Assessing individual equivalence in parallel group and crossover designs: Exact test and sample size procedures

The consideration of individual equivalence provides an essential alternative to average equivalence in two-group comparative studies. A common procedure for declaring individual equivalence adopts the tolerance intervals of the designated proportions of measurement differences. This statistical practice is a direct generalization of the widely used two one-sided tests (TOST) for average equivalence. Such TOST extensions often do not have adequate control of Type I error and result in excessively conservative tests. To signify and resolve the underlying issues of existing methods, this paper presents exact tests for assessing individual equivalence between two treatments under parallel group and crossover designs. Rigorous evaluations are conducted to clarify the discrepancy of critical values and Type I error probabilities between the equivalence procedures. The findings elucidate the shortcoming of the TOST technique and the advantage of the proposed approach. The associated power and sample size calculations are also justified through simulation studies.