Mathematical algorithm

A list of differential diagnoses is provided by the database with each set of input data.  The differential diagnoses have an assigned value of profile factor (PF).  The PF value for a neoplasm reflects how well its immunophenotyping pattern matches that of a given case.  In this project, accumulated data from published literature are utilized to enhance the sensitivity and specificity of the differential diagnosis.  The formula for calculating PF is as following:

                                                                          

Where   

PF  :   profile factor for a particular neoplasm

Cn   :   profile coefficient for an input data (0   Cn ≤ 1)

n    = 1 to N

N    :  the number of (not-NULL) attributes of a neoplasm that have input data

The profile coefficient is calculated as:

Cn  = PosRatio(i,j)    if input data is positive (+), and  Cn =NegRatio(i,j)  if input data is negative (-)

The ratio of cases that are positive for a certain marker for a disorder, PosRatio(i,j), is defined as:

         

Where   

 i:                          the i th  disorder

 j:                          the j th marker

:        number of cases that are positive for the j th marker for the ith disorder                

:              number of cases under study for the j th marker for the ith disorder                     

The ratio of cases that are negative for a certain marker for a disorder, NegRatio(i,j), is calculated as:

   =  1 -           

 

 with **tag in database indicates that the marker is very critical, its contribution will be twice as that of other markers (the increment will be 2x  in calculationg PF).

The normalized  profile factor (nPF)  is calculated to convert PF to a value between 0 and 1,  ie. (0   nPF ≤ 1) using a sigmoid function: