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Defensive Efficacy Interim Design

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This presentation proposes to use probability of success to design an efficacy interim in registration setting to address health authority concerns.

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Defensive Efficacy Interim Design

  1. 1. Defensive E¢ cacy IA Design: dynamic bene…t/risk assessment using probability of success (POS) Zhongwen Tang
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 11. Within Trial Predictive POS Assume a Gaussian prior ln (HR) = ~N 0; 2 0 = 1= (r (1 r) d0)
  12. 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. 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. 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. 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. 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. 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. 18. Success adjustment = + 1e= 2c. : HR success cuto¤ of e¢ cacy end point TTE : HR success cuto¤ of composite end point TTF
  19. 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. 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. 21. Optimal e¢ cacy interim design
  22. 22. Defensive e¢ cacy interim design
  23. 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. 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. 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. 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.

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