__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:

_{}