A note on the determination of non-inferiority margins with application in oncology clinical trials

Abstract

The goal of a non-inferiority trial is to evaluate whether the effect of an experimental treatment is not inferior to that of the active control. Determination of an appropriate non-inferiority margin is critical to the demonstration of non-inferiority. A commonly used method is called the fixed-margin approach recommended by the FDA. The fixed-margin approach consists of two steps: first the lower limit of the $1-{\alpha }^{\text{*}}$ two-sided confidence interval (CI) of the active-control effect versus placebo is calculated from relevant historical trials or meta-analysis; second, the non-inferiority margin is obtained as a fraction of the lower confidence limit of the control effect to preserve partial control effect. An alternative method is to use the point estimate, instead of the lower confidence limit, of the active-control effect. The fixed-margin approach based on the lower limit may be ultra-conservative with unconditional Type 1 error rate much smaller than target $\alpha /2$ level, while the margin based on the point estimate is liberal. We derive the Type 1 error rate as a function of variances of the effect estimates in the historical and the current non-inferiority trials. We also propose an alternative approach for the non-inferiority margin that maintains the target Type 1 error rate. For the endpoint of landmark survival, we conduct simulations to compare the fixed-margin methods and the proposed method. For illustration, we apply the proposed method to an oncology non-inferiority clinical trial to determine an alternative non-inferiority margin.

Keywords: Fixed-margin approach; Landmark survival; Non-inferiority test; Type 1 error.

Fig. 1

The ratio of the half-width with the confidence level $1-{\alpha }^{\text{*}}$ to.$z_{0.975}$

Fig. 2

Survival curves for the historical data in the simulation.

Fig. 3

Type 1 error rate for the 95%–95% fixed-margin CI approach.

Fig. 4

Type 1 error rate for the CI approach with the adjusted ${\alpha }^{\text{*}}$ value.

Fig. 5

Type 1 error rate for the CI approach with the NI trial sample size doubled.

Fig. 6

Kaplan-Meier curves by treatment for the reconstructed overall survival data for the ATTRACTION-2 trial.