Evaluation of Live Phase Results from Carcinogenicity Studies Wherly Hoffman, Ph.D. Statistics and...

Evaluation of Live Phase Results from Carcinogenicity Studies

Wherly Hoffman, Ph.D. Statistics and Information Sciences

Lilly Research Laboratories

2003 FDA/Industry Statistics Workshop Wherly Hoffman

Company ConfidentialCopyright © 2003 Eli Lilly and Company

2

Outline

Background Purpose and design

Statistical considerations

Growth data analysis

Summary



3

Background

The objectives of carcinogenicity studies are to identify

a tumorigenic potential in animals and to understand the

potential for such risk in humans.

Federal Register, Vol 61, No. 42. March 1996

• Required for most pharmaceuticals for global submissions



4

Background

Some Design factors

– Duration

– Species/strain

– Sample size

– Dose selection

– Allocation of animals to dose groups

….

Guidance for industry statistical aspects of the design,analysis, and interpretation of chronic rodent carcinogenicity studies of pharmaceuticals (draft guidance online) by Lin, K. K. (2001). http://www.fda.gov/cder/guidance/815dft.pdf. Accessed: 2003 May 27



5

Statistical Considerations

• Design– 2 years

– Control + 3 to 4 doses

– Body weight stratification (groups)

– 60 animals/group/sex

– Column randomization (location)

• Key response variables analyzed – Survival

– Tumor incidence

– Body weight and food consumption



6

Growth Parameters Measured/Derived

• Body weight

• Body weight gain (current-initial)

• Relative daily food consumption

(daily food consumption/day/avg wt)



7

Statistical Analyses on Growth Parameters

Primary Purpose: examine compound-related effects

– Is there a treatment effect? monotonic or not?

=> Evaluation of dose-response relationship without time consideration

will be illustrated prior to the repeated measures analysis

– Is the treatment effect consistent across time?=> Evaluate dose-response relationship with time consideration



8

Examples of Dose-response CurvesFigure 1. No trend

Dose Level0 1 2 3 4 5

Me

an

Re

sp

on

se

299

300

301

302

Figure 2. Monotonic Trend


Me

an

Re

sp

on

se

250

300

350

400

450

500

550

600

650



Me

an

Re

sp

on

se

250

300

350

400

450

500

550

600

650

Figure 4. Nonmonotonic Response

Dose Level

0 1 2 3 4 5

Mean R

esp

onse

250

300

350

400

450

500

550

600

650



9

Evaluation of Dose-response Relationship Without Time Considerations

Is there a monotonic dose-response relationship?

Want to identify the highest no-effect dose

Reference: Tukey JW, Ciminera JL, Heyse JF. 1985. Testing the statistical certainty of a response to increasing doses of a drug. Biometrics 41:295-301.



10

Sequential Trend Test with ANOVA:HypothesesNotation:

d1, d2, ...dk - dose levels of a compound.response of the ith subject in the ith dose group

Model:

Yij = i + ij ij ~ iid N(0, ) , i = 1 to k, j= 1 to n i

Hypotheses:

Ho: i = for all i,

Ha: 1 < 2 < ...i... < k, at least one inequality

Test for trends: test if the contrast is 0, i.e.

where i may be on the log scale

ci determines different types of trends

k

iiic

1

0



11

Sequential Trend Test with ANOVA: Test Statistic

))(ˆ()(2

2

i

iii n

csqrtYcs

Under the null hypothesis of no trend, the t-statisticis distributed as t(N-k). N= total # of subjects, k= # of dose levels

)(~)(

kNtYcs

Ycstatistict

ii

ii



12

Sequential Trend Test with ANOVA: Decision Process

Start at the high dose. Is the p < .05 (= for the high dose trend?

No - Stop. No monotonic trend at the high dose.

Yes - Continue to the next lower dose.

Test for trend at the next lower dose with 0 coefficient for the

high dose.Is the trend p-value < .05?

No - Stop. No monotonic trend at this dose.

Yes - Continue…



13

Sequential Trend Test with ANOVA: Illustration with Body Weight Data



Mea

n R

es

po

ns

e

250

300

350

400

450

500

550

600

650

Trend test up to the highest dose (4th) p<0.05

Trend up to the next lower dose (3rd) p<0.05

Trend up to the next lower dose (2nd) p>0.05

Stop and conclude 2nd dose is a no effect dose level



14

Sequential Trend Test with ANOVA: Approach to Non-monotonicity

What if there is no monotonic dose-response relationship

at the high dose (p>.05)? Need to look for a nonmonotonic trend in the treatment means F-test ( = .01)

Dunnett's t-test comparing each treated group to control ( = .05)

Reference: Dunnett CW. 1964. New tables for multiple comparisons with a control. Biometrics 20:482-491.



15

No

Perform linear trend test (=.05) &

trt F-test (=.01)

STP

Yes

1-Factor ANOVA with Trend Test & Dunnett’s Test

1

PerformDunnett’s t-test

(=.05)

No

Yes

SOP

STOP

STOP

STOP

STOP

STOP

Was trend significant?

p<.05

Was trt F-testsignificant?

p<.01



16

Evaluation of Dose-response Relationship With Time Considerations

• Is there a monotonic dose-response relationship? How is the effect changing with time?

- identify the highest no-effect dose

- test for a monotonic effect in treatment means

- evaluate the time effect

- evaluate the interaction between time and dose

Same for non-monotonic effects



17

Sequential Trend Test with One-Factor Repeated Measures Analysis: Data

N animals in total, k dose levels (including control), M time intervals

Test both compound and time effects

Dose Level Animal Time 1 Time 2 Time 3 …...Control 0001 x x xControl 0002 x x x...Low 1001 x x xLow 1002 x x x……...High 4001 x x xHigh 4002 x x x…..



18

Sequential Trend Test with One-Factor Repeated Measures Analysis: Model

Linear Mixed Effects Model

Fixed: dose, time. Random: animal, error.

y = X + Z +

y = (yijk)

yijk = body weight of ith dose, jth time, kth animal

= fixed effects- dose, time, dose*time, (covariates)

= random effects- animal

= errors

N(0, G), N(0R)

and are independent



19

Sequential Trend Test with One-Factor Repeated Measures Analysis: SAS code

PROC MIXED DATA=ONE;

CLASS DOSE TIME ANIMAL;

MODEL Y= DOSE TIME DOSE*TIME COVARIATE/

DDFM=KNEWARDROGER;

{RANDOM INT/ SUBJECT=ANIMAL(DOSE);}

{{REPEATED TIME/TYPE=XXX SUBJECT=ANIMAL(DOSE);}}

ESTIMATE "LINEAR TREND in DOSE AT TIME 1"

DOSE -3 -1 1 3

DOSE*TIME -3 0 0 0.. -1 0 0 0.. 1 0 0 0.. 3 0 0 0..;

CONTRAST …..

Note:This works on long data (transpose time). Either { } or {{ }} is included for

different covariance structures.



20

Sequential Trend Test with One-Factor Repeated Measures ANOVA: Monotonicity

Look for a monotonic effect in treatment means

Linear trend test on treatment means ( = .05) - at each time point if at least one of the following is significant

(1) linear treatment trend by linear time trend ( = .05)(2) linear treatment trend by quadratic time trend ( = .05)(3) linear treatment trend by time ( = .01)

- on means pooled across all time points otherwise



21

Sequential Trend Test with One-Factor Repeated Measures ANOVA: non-monotonicity

What if there is no monotonic dose-response relationship?

Look for a nonmonotonic effect in treatment means Bonferroni adjusted t-test comparing each treated group to control ( = .05) - at each time point if treatment by time interaction F-test p<.01 - on means pooled across all time points if main treatment F-test p<.01

Reference: Miller RG, Jr. 1981. Simultaneous statistical inference. 2nd ed. New York: Springer-Verlag. p 67-69.



22

NoNo

Perform Interaction Tests: LinTrt*LinTime(=.05) LinTrt*QrdTime(=.05) LinTrt*Time(=.01)

Perform LinTrt (=.05) pooled across time

No Yes

STO STP

Yes

1-Factor Repeated Measures

Yes

1

PerformBonferroni-adjusted pair-wise t-tests

Pooled across time STOPNo

Yes

SOPNo

Yes

STOP

STOP

1

Perform LinTrt (=.05) at each time point

Any p <

Was trend significant?

P<.05STOP

PerformBonferroni-adjusted

pair-wise t-testsat each time point

Was Trt*Time p<.01?

1

WasTrt F-test significant?

P<.01

STOP

STOP

STOP

STOP

Perform Trt*Time F-test (.01) & Trt F-test(.01) pooled across time

Was any trend significant?

p<.05

Go To 1



23

Rodent Growth Data

Two rodent growth parameters are statistically analyzed

– Interval body weight adjusted for baseline weight– Interval daily relative food consumption

(Interval food consumption/day/avg wt)

Body weight gains: descriptive statistics and %change relative to control (ICH, 1995)



24

Analysis Phases

Statistical Analysis Phases

• Growth Phase up to 3 months ( 9 time intervals)

• Maintenance Phase the rest ( 9 time intervals)



25

Data Preparation

Consolidate time intervals

First Month: take all or weekly (t=2 to 4)Months 2-3: every 2 wks (t=4,5)Months 4-6: every 4 wks (t=3)Months 7-12: every 3 mos (t=2)Months 13-24: every 3 mos (t=4)

t: number of time points



26

Example: Mouse Body Weights

27 Body Weight Summary During Treatment Study: MOUSE1A Compound: See Study Protocol Analysis Framework: 1-factor Repeated Measures ANOVA Route: IM Test System: CD1 Mouse Primary Factor: Treatment Group Code Study Type: Sex: Male Time Factor: Day on Study [--------------------------------------------Int BW g--------------------------------------------] Statistic Overall DAY 6 DAY 13 DAY 20 DAY 27 DAY 41 DAY 55 DAY 69 DAY 83 DAY 97 0 Mean NA 29.965 31.347 32.583 33.433 34.143 35.469 36.388 37.256 37.862 SD NA 1.811 1.898 2.053 2.108 2.211 2.494 2.506 2.696 2.848 N NA 60 60 60 60 60 60 60 60 60 LSMean NA 30.288 31.669 32.906 33.756 34.466 35.791 36.711 37.579 38.184 1 Mean NA 30.325 31.798 32.937 34.058 34.737 36.024 36.949 37.718 38.253 SD NA 2.074 2.213 2.368 2.486 2.495 2.668 2.892 3.139 3.310 N NA 60 60 60 60 60 60 60 60 60 LSMean NA 30.025 31.498 32.636 33.758 34.437 35.724 36.649 37.418 37.952 Linear Trend p-value# NA NT NT NT NT NT NT NT NT NT 2 Mean NA 30.075 31.678 32.985 34.052 34.798 36.079 36.903 37.661 38.132 SD NA 2.220 2.497 2.668 2.803 2.884 3.069 3.396 3.626 3.795 N NA 60 60 60 60 60 60 60 60 60 LSMean NA 29.801 31.404 32.711 33.777 34.524 35.805 36.629 37.387 37.858 Linear Trend p-value# NA 0.108 0.381 0.519 0.944 0.849 0.965 0.786 0.525 0.281 3 Mean NA 27.308 28.615 29.660 30.630 31.198 32.333 33.114 33.687 34.018 SD NA 2.093 2.194 2.232 2.308 2.326 2.335 2.361 2.313 2.342 N NA 60 60 60 60 60 60 60 60 60 LSMean NA 27.560 28.867 29.912 30.882 31.450 32.585 33.367 33.939 34.270 Linear Trend p-value# NA <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* INTN LinPrmy*Time p-val++ <0.001* LinPrmy*LinTime p-val+ <0.001* LinPrmy*QdrTime p-val+ 0.015* -------------------------------------------------------------------------------------------------------------------------------- # : Level of significance tested = .05; Two-sided test. ++ : Level of significance tested = .01. + : Level of significance tested = .05. * : Statistically significant. NT : Not tested. NA : Not available. BW Baseline was used as a covariate for: Int BW. NOT APPROVED FOR FINAL SUBMISSION. DATA IS NOT APPROVED FOR FINAL SUBMISSION.

28

Body Weight Summary During Treatment Study: MOUSE1A Compound: See Study Protocol Analysis Framework: 1-factor Repeated Measures ANOVA Route: IM Test System: CD1 Mouse Primary Factor: Treatment Group Code Study Type: Sex: Male Time Factor: Day on Study [---------------------------------------Int BW g---------------------------------------] Statistic Overall DAY 125 DAY 153 DAY 181 DAY 272 DAY 363 DAY 454 DAY 545 DAY 622 0 Mean NA 38.642 39.703 40.169 41.732 42.854 42.272 41.737 40.936 SD NA 3.071 3.315 3.526 4.182 4.508 4.358 4.408 4.296 N NA 60 59 59 57 53 53 46 36 LSMean NA 39.041 40.119 40.585 42.173 43.199 42.617 42.253 41.452 1 Mean NA 39.111 39.895 40.513 41.831 43.073 42.852 42.528 42.177 SD NA 3.599 3.997 4.344 5.194 5.750 6.184 6.392 6.024 N NA 60 60 60 60 59 57 51 46 LSMean NA 38.690 39.474 40.092 41.410 42.521 42.197 41.795 41.272 Linear Trend p-value# NA NT NT NT 0.227 0.286 0.510 0.480 0.788 2 Mean NA 38.785 39.425 39.851 40.940 41.230 41.141 40.481 39.516 SD NA 4.125 4.350 4.515 5.119 5.636 6.211 5.654 4.991 N NA 60 60 59 59 59 53 46 43 LSMean NA 38.398 39.038 39.385 40.474 40.764 40.654 40.251 39.307 Linear Trend p-value# NA 0.306 0.086 0.057 0.007* <0.001* 0.002* 0.002* 0.001* 3 Mean NA 34.452 35.004 35.252 35.837 36.025 35.875 35.879 35.564 SD NA 2.259 2.322 2.384 2.406 2.723 2.855 2.686 2.657 N NA 59 59 58 56 53 42 40 32 LSMean NA 34.781 35.333 35.600 36.093 36.235 36.293 36.148 35.868 Linear Trend p-value# NA <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* <0.001* INTN LinPrmy*Time p-val++ <0.001* LinPrmy*LinTime p-val+ <0.001* LinPrmy*QdrTime p-val+ <0.001* -------------------------------------------------------------------------------------------------------------------------------- # : Level of significance tested = .05; Two-sided test. ++ : Level of significance tested = .01. + : Level of significance tested = .05. * : Statistically significant. NT : Not tested. NA : Not available. BW Baseline was used as a covariate for: Int BW. NOT APPROVED FOR FINAL SUBMISSION. DATA IS NOT APPROVED FOR FINAL SUBMISSION.

29

Mean Body Weight (Interval)Gender=Male

GROUP 0 1 2 3

BO

DY

WE

IGH

T (

g)

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

DAY

-1

13

27

41

55

69

83

97

111

125

139

153

167

181

195

209

223

237

251

265

279

293

307

321

335

349

363

377

391

405

419

433

447

461

475

489

503

517

531

545

559

573

587

601

615

629



30

Analysis summary

• Body weight– Key time intervals (interval body weight)– Include all non-missing interval data– Baseline weight as a covariate– Two analysis phases– Covariance structure (historical control/current data)– Report %change of body weight gain relative to control (ICH, 1995)

• Food consumption– Key time intervals (interval daily food consumption)– Relative not absolute food consumption – Include all non-missing interval data– Two analysis phases– Covariance structure (historical control/current data)



31

General Strategy• No change proposed for body weight and food

consumption collection schedule

• Analyze key parameters: body weight and relative food consumption

• Identify key time points/intervals

• Perform appropriate/efficient statistical analyses

• Benefits– fewer statistical tests– fewer false positives– Succinct yet comprehensive interpretation of treatment

effects



32

Summary

• Perform repeated measures analysis on growth data measured across time in two analysis phases

• Implementation tools-one step at a time

• Regulatory acceptance

ReferenceAnalysis of Rodent Growth Data in Toxicology Studiesby Wherly P. Hoffman, Daniel Ness, and Robert van LierToxicological sciences 66, 313-319 (2002)



33

Daniel Ness Bob van LierCindy Lee Kathy PirooziKarl Lin Ray CarrollWendell Smith Mike DoratoGerald Long Mary Jeanne KallmanJudy Hoyt Patrick CockeSusan Christopher

For [email protected]

Acknowledgements

Evaluation of Live Phase Results from Carcinogenicity Studies Wherly Hoffman, Ph.D. Statistics and...

Documents

Transcript of Evaluation of Live Phase Results from Carcinogenicity Studies Wherly Hoffman, Ph.D. Statistics and...