Sample Size Calculation for Bioequivalence Studies Assessing Drug Effect and Food Effect at the Same Time With a 3-Treatment Williams Design

The US Food and Drug Administration issued a guidance in 2002, "Food-Effect Bioavailability and Fed Bioequivalence Studies," in which it states "in addition to a BE [bioequivalence] study under fasting conditions, we recommend a BE study under fed conditions for all orally administered immediate-release drug products" for abbreviated new drug applications. This statement involves 3 studies: a BE study under fasting status, a food-effect (FE) study, and a BE study under fed status. In practice, when it is known that there is no FE with a reference (R) formulation, a sponsor may choose to run a BE study that assesses the drug effect and food effect with a test (T) formulation in a single study that includes 3 treatments: R formulation at fasting status, T formulation at fasting status, and T formulation at fed status. Such a study combines the fasting BE study and the FE study on the T formulation and may justify the waiver of the fed BE study if conclusions can be made that there is no FE with the T formulation after this combined study completes. This article discusses how to calculate the sample size for this kind of study with different primary analysis models. Also discussed are (1) sample size calculations with more general BE studies and (2) how they can be implemented using commercial software in a standard 2-treatment, 2-period, and 2-sequence crossover design, as well as (3) a related practical issue of how to retrieve residual intrasubject mean squared error from historical summary results in the literature.