Roe and Metz identical-test simulation model for validating multi-reader methods of analysis for comparing different...

The most frequently used model for simulating multi-reader multi-case (MRMC) data that emulate confidence-of-disease ratings from diagnostic imaging studies has been the Roe and Metz model, proposed by Roe and Metz in 1997 and later generalized by Hillis (2012), Abbey et al. (2013), and Gallas and Hillis (2014). These models have been used for evaluating MRMC analysis and sample size methods. The models suggested in these papers for assessing type I error have been null models, where the expected area under the receiver-operating-characteristic curve across readers is the same for each test. However, for these null models, there are other differences that would not exist if the two tests were identical. None of the papers mentioned above discuss how to formulate a null model that is also an identical-test model, where the two tests are identical in all respects. The purpose of this paper is to show how to formulate a Roe and Metz identical-test model and to show its usefulness for validating the error covariance constraints employed by the Obuchowski-Rockette (1995) method.

For a given Roe-and-Metz model, the corresponding Roe-and-Metz identical-test model is derived by modifying the Roe and Metz null model under the assumption that the two tests are identical.

The importance of the Obuchowski-Rockette model constraints for avoiding negative variance estimates is established using data simulated from the Roe and Metz identical-test model. It is also shown that negative variance estimates can occur at nontrivial rates when the two tests are not identical but somewhat "close" to being identical.

The findings of this paper are important because it has recently been shown (Hillis, 2022) that the commonly used MRMC method proposed by Gallas (2006) and Gallas et al. (2009) uses the same test statistic as the unconstrained Obuchowski-Rockette method.