On Statistical Approaches for Demonstrating Analytical Similarity in the Presence of Correlation

Abstract

Analytical similarity is the foundation for demonstration of biosimilarity between a proposed product and a reference product. For this assessment, currently the U.S. Food and Drug Administration (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 demonstration of analytical similarity. For example, for Tier 1 assessment, an equivalence test can be used based on an equivalence margin of 1.5 σ_R, where σ_R is the reference product variability estimated by the sample standard deviation S_R from a sample of reference lots. The quality range for demonstrating Tier 2 analytical similarity is of the form X̄_R ± K × σ_R 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. In this paper, through both theoretical derivations and simulations, we show that when the reference drug product lots are correlated, the sample standard deviation S_R underestimates the true reference product variability σ_R. As a result, substituting S_R for σ_R 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. Also explored is the impact of correlation among drug product lots on Type I error rate and power. Three methods based on generalized pivotal quantities are introduced, and their performance is compared against a two-one-sided tests (TOST) approach. Finally, strategies to mitigate risk of correlation among the reference products lots are discussed.

LAY ABSTRACT: A biosimilar is a generic version of the original biological drug product. A key component of a biosimilar development is the demonstration of analytical similarity between the biosimilar and the reference product. Such demonstration relies on application of statistical methods to establish a similarity margin and appropriate test for equivalence between the two products. This paper discusses statistical issues with demonstration of analytical similarity and provides alternate approaches to potentially mitigate these problems.