Historical Control Borrowing: Overview, Advancement and New - PowerPoint PPT Presentation

Historical Control Borrowing: Overview, Advancement and New Methodologies Jianchang Lin, Ph.D. Veronica Bunn, Ph.D. Statistical and Quantitative Sciences, Data Sciences Institute Takeda Pharmaceutical Company Limited

Outline • Regulatory Guidance and Objectives • Review of Existing Historical Control Borrowing Methods • Proposed Bayesian Semiparametric Meta-Analytic Predictive Prior • Effective Sample Size • Simulations • Case Study: Ankylosing Spondylitis (AS) 1

Regulatory Guidance on Use of Historical Controls • The use of historical controls, e.g. in rare disease and oncology has become common in the regulatory setting (via 21 st Century Cures Act) • 2019 FDA guidance for Interacting with the FDA on Complex Innovative Clinical Trial Designs for Drugs and Biological Products - “ Some examples of trial designs that might be considered novel or CID are those that formally borrow external or historical information or borrow control arm data from previous studies to expand upon concurrent controls .” • 2019 FDA guidance for Rare Diseases: Natural History Studies for Drug Development: “….. FDA regulations recognize historical controls as a possible control group ”. Also indicates that subject level data needed for historical control can be gathered from previous clinical trials • 2019 FDA guidance for Rare Diseases: Common Issues in Drug Development - “The potential use of natural history data as a historical comparator for patients treated in clinical trial is often of interest… in general studies using historical controls are credible only when the effect is large in comparison to variability in disease course” • ICH E10: Choice of Control Group and Related Issues in Clinical Trials - Guideline discusses using historical controls and describes the usefulness of such controls under certain scenarios. Guideline describes situations where appropriately and carefully chosen historical controls are more persuasive and potentially less biased • EMA: Guideline on Clinical Trials in Small Populations - A Bayesian methodology with an informative prior built on historical data may be suitable 2

Objectives of Historical Control Borrowing Incorporate information from control arms of similar historical trials to augment data in early phase/proof-of-concept studies or rare disease studies Benefits Potential Risks • • Smaller control arms Historical data conflicts with the observed control data – Patient centricity – Bias – Cost and time effective – Decreased Power • Better estimates for inference – Increased type I error – Increased power – Decreased type I error rate 3

Notation Setting Control data from K historical trials H 1 H 2 H K Control and treatment data from current trial C T Binary Response: 𝑧 𝑘 ∼ 𝐶𝑗𝑜 𝑜 𝑘 , 𝑞 𝑘 𝑘 = 𝑈, 𝐷, 𝐼 1 , … , 𝐼 𝐿 𝑞 𝑘 𝜄 𝑘 = log 1 − 𝑞 𝑘 4

Outline • Regulatory Guidance and Objectives • Review of Existing Historical Control Borrowing Methods • Proposed Bayesian Semiparametric Meta-Analytic Predictive Prior • Effective Sample Size • Simulations • Case Study: Ankylosing Spondylitis (AS) 5

No Borrowing Prior Current Data Posterior C 𝜌(𝑞 C ) 𝜌(𝑞 C ) ෤ Bin(𝑧 𝐷 ; 𝑜 𝐷 , 𝑞 𝑑 ) Beta(𝛽 0 + 𝑧 𝐷 , 𝛾 0 + 𝑜 𝐷 − 𝑧 𝐷 ) Beta(𝛽 0 , 𝛾 0 ) Ignores the historical data H 1 H 2 H K 6

Pooling Prior Current Data Posterior H 1 H 2 𝜌(𝑞 C ) 𝜌(𝑞 C ) ෤ Control H K C 𝑜 = ෍ 𝑜 𝑗 𝑧 = ෍ 𝑧 𝑗 𝑗 𝑗 Beta(𝛽 0 , 𝛾 0 ) Bin(𝑧; 𝑜, 𝑞 𝑑 ) Beta(𝛽 0 + 𝑧, 𝛾 0 + 𝑜 − 𝑧 ) • Treats historic data as if it came from the current trial • Does not model heterogeneity 7

Power Prior Prior 𝑧 𝐷 |𝐼, 𝐷, γ, 𝑞 C ∼ 𝐶𝑗𝑜 𝑜 𝐷 , 𝑞 C H 1 𝑞 𝐷 |𝐼, γ ∝ 𝐶𝑗𝑜 𝑧 𝐼 ; 𝑜 𝐼 , 𝑞 C γ 𝜌(𝑞 C ) H 2 Historical Beta 𝑞 C ;γ𝑧 𝐼 , 𝛿[𝑜 𝐼 − 𝑧 𝐼 ] 𝜌(𝑞 C ) Control H K • 𝜹 Group all historical data together, raise likelihood to power γ , 0 ≤ γ ≤ 1 • Fixed amount of borrowing controlled by γ H 𝜌(𝑞 C ) Ibrahim and Chen (2000) 8

Modified Power Prior Prior H 1 𝑧 𝐷 |𝐼, 𝐷, γ, 𝑞 C ∼ 𝐶𝑗𝑜 𝑜 𝐷, 𝑞 C H 2 Historical 𝑞 𝐷 , γ|𝐼 ∝ 𝐷(𝛿)𝐶𝑗𝑜 𝑧 𝐼 ; 𝑜 𝐼 , 𝑞 C γ 𝜌 𝑞 C 𝜌(𝛿) Control • Place a prior on γ H K • Allows data to learn how much borrowing is 𝜹 needed • 𝐷(𝛿) is a normalizing constant to satisfy 𝜌(γ) likelihood principle 𝜌(𝑞 C ) H Duan et al (2006) Neuenschwander et al (2009) 9

Meta-Analytic Predictive (MAP) Prior 𝑧 𝑘 |𝐼, 𝐷, 𝜾 ∼ 𝐶𝑗𝑜 𝑜 𝑘, 𝑞 j where 𝑘 = 𝐷, 𝐼 1 , … , 𝐼 𝐿 Prior 𝑞 j 𝜄 𝑘 = log = 𝜈 0 + 𝜀 𝑘 1 − 𝑞 j 𝜾 𝑰 𝟐 2 ) 𝜀 𝑘 ~𝑂(0, 𝜏 𝜄 𝜾 𝑰 𝟑 2 ~𝜌(𝜏 𝜄 2 ) 𝜏 𝜄 𝜈 0 ~𝜌(𝜈 0 ) 𝜌(𝜄 C ) • Includes both historical control and current 𝜾 𝑰 𝑳 control • Random effects model on the log odds 2 ) N(𝜈 0 , 𝜏 𝜄 • Accounts for heterogeneity through the 2 ) variance of the random effects ( 𝜏 𝜄 Random Effects Neuenschwander et al. (2010) 10

Robust MAP Prior Prior 𝑧 𝑘 |𝐼, 𝜾 ∼ 𝐶𝑗𝑜 𝑜 𝑘, 𝑞 j where 𝑘 = 𝐼 1 , … , 𝐼 𝐿 𝜄 𝑘 = 𝜈 0 + 𝜀 𝑘 𝜾 𝑰 𝟐 2 ) 𝜀 𝑘 ~𝑂(0, 𝜏 𝜄 𝜌(𝜄 C ) 𝜾 𝑰 𝟑 𝜈 0 ~𝜌(𝜈 0 ) 2 ~𝜌(𝜏 𝜄 2 ) 𝜏 𝜄 𝑥 𝜌 𝑁𝐵𝑄 (𝜄 C ) 𝑧 𝐷 |𝐼, 𝐷, 𝜄 𝐷 ∼ 𝐶𝑗𝑜 𝑜 𝐷, 𝑞 𝐷 2 , 𝜈 0 ~ 𝑥𝜌 𝑁𝐵𝑄 + (1 − 𝑥)𝜌 𝑤𝑏𝑕𝑣𝑓 𝜄 𝐷 |𝐼, 𝜏 𝜄 𝜌 𝑤𝑏𝑕𝑣𝑓 (𝜄 C ) 1 − 𝑥 𝜾 𝑰 𝑳 • Mixture of MAP prior and a vague prior 2 ) N(𝜈 0 , 𝜏 𝜄 • Vague component allows for possibility of ignoring historical data Random Effects • Pre-specify the weight 𝑥 Schmidli et al. (2014) 11

Summary of Existing Historical Control Borrowing Priors Modified Power Power Prior MAP Robust MAP Prior Closed Form Capable of Using < 3 Historic Trials Adaptive Borrowing Models Trials Individually Allows for Prior Data Conflict No Requirement of Pre- Specification 12

FDA CID Guidance (Sept. 2019) on Borrowing Strategy • “A strategy for evaluating and addressing heterogeneity between the prior data and the concurrent Phase 3 data, such as the use of hierarchical models or other approaches that automatically downweight borrowing in the presence of heterogeneity, should be included. As discussed above, if Bayesian approaches are used, the proposal should include detailed discussions of decision criteria and prior distributions, including the effective sample size of the Phase 2 data to be borrowed and how it will be borrowed.” 13

Outline • Regulatory Guidance and Objectives • Review of Existing Historical Control Borrowing Methods • Proposed Bayesian Semiparametric Meta-Analytic Predictive Prior • Effective Sample Size • Simulations • Case Study: Ankylosing Spondylitis (AS) 14

Dirichlet Process Priors • A prior distribution over the space of probability distributions • Allows the data to learn what distribution it comes from G 0 DP G • Written as 𝑍|𝐻 ~ 𝐻 where 𝐻~𝐸𝑄 𝐻 0 , 𝛽 – 𝐻 0 : base distribution; prior “guess” for 𝐻 – 𝛽: concentration parameter; controls the derivation from the base distribution 𝛽 [Fox et al 2014] [Ghosal et al 1999] [Sudderth,Jordan 2009] [Arjas,Gasbarra 1994] 15

Dirichlet Process Prior Black curve : true distribution Blue curve : Normal distribution Red curve : Dirichlet process Dirichlet Process Prior can adapt to fit a wide variety of distributions 16

Chinese Restaurant Process Algorithm 3 1 New New New 5 Table 2 Table 1 Table Table Table 2 4 • Cluster assignment: 𝑂 𝑙 𝑗𝑔 𝑙 𝑗𝑡 𝑏𝑜 𝑝𝑚𝑒 𝑑𝑚𝑣𝑡𝑢𝑓𝑠 𝑂−1+𝛽 – 𝑄 𝑨 𝑘 = 𝑙 𝑨 1 , … , 𝑨 𝑘−1 , 𝛽 = ቐ 𝛽 𝑗𝑔 𝑙 𝑗𝑡 𝑏 𝑜𝑓𝑥 𝑑𝑚𝑣𝑡𝑢𝑓𝑠 𝑂−1+𝛽 • Historical studies in the same cluster, e.g.: 𝜄 1 = 𝜄 3 • Historical studies in different clusters, e.g.: 𝜄 1 , 𝜄 2 ~ 𝐼 17

Bayesian Semiparametric (BaSe) MAP Prior Prior 𝑧 𝑘 |𝐼, 𝐷, 𝜾 ∼ 𝐶𝑗𝑜 𝑜 𝑘, 𝑞 j where 𝑘 = 𝐷, 𝐼 1 , … , 𝐼 𝐿 𝑞 j 𝜾 𝑰 𝟐 𝜄 𝑘 = log = 𝜈 0 + 𝜀 𝑘 1 − 𝑞 j 2 ) 𝜀 𝑘 ~𝑂(0, 𝜏 𝑘 𝜾 𝑰 𝟑 2 |𝐻~𝐻 𝜏 𝑘 𝜈 0 ~𝜌(𝜈 0 ) 𝜌(𝜄 C ) 𝐸𝑄 𝐻 0 , 𝛽 𝜾 𝑰 𝑳 • Flexible error distribution that learns from the 2 ) 𝜄 𝑘 ~𝑂(𝜈 0 , 𝜏 𝑘 historical data • Accounts for heterogeneity through multiple 𝐸𝑄 𝐻 0 , 𝛽 𝐻 Normal distributions of differing variance Random Effects 18

Summary of Historical Control Borrowing Priors Modified Power Prior MAP Robust MAP BaSe MAP Power Prior Closed Form Capable of Using < 3 Historic Trials Adaptive Borrowing Models Trials Individually Allows for Prior Data Conflict No Requirement of Pre- Specification 19