UtilRSM2Intrinsic {RJafroc}

Convert from physical to intrinsic RSM parameters

Description

Convert physical RSM parameters \lambda_i' and \nu_i' to the intrinsic RSM parameters \lambda_i and \nu_i. The physical parameters are more meaningful but they depend on \mu. The intrinsic parameters are independent of \mu. See book for details.

Usage

UtilRSM2Intrinsic(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 \lambda_i parameter, which describes the distribution of random numbers of latent NLs (suspicious regions that do not correspond to actual lesions) per case; the mean of these random numbers asymptotically approaches lambda

nu

The \nu_i parameter; it is the success probability of the binomial distribution describing the random number of latent LLs (suspicious regions that correspond to actual lesions) per diseased case

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 zeta1. See also UtilIntrinsic2RSM.

Value

A list containing \lambda_i and \nu_i, the RSM search parameters

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.routledge.com/Observer-Performance-Methods-for-Diagnostic-Imaging-Foundations-Modeling/Chakraborty/p/book/9781482214840

Examples

mu <- 2;lambda <- 10;nu <- 0.9
lambda_i <- UtilRSM2Intrinsic(mu, lambda, nu)$lambda_i 
nu_i <- UtilRSM2Intrinsic(mu, lambda, nu)$nu_i 
## note that the physical values are only constrained to be positive, e.g., nu_i is not constrained
## to be between 0 and one.