A Specification of Treatment Difference in the Design of Clinical Trials with Active Controls

Abstract

Active control studies are often performed due to ethical reasons in life-threatening situations (1). Many difficulties and problems arise when the study objective of an active control study is to show that a new drug is effective by showing its similarity to a standard therapy (eg, Temple [2]; Temple, Pledger, and Hall [3]; Herson [4]; Pledger and Hall [5]; etc.). One of the difficulties in the design of such a study is the determination of a sufficient sample size. In practice, investigators often encounter the difficulty in specifying the treatment difference δ₀ one wishes to detect for sample size calculation.

A specification of δ₀ which depends on the magnitude of the therapeutic effect of the standard therapy as compared to placebo is proposed in this paper. The motivation for this proposal and the statistical implication of using such δ₀ in the conventional null hypothesis testing are discussed. It is argued that an active control equivalence study with adequate sample size may provide statistical evidence to support the efficacy of the test drug. Determination of adequate sample size through the specification of δ₀ is a statistical problem. Consequently, the specification of δ₀ in an active control equivalence study with the objective of showing the efficacy of the test drug should be determined by the statistician.