A Bayesian Design with Conditional Borrowing of Historical Data in a Rare Disease Setting Peng Sun* July 30, 2019 *Joint work with Ming-Hui Chen, Yiwei Zhang, John Zhong, Charlie Cao, Guochen Song, and Zhenxun Wang

Outline Introduction Bayesian design using power prior with conditional borrowing of historical data Comparison to the Bayesian hierarchical modelling approach Discussion

Introduction (1) Rare disease setting: An efficacious standard of care (S) is already on the market A new modality (N) for the treatment of the same disease: Synergistic effect of N and S is expected Efficacy endpoint: Change from baseline in HINE* total milestones score at Month 10 Despite strong efficacy of S, the gap remains: With the treatment of S, the observed mean change from baseline in Month 10 HINE total milestones score was 14.9 with a standard deviation of 4.12 (N=15) For healthy subjects, the expected change from baseline in Month 10 HINE total milestones score is 20 *HINE: Hammersmith Infant Neurological Examination

Introduction (2) Hypothesis of interest: The population mean change from baseline in Month 10 HINE total milestones score is greater for subjects treated with N+S comparing to subjects treated with S alone Historical data: 15 subjects treated with the standard of care (S) Study design: Randomized control trial with a total of 27 subjects and a 2:1 randomization ratio (N+S vs. S) Conditional borrowing through power prior to augment current control with historical data Without borrowing historical data, assuming an effect size of 4.5, the study has power 77% power with one-sided alpha of 0.025

Bayesian Design Notations

Bayesian Design Power Prior and Conditional Borrowing

Bayesian Design Simulation Set up Borrowing region: [13.9, 15.9], which is approximately one stand error around the historical mean of 14.9 a0 ranges from 0.2 to 0.7 Number of simulations: 5,000 Bayesian modeling: 10,000 posterior draws with 3000 as burn-ins Assumed standard deviation for Month 10 HINE change from baseline: 4.12 for the monotherapy arm (S) and 2.8 for the combination arm All simulations were conducted in R with the rstan package for Bayesian modeling

Bayesian Design Choice of Gamma Evaluated via numerical integration and simulation under no borrowing assuming a common mean of 15. Hence gamma=0.972 is selected for subsequent simulations.

Bayesian Design Type I Error under Fixed Borrowing

Bayesian Design Posterior Probability of Control Mean Exceeding a Reference Value Under Historical Data

Bayesian Design Type I Error under Conditional Borrowing a0=0.3 was selected: Maximum inflation is below 5% at a population mean with low posterior probability of exceeding it

Bayesian Design Power Gain under Fixed Effect Size of 4.5 (a0=0.3)

Bayesian Design Power Gain Assuming Pop Bayesian Design Power Gain Assuming Pop. Mean Change from Baseline of 19.5 for Combination (a0=0.3)

Bayesian Hierarchical Model

Comparison of Type I Error a0=0.3 for conditional borrowing

Comparison of Power a0=0.3 for conditional borrowing

Bias of Effect Size Estimate (True Effect Size = 0) a0=0.3 for conditional borrowing; bias is defined as the deviation of posterior mean estimate from the population parameter

Bayesian Design Discussion With conditional borrowing, the pre-specified borrowing region prevents borrowing if the observed historical data and the current control data drastically differ in efficacy With conditional borrowing, the Type I error is bounded within the range of population control mean. This is in contrast to the fixed borrowing approach with power prior The Bayesian estimator of treatment difference based on conditional borrowing is unbiased. This is in contrast to the Bayesian hierarchical modelling approach, where moderate bias* is observed. * Bias is defined as the deviation of posterior mean estimate from the population parameter

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