iRoeMetz: Simulate Roe & Metz model, Roe & Metz Model
Roe & Metz Model
Generalized Roe & Metz Model
iRoeMetz is an implementation of the updated Roe & Metz simulation model for creating reader ratings for diseased and non-diseased cases in two modalities[4]. This generalized model accounts for 18 variances as opposed to the six variances in the original model. The original six variances were of readers, cases, the interaction between readers and cases, and the interaction of modality with the three aforementioned variances. The generalized model takes these existing six and then accounts for the interaction of them against truth and differing modalities.
Simulation
We simulate the reading score with the following equations
The first two are nondiseased case scores for modality A and B. The other two are diseased case scores. Experiments are simulated by taking normally distributed random variables of the corresponding variance. The t-matrices produced by these equations can be used to estimate the components of variance and their respective decompositions, and to create simulated MRMC reading scores.
The random variables are created by using a pseudo-random number generator known as the Mersenne Twister. This method of random number generation is particularly suited to Monte Carlo trials, and is faster and more efficient than Java’s standard library pseudo-random number generator.
iRoeMetz has the ability to perform numerous simulations at once based on the same input variances. The effect is that the average estimated components of variance over a large number of simulations approaches the calculated components of variance. iRoeMetz scales to multi-core CPUs, providing a speed benefit when performing numerous simulations.
Calculation
Given the variances, means and experiment size, the components of variance can calculated via numerical integration.
