Design and analysis of non‐inferiority mortality trials in oncology

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Abstract
The recent revision of the Declaration of Helsinki and the existence of many new therapies that affect survival or serious morbidity, and that therefore cannot be denied patients, have generated increased interest in active‐control trials, particularly those intended to show equivalence or non‐inferiority to the active‐control. A non‐inferiority hypothesis has historically been formulated in terms of a fixed margin. This margin was historically designed to exclude a ‘clinically meaningful difference’, but has become recognized that the margin must also be no larger than the assured effect of the control in the new study. Depending on how this ‘assured effect’ is determined or estimated, the selected margin may be very small, leading to very large sample sizes, especially when there is an added requirement that a loss of some specified fraction of the assured effect must be ruled out. In cases where it is appropriate, this paper proposes non‐inferiority analyses that do not involve a fixed margin, but can be described as a two confidence interval procedure that compares the 95 per cent two‐sided CI for the difference between the treatment and the control to a confidence interval for the control effect (based on a meta‐analysis of historical data comparing the control to placebo) that is chosen to preserve a study‐wide type I error rate of about 0.025 (similar to the usual standard for a superiority trial) for testing for retention of a prespecified fraction of the control effect. The approach assumes that the estimate of the historical active‐control effect size is applicable in the current study. If there is reason to believe that this effect size is diminished (for example, improved concomitant therapies) the estimate of this historical effect could be reduced appropriately. The statistical methodology for testing this non‐inferiority hypothesis is developed for a hazard ratio (rather than an absolute difference between treatments, because a hazard ratio seems likely to be less population dependent than the absolute difference). In the case of oncology, the hazard ratio is the usual way of comparing treatments with respect to time to event (time to progression or survival) endpoints. The proportional hazards assumption is regarded as reasonable (approximately holding). The testing procedures proposed are conditionally equivalent to two confidence interval procedures that relax the conservatism of two 95 per cent confidence interval testing procedures and preserve the type I error rate at a one‐sided 0.025 level. An application of this methodology to Xeloda, a recently approved drug for the treatment of metastatic colorectal cancers, is illustrated. Other methodologies are also described and assessed – including a point estimate procedure, a Bayesian procedure and two delta‐method confidence interval procedures. Published in 2003 by John Wiley & Sons, Ltd.