When inferiority meets non-inferiority: implications for interim analyses.
BACKGROUND
The objective of a non-inferiority trial is to determine whether a new or existing treatment is not less effective than another existing or current treatment by more than a pre-specified margin, Δ, usually with the requirement that the new treatment has some other advantage such as reduced cost or lower toxicity. A possible but unusual result in a non-inferiority trial is for the confidence interval for the treatment effect to lie between zero and Δ, implying that the new treatment is both inferior and non-inferior to the control. Such a result could occur in non-inferiority trials with large sample sizes or large non-inferiority margins. The possibility of this scenario occurring has implications for interim analyses. In standard superiority trials, stopping guidelines are often based on the p value obtained from testing whether treatments are equally effective. In non-inferiority trials, however, even if a new treatment is found to be inferior to the control at an interim analysis, there may still be a reasonable chance of demonstrating non-inferiority in the final analysis.


OBJECTIVE
To explore the issues arising from trials where a simultaneously inferior and non-inferior result could occur and to describe appropriate methods for deciding whether such trials should be stopped for futility at an interim analysis.


METHODS
Conditional power is used to assess futility or the inability of the trial to show non-inferiority at the final analysis, by calculating the probability of demonstrating non-inferiority in the final analysis conditional on the observed results and upon assumptions on the future results of the trial. The Bullous Pemphigoid Steroids and Tetracyclines Study (BLISTER) trial is an example of a trial where a simultaneous inferior and non-inferior result could occur. A method for calculating conditional power for non-inferiority using simulations is described and applied at a hypothetical interim analysis of this trial.


RESULTS
Stopping guidelines for futility based on conditional power are shown to be better suited to non-inferiority trials than the typical methods used in superiority trials. Simulations are a straightforward and flexible way of calculating conditional power.


CONCLUSIONS
Calculating conditional power relies on assumptions about future treatment efficacy, and therefore, a number of different conditional power values can be obtained. Careful consideration should be given to which assumptions are most likely to be true. Additionally, when choosing a stopping guideline for futility, consideration needs to be given to avoid overinflating the type II error rate.


CONCLUSIONS
Conditional power is an appropriate tool for defining stopping guidelines for futility in non-inferiority trials, particularly those with large non-inferiority margins.
MRC Clinical Trials Unit, London, UK. daniel.bratton@ctu.mrc.ac.uk
Daniel J
DJ
Bratton
Hywel C
HC
Williams
Brennan C
BC
Kahan
Patrick P J
PP
Phillips
Andrew J
AJ
Nunn
D000305:Adrenal Cortex Hormones / Q000627:therapeutic use; D000900:Anti-Bacterial Agents / Q000627:therapeutic use; D003198:Computer Simulation; D004318:Doxycycline / Q000627:therapeutic use; D006801:Humans; D015233:Models, Statistical; D010391:Pemphigoid, Bullous / Q000188:drug therapy; D011239:Prednisolone / Q000627:therapeutic use; D011336:Probability; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D012107:Research Design; D018401:Sample Size
D000305:Adrenal Cortex Hormones; D000900:Anti-Bacterial Agents; D011239:Prednisolone; D004318:Doxycycline