RJafroc (version 1.0.1)

UtilIntrinsic2PhysicalRSM: Convert from intrinsic to physical RSM parameters

Description

Convert intrinsic RSM parameters \(lambda\) and \(nu\) correspond to the physical RSM parameters \(lambda'\) and \(nu'\). The physical parameters are more meaningful but they depend on \(mu\). The intrinsic parameters are independent of \(mu\). See book for details.

Usage

UtilIntrinsic2PhysicalRSM(mu, lambda, nu)

Arguments

mu

The mean of the Gaussian distribution for the ratings of latent LLs, i.e. continuous ratings of lesions that were found by the search mechanism ~ N(\(\mu\),1). The corresponding distribution for the ratings of latent NLs is N(0,1).

lambda

The Poisson intrinsic parameter, related to \(\lambda\)', the latter is the mean of the Poisson distribution of numbers of latent NLs (suspicious regions that do not correspond to actual lesions) per case.

nu

The intrinsic \(\nu\) parameter; the corresponding physical parameter is the success probability of the binomial distribution of random numbers of latent LLs (suspicious regions that correspond to actual lesions) per diseased case, i.e., the chance that a lesion is "found".

Value

A list containing \(\lambda\)' and \(\nu\)'

Details

RSM is the Radiological Search Model described in the book. A latent mark becomes an actual mark if the corresponding rating exceeds the lowest reporting threshold \(\zeta\)1. See also UtilPhysical2IntrinsicRSM.

References

Chakraborty DP (2006) A search model and figure of merit for observer data acquired according to the free-response paradigm, Phys Med Biol 51, 3449--3462.

Chakraborty DP (2006) ROC Curves predicted by a model of visual search, Phys Med Biol 51, 3463--3482.

Chakraborty DP (2017) Observer Performance Methods for Diagnostic Imaging - Foundations, Modeling, and Applications with R-Based Examples, CRC Press, Boca Raton, FL. https://www.crcpress.com/Observer-Performance-Methods-for-Diagnostic-Imaging-Foundations-Modeling/Chakraborty/p/book/9781482214840

Examples

# NOT RUN {
mu <- 2;lambda <- 20;nu <- 1.1512925 
lambdaP <- UtilIntrinsic2PhysicalRSM(mu, lambda, nu)$lambdaP 
nuP <- UtilIntrinsic2PhysicalRSM(mu, lambda, nu)$nuP 
## note that the physical values are only constrained to be positive, but the physical variable nuP
## must obey 0 <= nuP <= 1


# }