Defensive E¢ cacy IA Design:dynamic bene�t/risk assessmentusing probability of success (POS)

Zhongwen Tang

Outline

� Motivation

� POS (probability of success) supported defensive e¢ cacy IA design

� Design paradigm

� POS calculation

� Dynamic decision making

� Numerical example

� Take home messages

HA: Bene�t/risk assessment

� FDA: Assessments of a products bene�ts and risks involves an analysis of the severityof the condition treated and the current treatment options available for the givendisease (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 thata set level of quality, e¢ cacy, and safety of the new medical product has beendemonstrated (CHMP bene�t-risk re�ection paper, 2007).

HA: e¢ cacy IA

� FDA: It is important to bear in mind that early termination for e¢ cacy shouldgenerally be reserved for circumstances where there is the combination of compellingethical 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 withoutfurther justi�cation ... (CHMP adaptive design re�ection paper, 2007)

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

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

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

Defnesive POS Optimal Design

Finding the optimal design is equivalent to �nd the solution to the following equationswith respect to the design parameters.

f center of POS() = cut1� � 100th POS percentile () = cut2

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

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��; �21 = 1= (r (1� r) d)

�d is the number of events at the time of interim analysi t.

where r is the randomization ratio

Within Trial Predictive POS

Assume a Gaussian prior ln (HR) = �~N��0; �

20 = 1= (r (1� r) d0)

�

Within Trial Predictive POS

The posterior distribution is

�j�̂ (t) ~N�'�̂ (t) + (1� ') �0; �20 (1� ')

�

where ' =�1 +

�21�20

��1=�

�20�20+�

21

�

Within Trial CPOS

Under proportional hazard assumption

� CPOS(�) = P (Z(1) < �j�) = P��̂ < � � �

�where �2 = 1=(r (1� r) dmax)

� Z� =ptZ (t) +

p1� t

pdmaxZ(1)�

pdZ(t)p

dmax�dand Z(1) have same distribution.

� CPOS(�) = ����ptz(t)p1�t � �

qr (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.

CPOS Credible Interval

� median CPOS=mCPOS = CPOS(median of �)

� low percentile (width of CI): � � 100 percentile ofCPOS = CPOS((1� �) � 100 percentile of �).

� mCPOS and � � 100th CPOS percentile is an equivalent statistic of observedhazard ratio and number of events.

PPOS and Credible Interval

� PPOS��̂ (t)

�= �

0B@ ��ptz(t)p1�t =

pr(1�r)(dmax�d)�

h'�̂(t)+(1�')�0

iq�20(1�')+�

22

1CA where �22 =1=(r (1� r) (dmax � d))

� median PPOS=mPPOS��̂ (t)

�= �

0B@ ��ptz(t)p1�t =

pr(1�r)(dmax�d)�

h'�̂(t)+(1�')�0

iq�20(1�')+�

22

1CA

� low percentile (width of CI): � � 100 percentile ofPPOS = PPOS ((1� �) � 100 percentile of �).

� mPPOS and � � 100th PPOS percentile is an equivalent statistic of observedhazard ratio and number of events.

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.

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).

Success adjustment

�� = � + �1e=�2c.

� : HR success cuto¤ of e¢ cacy end point TTE

�� : HR success cuto¤ of composite end point TTF

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 �nalanalysis.

� Prior information

� Non-informative prior: prior variance = in�nity (equivalent to 0 event)

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.

Optimal e¢ cacy interim design

Defensive e¢ cacy interim design

Example: defensive design with newly emerged safety signal

� The time to the grade3/4 QT prolongation has approximate exponential distributionwith 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 �nalanalysis 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.

Take home messages

� POS is an information dependent statistic.

� POS defensive design can faciliate buying from HAs when the submission is basedon IA data.

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 anadaptive 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 currenttools 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 Drugsand Biologics, 2010

FDA PDUFA V draft implementation plan: structured approach to bene�t-risk assess-ments in drug regulatory decision-making. 2013

Reference

Tang, Z. Dey, J. (2011). Bayesian PPOS design for clinical trials. PaSIPHIC anualmeeting.

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 withtime 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.