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.