Quasi-likelihood approach to bioavailability and bioequivalence analysis

The outcomes AUCT (area-under-curve from time zero to time t) of n individuals randomized to one of two groups TR or RT, where the group name denotes the order in which the subjects receive a test formulation (T) or a reference formulation (R), are used to assess average bioequivalence for the two formulations. The classical method is the mixed model, for example, proc mixed or proc glm with random statement in SAS can be used to analyze this type of data. This is equivalent to the marginal likelihood approach in a normal-normal model. There are some limitations for this approach. It is not appropriate if the random effect is not normally distributed. In this article, we introduce a hierarchical quasi-likelihood approach. Instead of assuming the random effect is normal, we make assumptions only about the mean and the variance function of the random effect. Our method is flexible to model the random effect. Since we can estimate the random effect for each individual, we can check the adequacy of the distribution assumption about the random effect. This method can also be used to handle high-dimensional crossover data. Simulation studies are conducted to check the finite sample performance of the method under various conditions and two real data examples are used for illustration.