dataset 2: Original Peto p-value = 0.006 Dataset 3: Original Peto p-value = 0.1038Dataset 3: Original Peto p-value = 0.1038
Additional:Additional: Dataset 4: Original Peto p-value = 0.0031Dataset 4: Original Peto p-value = 0.0031 Dataset 5: Original Peto p-value = 0.1067Dataset 5: Original Peto p-value = 0.1067
Survival in Data 1Survival in Data 1
TimeTime CC T1T1 T2T2 T3T3
0-75 weeks0-75 weeks 1818 1414 88 77
76-88 weeks76-88 weeks 1515 77 1818 1111
89-103 weeks89-103 weeks 2929 88 99 1111
104 weeks104 weeks 3838 2121 1515 2121
Data 1 - Tumor Incidence 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 0.0253Initial Peto test p-value of 0.0253
Tumor Tumor typetype
CC T1T1 T2T2 T3T3
no tumorno tumor 9898 4848 4747 4545
incidentalincidental 11 11 11 22
fatalfatal 11 11 22 33
Data 1: All Combinations Of Two Data 1: All Combinations Of Two Tumors Changing From Incidental To Tumors Changing From Incidental To
FatalFatalIDID IDID P-valueP-value
4141 116116 0.02800.0280
4141 185185 0.02560.0256
4141 210210 0.02540.0254
4141 224224 0.02310.0231
116116 185185 0.02750.0275
116116 210210 0.02700.0270
116116 224224 0.02450.0245
185185 210210 0.02510.0251
185185 224224 0.02270.0227
210210 224224 0.02220.0222
Results - Data 1Results - Data 1Misclassification
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
IF 3
FI 1
FI 2
FI 3
IF 2
IF 1
FI3
3
FI1
2
FI2
1
Graphical ResultsGraphical Results
Original p-value = 0.0253
Graphical ResultsGraphical Results
Original p-value = 0.0253
Graphical ResultsGraphical Results
Original p-value = 0.0253 Original p-value =
0.0253
Data 2 - Tumor Incidence Data 2 - Tumor Incidence Data 2 has 4 incidental and 9 fatal tumorsData 2 has 4 incidental and 9 fatal tumors Initial Peto test p-value of 0.0060Initial Peto test p-value of 0.0060
Tumor Tumor typetype
CC T1T1 T2T2 T3T3
no tumorno tumor 9898 4949 4646 4444
incidentalincidental 11 00 11 22
fatalfatal 11 11 33 44
Results- Data 2Results- Data 2Misclassification
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
IF 3
FI 1
FI 2
FI 3
IF 2
IF 1
FI3
3
FI1
2
FI2
1
Data 3 - Tumor Incidence Data 3 - Tumor Incidence Data 3 has 8 incidental and 6 fatal tumorsData 3 has 8 incidental and 6 fatal tumors Original Peto test p-value of 0.1038Original Peto test p-value of 0.1038
Tumor Tumor typetype
CC T1T1 T2T2 T3T3
no tumorno tumor 9797 4747 4646 4646
incidentalincidental 11 11 33 33
fatalfatal 22 22 11 11
Data 3 - SurvivalData 3 - Survival
TimeTime CC T1T1 T2T2 T3T3
0-75 weeks0-75 weeks 1919 88 1313 99
76-88 weeks76-88 weeks 2424 1313 1010 1010
89-103 weeks89-103 weeks 1414 1313 99 1212
104 weeks104 weeks 4343 1616 1818 1919
Survival – Data 3Survival – Data 3•p-value=0.1038
•8 incidental, 6 fatal tumors
Results- Data 3Results- Data 3MisclassificatioMisclassificationn
NN Min p-Min p-valuevalue
Max p-Max p-valuevalue
88 0.09410.0941 0.10750.1075
2828 0.08880.0888 0.10830.1083
5656 0.08670.0867 0.10860.1086
66 0.09820.0982 0.11290.1129
1515 0.09110.0911 0.11540.1154
2020 0.08460.0846 0.11460.1146
168168 0.08380.0838 0.11770.1177
120120 0.08230.0823 0.11940.1194
11201120 0.07010.0701 0.11620.1162
IF 3
FI 1
FI 2
FI 3
IF 2
IF 1
FI3
3
FI1
2
FI2
1
Data 3 - Animal death Data 3 - Animal death times times
Conclusions & Work in Conclusions & Work in ProgressProgress
Mis-classification does not impact the Mis-classification does not impact the original data findings.original data findings.
Fatal to incidental seems to have Fatal to incidental seems to have (relatively) more of an effect – why?(relatively) more of an effect – why?
In Progress:In Progress: Early deaths in High dose group.Early deaths in High dose group. Opposing incidence trends for fatal Opposing incidence trends for fatal
and incidental tumors.and incidental tumors.