Bayesian Approach for Demonstrating Analytical Similarity

The advance in regulatory guidance on biosimilars, including the passage of the Biologics Price Competition and Innovation Act of 2009, has created abbreviated licensure pathways for biological products shown to be biosimilar or interchangeable with a reference product. Common to these regulator guidelines is the stepwise approach which starts with the assessment of critical quality attributes used to characterize the biosimilar products. Furthermore, the FDA recommends a tiered system in which quality attributes are categorized into three tiers commensurate with their risk, and approaches of varying statistical rigor are subsequently used for the three-tier quality attributes. Key to the analyses of Tiers 1 and 2 quality attributes is the establishment of equivalence acceptance criterion and quality range. For particular licensure applications, the FDA has provided advice on statistical methods for the demonstration of analytical similarity. For example, for Tier 1 assessment, an equivalence test can be used based on an equivalence margin of https://www.w3.org/1998/Math/MathML"> 1.5 σ R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , where https://www.w3.org/1998/Math/MathML"> σ R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is the reference product variability estimated by the sample standard deviation https://www.w3.org/1998/Math/MathML"> S R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> from a sample of reference lots. The quality range for demonstrating Tier 2 analytical similarity is of the form https://www.w3.org/1998/Math/MathML"> X - R ± K × σ R , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where the constant K is appropriately justified. To demonstrate Tier 2 analytical similarity, a large percentage (e.g., 90%) of test product must fall in the quality range. As previously demonstrated by Yang et al. (2016), when the reference drug product lots are correlated, the sample standard deviation https://www.w3.org/1998/Math/MathML"> S R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> underestimates the true reference product variability https://www.w3.org/1998/Math/MathML"> σ R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_7.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . As a result, substituting https://www.w3.org/1998/Math/MathML"> S R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_8.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> for https://www.w3.org/1998/Math/MathML"> σ R https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003255093/d6d4784f-431d-40d5-91bc-888df4ca45e4/content/math0_9.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> in the Tier 1 equivalence acceptance criterion and the Tier 2 quality range inappropriately reduces the statistical power and the ability to declare analytical similarity. Three methods based on generalized pivotal quantities, which were introduced by Yang et al. (2016) provide better performance when compared to the two-one-sided tests (TOST) approach recommended in the regulatory guidance. In this chapter, we propose three alternate Bayesian methods for demonstrating analytical similarity. The performance of these methods was evaluated through a simulation study and practice guide on the use of these methods discussed.