Venita DePuy, PhD Bowden Analytics } Pr Pre-pl planned (a d (and - - PowerPoint PPT Presentation

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Venita DePuy, PhD Bowden Analytics } Pr Pre-pl planned (a d (and - - PowerPoint PPT Presentation

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Venita DePuy, PhD Bowden Analytics } Pr Pre-pl planned (a d (and pr d pre-speci cified!) looks at the da data a at s spe pecific i interva vals } If If da data i is o ove verwhelmingl gly go good (o d (or ba bad), i d), it ma

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Venita DePuy, PhD Bowden Analytics

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PhUSE Connect 05June2018 Bowden Analytics

} Pr

Pre-pl planned (a d (and pr d pre-speci cified!) looks at the da data a at s spe pecific i interva vals

} If

If da data i is o

  • ve

verwhelmingl gly go good (o d (or ba bad), i d), it ma may w warra rrant nt st stopping ng t the he t tri rial

} Many

Many different erent ap appro roac aches hes: O’Bri Brien en-Fl Fleming, Po Pocock, La , Lan-De DeMets ap appro roac aches hes to tho hose, e, and and many any others hers

} We

We w will u use L Lan-De DeMets ap appro roac ach h to O’B O’B-F

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PhUSE Connect 05June2018 Bowden Analytics

} Sa

Sample e Si Size e Calculations

} In

Interim A Analysis De Design gn

} Pe

Performing the Interim Analysis

  • Analysi

sis s (PROC LI LIFETEST, , PH PHREG EG)

  • Interim Analysi

sis

} Ca

Can be perfor

  • rmed in SAS, EAST,

T, PASS, and

  • th
  • thers
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PhUSE Connect 05June2018 Bowden Analytics

} SAS

  • Calculate sample size & boundaries for interim: Proc Seqdesign
  • Survival calculation: Proc Lifetest or PHReg
  • Interim analysis in Proc Seqtest (bring in data from Seqdesign and

Lifetest/PHReg)

} EAST

  • Point & click interfaces
  • Many options for sample size & boundary calculations
  • Perform survival analysis
  • Enter parameter estimates (δ) calculated earlier to perform interim

analysis

  • Many output options (graphs)

} PASS

  • Point & click interface for sample size & boundaries
  • Separate software required for interim analysis
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PhUSE Connect 05June2018 Bowden Analytics

} Treatment Arms A (active) and B (control)

  • Randomized 1:1

} Primary Endpoint is Increase in Lab X Value

past a predetermined threshold

  • Expect median time to hit threshold to be 20 days in

treatment A and 30 days in treatment B

} Slow enrollment: 50 subjects every 6 months } 6 month duration of study (censored after) } Testing whether duration differs between

treatments

  • H0: θ = 0 against Ha: θ ≠ 0 where θ = - ln (λ), and λ is

the hazard ratio

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proc power; twosamplesurvival test=logrank alpha=0.05 groupmedsurvtimes=(20 30) npergroup=. accrualtime=730 followuptime=180 power=.80; run;

6 month f/up = 180 days

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proc seqdesign boundaryscale=StdZ; OverallStudy: Design nstages=1 alpha=0.05 beta=.2; Samplesize model=TWOSAMPLESURVIVAL (medsurvtime=20 nullmedsurvtime=30 ref= hazard accrual=uniform acctime=730 foltime=180); run;

Default is standardized Z scale 1 stage = no interim analysis

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PhUSE Connect 05June2018 Bowden Analytics

Sa Sample e Si Size e Su Summary Te Test Two-Sample Survival Nu Null Hazard Rate 0.023105 Ha Haza zard Rate (Group A) A) 0.034657 Ha Haza zard Rate (Group B) 0.023105 Ha Haza zard Ratio 1.5 lo log(H (Hazard R Ratio io) 0.405465 Re Reference Hazards Alt Ref Ac Accrual Uniform Bo Boundary In Information (St Standardized ed Z Sca Scale) e) Nu Null Reference = 0

_S _Stage_

Alternative Boundary Values Information Level Reference Lower Upper Proportion Actual Events Lower Upper Alpha Alpha

1

1.0000 47.74201 190.968 -2.80159 2.80159 -1.95996 1.95996 Sa Sample e Si Size e Su Summary Ac Accrual Rate 0.261731 Ac Accrual Time 730 Fo Follow-up up Time 180 Tot Total Ti Time 910 Max Number er of f Even ents 190.968 Max Sa Sample e Si Size 191.0639 Ex Expected Sample Size (Null Re Ref) 191.0639 Ex Expected Sample Size (Alt Re Ref) 191.0639

  • θ1 =

I0 is based on α, β, θ1 ±1.96

± θ1Ö I0

  • vs. 198

from Proc Power

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PhUSE Connect 05June2018 Bowden Analytics

proc seqdesign boundaryscale=stdz ALTREF = -0.40547; TwoSidedOBF_Lan: design nstages=2 alpha=0.05 beta=.2 method=errfuncOBF info=cum(85 198) stop=both (betaboundary=nonbinding);

  • ds output Boundary=BoundZ;

run;

θ1 = -ln (30/20) = -0.40547 Analyses at 85 & 198 subjects

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PhUSE Connect 05June2018 Bowden Analytics

Almost 1.96

De Design In Information (sel elec ect rows) Bo Boundary Sca Scale Standardized Z Ea Early Stop

  • p

Accept (Nonbinding)/ Reject Null Met ethod Error Spending Nu Number of Stages 2 Al Alpha (Binding Beta Boundary) 0.04712 Al Alpha (Nonbinding Beta Boundary) 0.05 Max Info formation (Per ercen cent of f Fixed ed Sa Sample) e) 104.9799 Max Info formation 50.1183 Nu Null Ref ASN N (Percent of Fixe xed Sample) 88.39329 Al Alt Ref AS ASN (Percent of Fixed Sample) 96.62317 _S _Sta tage_ Bo Boundary In Information (St Standardized ed Z Sca Scale) e) No Nonbinding Beta Boundary, Nu Null Reference = 0 Alternative Boundary Values Information Level Reference Lower Upper

Proportion

Actual Lower Upper Alpha Beta Beta Alpha 1 0.4293 21.5154 -1.8808 1.8808 -3.2276 -0.3526 0.3526 3.2276 2 1.0000 50.118

  • 2.8705 2.8705 -1.9636 -1.9636

1.9636 1.9636

Very stringent at interim

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PhUSE Connect 05June2018 Bowden Analytics

Stage 2: Final Analysis (I=50.12) Stage 1: Interim Analysis (I=21.52)

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proc lifetest data=samp; time mTIME*CENSOR(1); test TRT;

  • ds output logunichisq=PARMS;

run; PA PARMS da dataset:

Var ariab able St Statistic St StdErr Ch ChiSq Pr ProbChiS iSq tr trt 4.6995 4.0794 1.3271 0.2493 Randomly generated data N=85

Exponential distributions 20% censored at mean 14d Subjects on study censored at 180d

Results 38 in Trt A (1), 47 in Trt B (2) 5 & 8 censored respectively Mean time in uncensored=22.4, 28.5d

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} Proc Seqdesign with output in

correct units

  • Score statistic for Proc Lifetest
  • MLE for Proc PHReg

} Perform survival analysis (Lifetest or

PHReg)

} Proc Seqtest to combine results

from both

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proc seqdesign boundaryscale=SCORE altref = -0.40547; TwoSidedOBF_Lan: design nstages=2 alpha=0.05 beta=.2 method=errfuncOBF info=cum(85 198) stop=both (betaboundary=nonbinding);

  • ds output Boundary=BoundS;

run;

Pr Proc Li Lifetest Pa Parameter Out Output ut Mani nipul ulation

data PARMSs (keep = VARIABLE _SCALE_ _STAGE_ STDERR ESTIMATE); set PARMS (rename=(Statistic=Estimate)); if VARIABLE='TRT'; _SCALE_='Score'; _STAGE_=1; run;

If If using Proc PH PHReg… Limit to PARAMETER=‘TRT’, no rename statement, _SCALE_=‘MLE’

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proc seqtest boundary=BoundS parms(Testvar=trt) = parmsS infoadj=prop boundaryscale=Score;

  • ds output test=testS;

run;

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Te Test Inf nformation n (Score Scale) Nu Null Reference = 0 _S _Stage_ e_ Alternative Boundary Values Test Information Level Reference Lower Upper TRT Proportion Actual Lower Upper Alpha Beta Beta Alpha Estimate Action 1 0.3320 16.6411

  • 6.74747

6.74747

  • 13.4636

. . 13.46356 4.69946 Continue 2 1.0000 50.1183

  • 20.3215

20.3215

  • 14.0831
  • 14.0831

14.0831 14.0831 .

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PhUSE Connect 05June2018 Bowden Analytics _S _Stage_ Bo Boundary Information (S (Score Sc Scale le) Non Nonbinding g Beta ta Bou

  • undary, Nu

Null Reference = 0 Alternative Boundary Values Information Level Reference Lower Upper

Proportion

Actual Lower Upper Alpha Beta Beta Alpha 1 0.4293 21.51543

  • 8.72386

8.72386

  • 14.97129
  • 1.63544

1.63544 14.97129 2 1.0000 50.1183

  • 20.32147

20.32147

  • 13.90099
  • 13.90099

13.90099 13.90099 Te Test In Informa mation (Score Scale) Nu Null Reference = 0 _S _Stage_ Alternative Boundary Values Test Information Level Reference Lower Upper TRT

Proportion

Actual Lower Upper Alpha Beta Beta Alpha Estimate Action 1 0.3320 16.6411 -6.74747 6.74747 -13.4636 . . 13.46356 4.69946 Continue 2 1.0000 50.1183 -20.3215 20.3215 -14.0831 -14.0831 14.0831 14.0831 .

Plan anned Ac Actual al

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Default values (not yet changed)

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PhUSE Connect 05June2018 Bowden Analytics Nu Numeric Re Results for Tw Two-Sid Sided Lo Logrank Te Test (Assumi ming Exponential Survival) To Total To Total Sa Sample le Re Required Pr Proportion Pr Proportion Ha Hazard Po Power Siz Size (N) Ev Events Al Alpha Be Beta Su

  • Surv. (

. (S1) Su

  • Surv. (

. (S2) Ra Ratio 0.941273 198 191 0.050000 0.058727 0.0098 0.0625 0.6000

Su Summary St Statements A total sample size of 198 (split equally between the two groups), or 191 events, achieves 94% power to detect a hazard rate of 0.6000 when the proportions surviving in each group are 0.0098 and 0.0625 at a significance level (alpha) of 0.050000 using a two-sided log rank test. These results assume that 2 sequential tests are made using the O'Brien-Fleming spending function to determine the test boundaries and that the survival times are exponential. Details when Spending = O'Bri rien-Fl Fleming, N = 198, d = 191, S1 = 0.0098, S2 = 0.0625

Lo Lower Up Upper Nom Nominal Inc Inc To Total Inc Inc To Total Lo Look Ti Time me Inf Info Bn Bndry Bn Bndry Al Alpha Al Alpha Al Alpha Po Power Po Power 1 85.0000

  • 3.22763

3.22763 0.001248 0.001248 0.001248 0.179880 0.179880 2 198.0000 1

  • 1.96357

1.96357 0.049580 0.048751 0.050000 0.761393 0.941273 Drift 3.52838

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PhUSE Connect 05June2018 Bowden Analytics

} SAS Proc Power and Proc Seqdesign may give

different overall sample size calculations (different algorithms)

} Interim analysis design similar between SAS

Proc Seqdesign, EAST, and PASS

} SAS and EAST will perform interim analyses

but need additional software from PASS manufacturer to perform it

} Estimated information levels & cutoffs change

between design & analyses (censoring)

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PhUSE Connect 05June2018 Bowden Analytics Te Test In Informa mation (Score Scale) Nu Null Reference = 0 _S _Stage_ Alternative Boundary Values Test Information Level Reference Lower Upper TRT

Proportion

Actual Lower Upper Alpha Beta Beta Alpha Estimate Action 1 0.4115 20.6222

  • 8.36169 8.36169
  • 14.7122 -1.44551 1.44551

14.7122 3.71791 Continue 2 1.0000 50.1183

  • 20.3215 20.3215
  • 13.9038 -13.9038 13.9038

13.9038 .

  • 103

103 pts = 85 85 not censored

  • St

Still ill not 0.4293 of in info

  • In

Interim b m bou

  • undar

aries n not

  • t ±1.

1.635 635 & & ±14. 14.97 97

  • Fi

Final boundaries es close e but not ex exact (±13. 13.90099) 90099)

  • Mi

Middle of f graph do does sho show

  • St

Still ill contin inue

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PhUSE Connect 05June2018 Bowden Analytics } Changed Trt A mean

duration to 10 days (vs 30d) in dummy trial

(previously 20d vs 30d)

} Graph shows dot in

rejection region

} Action=“Reject Null” Te Test In Informa mation (Score Scale) Nu Null Reference = 0 _S _Stage_ Alternative Boundary Values Test Information Level Reference Lower Upper TRT

Proportion

Actual Lower Upper Alpha Beta Beta Alpha Estimate Action 1 0.2598 13.0219

  • 5.28000

5.28000

  • 12.156

. . 12.156 13.9049 Reject Null 2 1.0000 50.1183

  • 20.3215

20.3215

  • 14.081
  • 14.081

14.081 14.081 .

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} Changed Trt A mean

duration to 29 days (vs 30d) & removed censoring in dummy trial

(previously 20d vs 30d) } Graph shows dot in

rejection region

} Action=“Accept Null”

Te Test In Informa mation (Score Scale) Nu Null Reference = 0 _S _Stage_ Alternative Boundary Values Test Information Level Reference Lower Upper TRT

Proportion

Actual Lower Upper Alpha Beta Beta Alpha Estimate Action 1 0.4128 20.6891

  • 8.3888

8.3888

  • 14.732
  • 1.4592

1.4592 14.732

  • 1.45914

Accept Null 2 1.0000 50.1183

  • 20.3215

20.3215

  • 13.904
  • 13.904

13.904 13.904 .

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} After performing an interim analysis, you

need to adjust the final analysis for “double dipping”

} With a single interim analysis, typically very

small adjustment

} Multiple interims can result in large

adjustments (final results must be more significant)

} In SAS: Perform same steps (Seqdesign,

Lifetest, Seqtest), indicating that parameter values from Lifetest are for _STAGE_ = 2

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} Virtually every study has dropout and resulting

censoring of time-to-event data

} Cutoff values are likely to change between interim

analysis design and actual interim analysis

} Clearly specify how analysis will be performed

(which method, etc.) but avoid stating specific boundary values in protocol or SAP

} Consider stating that interim analysis will be

performed after information is available on “approximately xx subjects” or “after xx subjects have completed xx time on study or withdrawn from study”

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PhUSE Connect 05June2018 Bowden Analytics

Comments welcomed: bowden.analytics@gmail.com