The document discusses a design paradigm for assessing defensive efficacy in clinical trials using the concept of probability of success (POS), emphasizing dynamic decision-making and benefit/risk assessment as mandated by FDA and EMA guidelines. It outlines various types of POS calculations and their applications in interim analysis, detailing the importance of statistical evidence and ethical considerations in drug development. Key takeaways include the adaptability of POS in design modifications and the impact of newly emerged safety signals on efficacy declarations.

1. Defensive E¢ cacy IA Design:
dynamic bene…t/risk assessment
using probability of success (POS)
Zhongwen Tang

2. Outline
Motivation
POS (probability of success) supported defensive e¢ cacy IA design
– Design paradigm
– POS calculation
– Dynamic decision making
Numerical example
Take home messages

3. HA: Bene…t/risk assessment
FDA: Assessments of a products bene…ts and risks involves an analysis of the severity
of the condition treated and the current treatment options available for the given
disease (FDA PDUFA V, 2013).
EMA: The assessment of the bene…ts and risks in the context of a new drug ap-
plication must reach, as objectively as possible, a su¢ cient level of con…dence that
a set level of quality, e¢ cacy, and safety of the new medical product has been
demonstrated (CHMP bene…t-risk re‡ection paper, 2007).

4. HA: e¢ cacy IA
FDA: It is important to bear in mind that early termination for e¢ cacy should
generally be reserved for circumstances where there is the combination of compelling
ethical concern and robust statistical evidence" (FDA adaptive design guidance,
2010).
EMA: To argue for design modi…cations in a phase III trial (...) is then a contradic-
tion to the con…rmatory nature of such studies and will be rarely acceptable without
further justi…cation ... (CHMP adaptive design re‡ection paper, 2007)

5. Spending functions vs POS
Current e¢ cacy IA group sequential designs are based on alpha spending.
– Spending function only has e¢ cacy component.
– Spending function choice is arbitrary.
– Static
Propose to use probability of success (POS) to design e¢ cacy IA
– ‡exible success criteria to incorporate safety, severity of disease and other com-
poents
– link e¢ cacy IA to …nal design
– Dynamic

6. POS is a random variable
Power
– Conditional power: probability of observing statistical signi…cance in the …nal analysis given the
obsrerved data and the treatment e¤ect parameter equals to a speci…c value.
– Predictive power: probability of observing statistical signi…cance in the …nal analysis given the
obsrerved data.
Probability of success (POS)
– Conditional probability of success (CPOS): probability of success in terms of estimated treatment
e¤ect in the …nal analysis given the observed data and the treatment e¤ect parameter equals
to a speci…c value.
– Predictive probability of success (PPOS): probability of success in terms of estimated treatment
e¤ect in the …nal analysis given the observed data.
– Posterior probability of success (OPOS): probability of success in terms of the treatment e¤ect
parameter given the observed data

7. Defensive Decision Rule for E¢ cacy IA
f
center of POS() cut1
100th POS percentile () cut2
for declaring e¢ cacy
where cut1 > cut2 are values close to 1. is a value close to 0.
POS can be PPOS or CPOS

8. Defnesive POS Optimal Design
Finding the optimal design is equivalent to …nd the solution to the following equations
with respect to the design parameters.
f
center of POS() = cut1
100th POS percentile () = cut2

9. Types of POS
Type of data: binary, normal, time to event
Function:
– Inference: Make inference about general population using trial data.
– Predictive: Use available data to predictive future analysis.
Relationship between the trial providing data and the trial to be predicted
cross trial: using data from one trial to predict another independent trial
within trial: using IA to predict …nal anlaysis
Relationship between the end point providing information and the end point to be predicted
1:1 Using 1 end point to predict same end point
1:1 Using 1 end point to predict di¤erent end point

10. Within Trial Predictive POS
End point: time to event
Parameter of interest: ln (HR)
^(t) is the estimated ln (HR) at the interim analysis
^ (t) j ~N ; 2
1 = 1= (r (1 r) d)
d is the number of events at the time of interim analysi t.
where r is the randomization ratio

11. Within Trial Predictive POS
Assume a Gaussian prior ln (HR) = ~N 0; 2
0 = 1= (r (1 r) d0)

12. Within Trial Predictive POS
The posterior distribution is
j^ (t) ~N '^ (t) + (1 ') 0; 2
0 (1 ')
where ' = 1 +
2
1
2
0
1
=
2
0
2
0+ 2
1

13. Within Trial CPOS
Under proportional hazard assumption
CPOS( ) = P (Z(1) < j ) = P ^ < where 2 = 1=(r (1 r) dmax)
Z =
p
tZ (t) +
p
1 t
p
dmaxZ(1)
p
dZ(t)p
dmax d
and Z(1) have same distribution.
CPOS( ) =
p
tz(t)p
1 t
q
r (1 r) (dmax d)
where z(t) = ^ (t) = 1, dmax is the total number of events in the …nal analysis. (:)
is the CDF of standard normal distribution.

14. CPOS Credible Interval
median CPOS=mCPOS = CPOS(median of )
low percentile (width of CI): 100 percentile of
CPOS = CPOS((1 ) 100 percentile of ).
mCPOS and 100th CPOS percentile is an equivalent statistic of observed
hazard ratio and number of events.

15. PPOS and Credible Interval
PPOS ^ (t) =
0
B
@
p
tz(t)p
1 t
=
p
r(1 r)(dmax d)
h
'^(t)+(1 ') 0
i
q
2
0(1 ')+ 2
2
1
C
A where 2
2 =
1=(r (1 r) (dmax d))
median PPOS=mPPOS ^ (t) =
0
B
@
p
tz(t)p
1 t
=
p
r(1 r)(dmax d)
h
'^(t)+(1 ') 0
i
q
2
0(1 ')+ 2
2
1
C
A
low percentile (width of CI): 100 percentile of
PPOS = PPOS ((1 ) 100 percentile of ).
mPPOS and 100th PPOS percentile is an equivalent statistic of observed
hazard ratio and number of events.

16. Decision making is dynamic
Big registration trials often involve protracted decision making.
Drug development landscape changes quickly.
Long term and rare adverse events may only emerge after the exploratory stage.

17. Time to treatment failure
TTF=min(TTE, TTS).
TTE: time to e¢ cacy failure
TTS: time to safety failure
TTF: time to treatment failure.
Assuming exponential distribution: HRTTE HRTTF 1e= 2c.
For the experimental arm, TTS ~exp( 1e) and TTE ~exp( 2e).
For the control arm, TTE ~exp( 2c).

18. Success adjustment
= + 1e= 2c.
: HR success cuto¤ of e¢ cacy end point TTE
: HR success cuto¤ of composite end point TTF

19. Example
Primary end point: PFS (progression free survival)
Sample size: 324 events in …nal analysis.
Randomization ratio: 1:1
Success criteria at design stage: HR 2=3 (clinical meaningful) in the …nal
analysis.
Prior information
– Non-informative prior: prior variance = in…nity (equivalent to 0 event)

20. Example: optimal defensive e¢ cacy interim design
When the following 2 conditions must be satis…ed to declare e¢ cacy.
1. mCPOS 99%.
2. 10th percentile of the CPOS is 95%.
Optimal e¢ cacy IA design:t = 0:78; d1 = 253 and cuto¤ HR at IA to be 0:59.

21. Optimal e¢ cacy interim design

22. Defensive e¢ cacy interim design

23. Example: defensive design with newly emerged safety signal
The time to the grade3/4 QT prolongation has approximate exponential distribution
with rate parameter equals to 0.0052 ( 1e = 0:0052).
The median PFS of the control arm is estimated to be 9 month ( 2c = log(2)=9 =
0:077).
To o¤set the QT toxicity, the cuto¤ HR of PFS to declare success in the …nal
analysis is adjusted from 2/3 ( HR = 2=3) to 0.6 ( HR = 0:6).
Optimal e¢ cacy IA design:t = 0:78 and cuto¤ HR at IA to be 0:53.

24. Take home messages
POS is an information dependent statistic.
POS defensive design can faciliate buying from HAs when the submission is based
on IA data.

25. Reference
CHMP adaptive design re‡ection paper, 2007, London, UK, European Medicines Agency,
Re‡ection paper on methodological issues in con…matory clinical trials planned with an
adaptive designs. http://www.ema.europa.eu/docs/en_GB/document_library/
Scienti…c_guideline/2009/09/WC500003616.pdf
Dubey SD, Chi GYH, and Kelly RE, the FDA and IND/NDA statistical review process,
statistics in the pharmaceutical industry, 3rd ed. edited by Buncher CR and Tsay J,
2006, p55-78.
EMA Bene…t-risk methodology project: work package 2 report: applicability of current
tools and processes for regulatory bene…t-risk assessment. 2010, http://www.ema.europa.eu/
docs/en_GB/document_library/Report/2010/10/WC500097750.pdf
FDA Adaptive design Guidance for Industry: Adaptive Design Clinical Trials for Drugs
and Biologics, 2010
FDA PDUFA V draft implementation plan: structured approach to bene…t-risk assess-
ments in drug regulatory decision-making. 2013

26. Reference
Tang, Z. Dey, J. (2011). Bayesian PPOS design for clinical trials. PaSIPHIC anual
meeting.
Tang Z, (2015), PPOS design, slideshare. http://www.slideshare.net/ZhongwenTang/ppos-
design-48730837
Tang, Z. (2015). Optimal futility interim design: a predictive probability approach with
time to event ene point. Journal of Biopharmaceutical Statistics. 25(6), 1312-1319.
Tang, Z. (2016). Defensive e¢ cacy interim design: structured bene…t/risk assesse-
ment using probability of success. Journal of Biopharmaceutical Statistics, 2016,.
doi:10.1080/10543406.2016.1198370.