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Keaven Anderson, Ph.D.

Amy Ko, MPH

Nancy Liu, Ph.D.

Yevgen Tymofyeyev, Ph.D.

Merck Research Laboratories

June 9, 2010June 9, 2010

Information-Based Sample SizeRe-estimation for Binomial Trials

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Objective: Fit-for-purpose sample-size adaptation

Examples here restricted to binary outcomes Wish to find sample size to definitively test for

treatment effect ≥ min

Minimum difference of clinical interest, min, is KNOWN

May be risk difference, relative risk, odds-ratio Do not care about SMALLER treatment differences

Desire to limit sample size to that needed if ≠ min

Control group event rate UNKNOWN Follow-up allows interim analysis to terminate

trial without ‘substantial’ enrollment over-running

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Case Study 1 CAPTURE Trial (Lancet, 1997(349):1429-35)

Unstable angina patients undergoing angioplasty 30-day cardiovascular event endpoint Control event rate may range from 10%-20% Wish 80% power to detect min = 1/3 reduction

(RR)

0.10 0.12 0.14 0.16 0.18 0.20

1000

1400

1800

2200

Control event rate

Sa

mp

le s

ize

fo

r 8

0%

po

we

r

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Case Study 2

Response rate study Control rate may range from 10% to 25% min = 10% absolute difference

0.10 0.15 0.20 0.25 0.30 0.35

600

700

800

900

1000

Control event rate

Sa

mp

le s

ize

fo

r 9

0%

po

we

r

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Can we adapt sample size? Gao, Ware and Mehta [2010] take a conditional power

approach to sample size re-estimation Presented by Cyrus Mehta at recent KOL lecture Would presumably plan for null hypothesis 0 > min

and adapt sample size up if interim treatment effect is “somewhat promising”

Information-based group sequential design

1. Estimate statistical information at analysis (blinded)

2. Do (interim or final) analysis based on proportion of final desired information (spending function approach)

3. If max information AND max sample size not reached– If desired information likely by next analysis, stop there– Otherwise, go to next interim– Go back to 1.

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Fair comparison?

The scenarios here are set up for information-based design to be preferred Other scenarios may point to a conditional power

approach Important to distinguish your situation to choose

the appropriate method! Scenarios where the information-based approach

works well are reasonably common Blinded approaches such as information-based

design are considered “well-understood’’ in the FDA draft guidance

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Information-based approach

Enroll patients continuously

Estimate current information

Analyze data

Estimate information @ next analysis

Go to final(may adapt) Go to next IA

Stop if done

Stop enrollment

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Example adaptation

200

325

200

200

275

200

334

525

200 200 300

Actual n

Observed

information

Planned n

A1

A2

A3

A4

A5

Target

Information is re-scaled

Adapted up to finish

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Estimating information: Notation

grouperimentalinproportion

sizesampleoveralln

_exp__

__

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Variance of (Note: =proportion in Arm E)

General formula

Absolute difference ( = pC – pE)

Relative risk ( = log(pE / pC ))

nVar /)ˆ( 2

/)1()1/()1(2EECC pppp

E

E

C

C

p

p

p

p )1(

)1(

)1(2

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Estimating variance and information

nraV /ˆ)ˆ(ˆ 2

Event rates estimated Assume overall blinded event rate Assume alternate hypothesis Use MLE estimate for treatment group

event rates (like M&N method) Use these event rates to estimate

Statistical information

21 ˆ/)ˆ(ˆ nraVI

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13

14

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CAPTURE information-based approach

Plan for maximum sample size of 2800 Analyze every 350 patients At each analysis

Compute proportion of planned information Analyze Adapt appropriately

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17

18

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Case Study 2

Response rate study Control rate may range from 10% to 25% min = 10% absolute difference

0.10 0.15 0.20 0.25 0.30 0.35

600

700

800

900

1000

Control event rate

Sa

mp

le s

ize

fo

r 9

0%

po

we

r

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Execution of the IA Strategy:Conditional power approach of Gao et al

Interim Analysis, calculate: • Rate Difference

Stop for futility

Diff<3.86%†

3.86%≤Diff<16.7%

Stop for efficacy

Diff≥16.7%‡

†Corresponding to a CP of 15%; ‡Corresponding to a P<0.0001.

Continue

Re-estimate Sample Size

CP<0.35 or CP> 0.85

0.35≤CP≤0.85

Compute Conditional Power

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Overall Power of the Study IA without SSR and IA with SSR

• Initial sample size is 289 in each case.• Maximum possible sample size is 578 (2 times of 289, cap of the SSR)

NSAIDS Response

Rate

DrugAResponse

Rate

gsDesign (Efficacy, Futility)

Adaptive (gsDesign+SSR)

E(N) †

/Group Power E(N) †

/Group Power

10% 20%

15% 25%

20% 30%

25% 35%

† E(N) = expected sample size, which is the average of the sample size for such a design. The actual sample size the study might end up with varies.

90.0%90.0% 92.4%92.4%278278

82.6%82.6%

78.2%78.2%

73.3%73.3%

86.8%86.8%

81.9%81.9%

78.0%78.0%

303303

273273

269269

266266

305305

306306

304304

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Information-based approach

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Information-based approach

Maximum sample size of 1100 Plan analyses at 200, 400, 600, 800, 1100

Adapt assume targetmin = .10 Absolute response rate improvement

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Some comments

Computations performed using gsDesign R package Available at CRAN For CAPTURE example, 10k simulations were

performed for a large # of scenarios– Parallel computing was easily implemented using

Rmpi (free) or Parallel R (REvolution Computing) For smaller # of scenarios used for 2nd case study,

sequential processing on PC was fine My objective is to produce a vignette making this

method available

Technical issues Various issues such as over-running and

“reversing information time” need to be considered

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Objective: Fit-for-purpose sample-size adaptation

Examples here restricted to binary outcomes Wish to find sample size to definitively test for

treatment effect ≥ min

Minimum clinical difference of interest, min, is KNOWN

May be risk difference, relative risk, odds-ratio Do not care about SMALLER treatment differences

Desire to limit sample size to that needed if ≠ min

Control group event rate UNKNOWN Follow-up allows interim analysis to terminate

trial without ‘substantial’ enrollment over-running

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Summary

Information-based group sequential design for binary outcomes is Effective at adapting maximum sample size to

power for treatment effect ≥ min

Group sequential aspects terminate early for futility, large efficacy difference

Results demonstrated for absolute difference and relative risk examples

If you can posit a minimum effect size of interest, this may be an effective adaptation method