The Smooth Away From Expected (SAFE) non-inferiority frontier: theory and implementation with an application to the...

In a non-inferiority trial, the choice of margin depends on the expected control event risk. If the true risk differs from expected, power and interpretability of results can be affected. A non-inferiority frontier pre-specifies an appropriate non-inferiority margin for each value of control event risk. D3 is a non-inferiority trial comparing two treatment regimens in children living with HIV, designed assuming a control event risk of 12%, a non-inferiority margin of 10%, 80% power and a significance level (α) of 0.025. We consider approaches to choosing and implementing a frontier for this already funded trial, where changing the sample size substantially would be difficult.

In D3, we fix the non-inferiority margin at 10%, 8% and 5% for control event risks of ≥9%, 5% and 1%, respectively. We propose four frontiers which fit these fixed points, including a Smooth Away From Expected (SAFE) frontier. Analysis approaches considered are as follows: using the pre-specified significance level (α=0.025); always using a reduced significance level (to achieve α≤0.025 across control event risks); reducing significance levels only when the control event risk differs significantly from expected (control event risk <9%); and using a likelihood ratio test. We compare power and type 1 error for SAFE with other frontiers.

Changing the significance level only when the control event risk is <9% achieves approximately nominal (<3%) type I error rate and maintains reasonable power for control event risks between 1 and 15%. The likelihood ratio test method performs similarly, but the results are more complex to present. Other analysis methods lead to either inflated type 1 error or badly reduced power. The SAFE frontier gives more interpretable results with low control event risks than other frontiers (i.e. it uses more reasonable non-inferiority margins). Other frontiers do not achieve power close (i.e. within 1%) to SAFE across the range of likely control event risks while controlling type I error.

The SAFE non-inferiority frontier will be used in D3, and the non-inferiority margin and significance level will be modified if the control event risk is lower than expected. This ensures results will remain interpretable if design assumptions are incorrect, while achieving similar power. A similar approach could be considered for other non-inferiority trials where the control event risk is uncertain.