Efficient and powerful equivalency test on combined mean and variance with application to diagnostic device comparison studies
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In medical device comparison studies, equivalency test is commonly used to demonstrate two measurement methods agree up to a pre-specified performance goal based on the paired repeated measures. Such equivalency test often involves controlling the absolute differences that depend on both the mean and variance parameters, and poses some challenges for statistical analysis. For example, for the oximetry comparison study that motivates our research, FDA has clear guidelines approving an investigational pulse oximeter in comparison to a standard oximeter via testing the root mean squares (RMS), a composite measure of both mean and variance parameters. For the hypothesis testing of this composite measure, existing methods have been either exploratory or relying on the large-sample normal approximation with conservative and unsatisfactory performance. We develop a novel generalized pivotal test to rigorously and accurately test the system equivalency based on RMS. The proposed method has well-controlled type I error and favorable performance in our extensive numerical studies. When analyzing data from an oximetry comparison study, aiming to demonstrate performance equivalency between an FDA-cleared oximetry system and an investigational system, our proposed method resulted in a highly significant test result strongly supporting the system equivalency. We also provide efficient R programs for the proposed method in a publicly available R package. Considering that many practical equivalency studies of diagnostic devices are of small to medium sizes, our proposed method and software timely bridge an existing gap in the field.
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