Equivalence tests for binary efficacy-toxicity responses

TL;DR

This paper introduces new statistical tests for assessing equivalence between treatments in clinical trials with binary efficacy and toxicity outcomes, using bootstrap methods and bivariate models.

Contribution

It develops novel bootstrap-based tests for equivalence over covariate ranges for univariate and bivariate binary outcomes, extending existing methods.

Findings

The proposed tests effectively assess treatment equivalence in simulations.

The methods handle both univariate and correlated binary outcomes.

A case study demonstrates practical application.

Abstract

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.