Helper functions

Main code and output

#> Fig. A : mu =  1 , alpha =  0.2
#> Fig. B : mu =  3 , alpha =  0.2
#> Fig. C : mu =  1 , alpha =  0.8
#> Fig. D : mu =  3 , alpha =  0.8

Comments

Plots A - D show ROC curves predicted by the CBM model; the corresponding values of the \(mu\) and \(alpha\) parameters are indicated above the plots. For small \(mu\) and/or \(alpha\) the curve approaches the chance diagonal, consistent with the notion that if the lesion is not visible, performance can be no better than chance level.

pdf plots

#> Fig. E : mu =  1 , alpha =  0.2
#> Fig. F : mu =  3 , alpha =  0.2
#> Fig. G : mu =  1 , alpha =  0.8
#> Fig. H : mu =  3 , alpha =  0.8

Comments

The dark line is the diseased distribution. The grey line is the non-diseased distribution. The bimodal diseased distribution is clearly evident in plots F and H.

likelihood ratio plots

#> Fig. I : mu =  1 , alpha =  0.2
#> Fig. J : mu =  3 , alpha =  0.2
#> Fig. K : mu =  1 , alpha =  0.8
#> Fig. L : mu =  3 , alpha =  0.8

Comments

Close examination of the region near the flat part shows it does not plateau at zero; rather the minimum is at 1 - \(alpha\), explaining the non-zero limiting slope of the predicted curve near (1, 1).