  Clinical trials often aim to compare a new drug with a reference treatment in
terms of efficacy and/or toxicity depending on covariates such as, for example,
the dose level of the drug. Equivalence of these treatments can be claimed if
the difference in average outcome is below a certain threshold over the
covariate range. In this paper we assume that the efficacy and toxicity of the
treatments are measured as binary outcome variables and we address two
problems. First, we develop a new test procedure for the assessment of
equivalence of two treatments over the entire covariate range for a single
binary endpoint. Our approach is based on a parametric bootstrap, which
generates data under the constraint that the distance between the curves is
equal to the pre-specified equivalence threshold. Second, we address
equivalence for bivariate binary (correlated) outcomes by extending the
previous approach for a univariate response. For this purpose we use a
2-dimensional Gumbel model for binary efficacy-toxicity responses. We
investigate the operating characteristics of the proposed approaches by means
of a simulation study and present a case study as an illustration.
