BayesianFROC (version 1.0.0)

hits_creator_from_rate: MRMC Dataset Creator From Hit Rate.

Description

From hit rates, data of hits are created.

Usage

hits_creator_from_rate(NL = 252, seed = 123, p.truth = BayesianFROC::p_truth)

Arguments

NL

Number of Lesions.

seed

The seed for creating data consisting of the number of hits synthesized by the binomial distributions with the specified seed.

p.truth

Array of dimension (C, M, Q), where C = number of confidence levels, M = number of modalities, Q = number of readers.

Value

Hits Data, an array of dimension [Confidence, Modality, Reader].

Details

Random variables of hits are distributed as follows.

$$h_{5,m,r} \sim Binomial (p_{5,m,r}, N_L ),$$

then \(h_{4,m,r}\) should be drawn from the binomial distribution with remaining targets

$$h_{4,m,r} \sim Binomial (\frac{p_{4,m,r}}{1-p_{5,m,r}}, N_L - h_{5,m,r}).$$

Similarly,

$$h_{3,m,r} \sim Binomial (\frac{p_{3,m,r}}{1-p_{5,m,r}-p_{4,m,r}}, N_L - h_{5,m,r} -h_{4,m,r}).$$

$$h_{2,m,r} \sim Binomial (\frac{p_{2,m,r}}{1-p_{5,m,r}-p_{4,m,r}-p_{3,m,r}}, N_L - h_{5,m,r} -h_{4,m,r}-h_{3,m,r}).$$

$$h_{1,m,r} \sim Binomial (\frac{p_{1,m,r}}{1-p_{5,m,r}-p_{4,m,r}-p_{3,m,r}-p_{2,m,r}}, N_L - h_{5,m,r} -h_{4,m,r}-h_{3,m,r}-h_{2,m,r}).$$

p.truth is an array representing \(p_{c,m,r}\). Specifying the array p.truth ( and hence \(p_{c,m,r}\) ), with the above model, we can calculate hit data \(h_{c,m,r}\) for each \(c,m,r\).

Examples

# NOT RUN {
#========================================================================================
#2019 Sept 6 1)    Using the default hit values, hit data are created as follows;
#========================================================================================


           hits <- hits_creator_from_rate()








#========================================================================================
#2019 Sept 6 2)   If user want to use their own hit rates, then use the following codes:
#========================================================================================



 h <- hits_creator_from_rate(

  NL=252,
  seed =123,
  p.truth =
   array(c(
     c(0.03,0.13,0.2,0.3,0.4,   #for M=1 Q=1
       0.04,0.23,0.3,0.4,0.5) , #for M=2 Q=1 ,

     c(0.05,0.33,0.4,0.5,0.6,   #for M=1 Q=2
       0.06,0.43,0.5,0.6,0.7)  ,#for M=2 Q=2 ,

     c(0.07,0.53,0.6,0.7,0.8,   #for M=1 Q=3
       0.08,0.63,0.7,0.8,0.9)   #for M=2 Q=3 ,
       ),

  dim = c(5,2,3) #C M Q
  )#array

)






#========================================================================================
#2019 Sept 6 3)   If user want to use their own hit rates, then use the following codes:
#========================================================================================







 h <- hits_creator_from_rate(

  NL=252,
  seed =123,
  p.truth =
   array(c(

     c(0.03,0.1,0.2,0.3,0.4,   #for M=1 Q=1
       0.04,0.2,0.3,0.4,0.5,   #for M=2 Q=1
       0.05,0.3,0.4,0.5,0.6),  #for M=3 Q=1

     c(0.05,0.33,0.4,0.5,0.6,   #for M=1 Q=2
       0.06,0.43,0.5,0.6,0.7,   #for M=2 Q=2
       0.05,0.3,0.4,0.5,0.6),   #for M=3 Q=2

     c(0.07,0.53,0.6,0.7,0.8,   #for M=1 Q=3
       0.08,0.63,0.7,0.8,0.9,   #for M=2 Q=3
       0.05,0.3,0.4,0.5,0.6)    #for M=3 Q=3

       ),

  dim = c(5,3,3) #C M Q

  )#array

)






#========================================================================================
#2019 Sept 6 3)   Only one reader
#========================================================================================



 h <- hits_creator_from_rate(

  NL=252,
  seed =123,
  p.truth =
   array(c(

     c(0.03,0.1,0.2,0.3,0.4,   #for M=1 Q=1
       0.04,0.2,0.3,0.4,0.5,   #for M=2 Q=1
       0.05,0.3,0.4,0.5,0.6)   #for M=3 Q=1

       ),

  dim = c(5,3,1) #C M Q

  )#array

)




#========================================================================================
#
#========================================================================================

#================The third example======================================

#     The hits rate cannot take any values, since there is a trend that a hit rate of
#   a higher confidence level is a higher. So, If it is difficult for user to create
#   a true hit rates, then  by taking estimates as true parameters,
#   user can replicate datasets.
#     To do so, work follow is first fitting, secondly extracting estimates,
#   thirdly apply this function (hits_creator_from_rate() ).


# * Fitting

     fit <- fit_Bayesian_FROC(
             dataList.Chakra.Web.orderd,
             ite = 1111,  #  For simplicity, we take small MCMC samples.
             summary =FALSE)

# * Extracting

        estimates <- extract_estimates_MRMC(fit)

         ppp <- estimates$ppp.EAP

#      Note that ppp is an array
#     whose dimension is constituted by number of confidence levels, modalities, readers.


# *  Replicating as an true values is ppp


        hits  <-   hits_creator_from_rate(p.truth = ppp )


# <<Remark>>
#     ppp is an array.  ignoring its indices, we can write that

#          hits ~ Binomial(ppp, NL)

#    Where NL is a number of lesions.

#   By writing its component explicitly, we can write

#        Hits[c,m,r] ~ Binomial(ppp[c,m,r], NL)

#        Where c means the c-th confidence level,
#              m  means the m-th modality,
#              r means the r-th reader.
# }
# NOT RUN {
# dottest
# }