A Sequential Approach for Noninferiority or Equivalence of a Linear Contrast Under Cost Constraints

Planning an appropriate sample size for a study involves considering several issues. Two important considerations are cost constraints and variability inherent in the population from which data will be sampled. Methodologists have developed sample size planning methods for two or more populations when testing for equivalence or noninferiority/superiority for a linear contrast of population means. Additionally, cost constraints and variance heterogeneity among populations have also been considered. We extend these methods by developing a theory for sequential procedures for testing the equivalence or noninferiority/superiority for a linear contrast of population means under cost constraints, which we prove to effectively utilize the allocated resources. Our method, due to the sequential framework, does not require prespecified values of unknown population variance(s), something that is historically an impediment to designing studies. Importantly, our method does not require an assumption of a specific type of distribution of the data in the relevant population from which the observations are sampled, as we make our developments in a data distribution-free context. We provide an illustrative example to show how the implementation of the proposed approach can be useful in applied research.