Validation for a Single Reader and Single Modality

Issei Tsunoda

2019-05-04

The Aim

The aim of this vignette is to explain what functions are used in this package to validate our Bayesian model for the case of a single reader and single modality.

The function for validations.

For the user it is sufficient to know only one function validation.dataset_srsc_for_different_NI_NL(). This function replicate many datasets from known distributions which user specified before execution. In FROC data, the number of lesions and images corresponds samples size. So, large number of image gives us more small bias which will be confirmed by the function validation.dataset_srsc_for_different_NI_NL().

The following, the important variables of validation.dataset_srsc_for_different_NI_NL() are shown.

Output

Each number means the errors, i.e., the mean values of estimates minus true parameter over all replications. We can see that the number of images and lesions become more large, then these error tends to zero. That is, in FROC models, the number of lesions and images corresponds sample size, so if these values are larger, then the hits and false alarms also become larger, and it leads us to smaller biases.

       validation.dataset_srsc_for_different_NI_NL()
Name.of.Parameters 1-th model 2-th model 3-th model 4-th model
Number of Images 200.0000000 20000.0000000 2.00000e+06 2.0000e+08
Number of Lesions 100.0000000 10000.0000000 1.00000e+06 1.0000e+08
z[ 1 ] 0.1055186 0.0103358 1.01020e-03 1.0720e-04
z[ 2 ] 0.1956183 0.0132404 1.20850e-03 1.3030e-04
z[ 3 ] 1.1307551 0.0309471 2.52580e-03 2.9210e-04
mean.of.signal -0.4843169 -0.0463222 -4.95890e-03 -4.2730e-04
sd.of.signal 3.8036830 0.1160011 1.07218e-02 1.0843e-03
AUC -0.0348429 -0.0041814 -4.49200e-04 -4.0100e-05
dz[ 1 ] 0.0900996 0.0029046 1.98300e-04 2.3100e-05
dz[ 2 ] 0.9351368 0.0177067 1.31730e-03 1.6170e-04
p[ 1 ] -0.0384759 -0.0019671 -1.90400e-04 -1.9200e-05
p[ 2 ] -0.0119591 -0.0015342 -1.72000e-04 -1.5200e-05
p[ 3 ] -0.0121365 -0.0026324 -2.75400e-04 -2.5300e-05
lambda[ 1 ] -0.0384759 -0.0019671 -1.90400e-04 -1.9200e-05
lambda[ 2 ] -0.0119591 -0.0015342 -1.72000e-04 -1.5200e-05
lambda[ 3 ] -0.0121365 -0.0026324 -2.75400e-04 -2.5300e-05