Equivalence Testing Overview

In many fields of pharmaceutical and biotechnological research, including biosimilar development, the goal is not to demonstrate a difference between two products, but rather to show that they are sufficiently similar. This leads us to the concept of equivalence testing, which aims to statistically verify that any difference between two treatments is small enough to be considered negligible within a pre-specified margin.

Why Equivalence Matters in Biosimilar Development

Unlike traditional hypothesis testing—where the null hypothesis assumes no difference—equivalence testing reverses the logic:

  • Null Hypothesis (H₀): The two treatments are not equivalent, i.e., the difference exceeds the acceptable margin.
  • Alternative Hypothesis (H₁): The treatments are equivalent, i.e., the difference lies within the predefined equivalence margin.

This approach is critical in biosimilar development, where regulatory agencies (e.g., FDA, EMA) require evidence that the biosimilar is neither inferior nor superior beyond a certain threshold relative to the reference product.

The Problem with Traditional t-tests

A common misconception is that a non-significant result in a traditional t-test implies equivalence. However, this is incorrect. A non-significant p-value simply indicates insufficient evidence to claim a difference—it does not confirm similarity.

To formally assess equivalence, we need a dedicated method: the Two One-Sided Tests (TOST) procedure.

Introducing TOST (Two One-Sided Tests)

TOST evaluates whether the true difference between two treatments falls entirely within an equivalence interval.

The procedure involves two one-sided hypothesis tests:

  1. Test if the treatment difference is greater than the lower bound (i.e., not too small).
  2. Test if the treatment difference is less than the upper bound (i.e., not too large).

Only if both tests are statistically significant (p < α), equivalence is concluded.

This method directly aligns with regulatory guidelines and is considered a gold standard for equivalence assessment.

Visualizing Equivalence

A helpful way to understand equivalence testing is through confidence intervals. If the entire 90% or 95% confidence interval of the treatment difference lies within the equivalence bounds, equivalence is supported.

Note: Equivalence bounds must be pre-specified based on clinical relevance or regulatory guidance.

Summary

Test Type Null Hypothesis H₀ Alternative H₁ When Used?
t-test No difference Difference (Δ ≠ 0) To detect differences
TOST Not equivalent Equivalent To demonstrate equivalence

In the next chapter, we will explore the mathematical formulation of TOST and implement it in R, comparing it with traditional t-tests to highlight key differences in interpretation.