Clinical trials often aim to compare a new drug with a reference treatment in terms of e cacy 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 e cacy-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.