Explaining Medical Model Exceptions - Computational Intelligence in Healthcare: Advanced Methodologies - page 267

grades, they are denoted as F0 - the initial measurement of factor F, and F3, F6, and
F12 - the measurements of factor F after 3, 6, and 12 months.
All performed measurements are stored in the observed database, which contains
150 records (one patient - one record) with 460 variables per record. 12 variables are
constants; the other 448 variables represent 112 different parameters.
The factors can not be considered as completely independent from each other, but
there are different types of dependency among specific factors. Even a strict mathemati-
cal dependency can occur, for example the triple: “time of controlled training, work
performed during this time, and average achieved power”, can be expressed as Power =
Work/Time. Less strict are relations between factors of biochemical nature. An increase
of parathyroid hormone, for example, implies an increase of blood phosphorus. Such
relations between factors enable us to fill some missing data in the data set.

4.2 Imputation of Missing Data

In ISOR, again CBR is applied, now to impute missing data; the calculated values are
filled in the observed database. The knowledge is contained in the case base, namely
in form of solutions of former cases.

4.2.1 Types of Solutions
There are three types of numerical solutions: exact, estimated, and binary. Some ex-
amples and imputation formulas are shown in table 3. All types of solutions are dem-
onstrated by examples in the next section.
When a missing value can be completely imputed, it is called an exact solution.
Exact solutions are based on other parameters. A medical expert has defined them as
specific relations between parameters, using ISOR. As soon as they have been used
once, they are stored in the case base of ISOR and can be retrieved for further cases.

Table 3. Some examples of solutions and imputation formulas. Abbreviations: BC = Breath
consumption, BF = Breath frequency, BV = Breath volume, HAT = Hematocrit, P = Phospho-
rus, PTH = Parathyroid hormone, PV = plasma volume

Missing
parameter

Type of
solution

Numeric
solution
(examples)

Description Parameters Time

points

PTH Binary 1 If P(T) >= P(t)

then PTH(T) >= PTH(t)
Else PTH(T) < PTH(t)

P, PTH 0 and 6

HT Exact 36,2 HT = 100 *

(1-PV/0.065 * Weight)

PV, Weight 6

HT Estimated 29,1 Y(6) = Y(3)*0.66

+ Y(12) * 0.33

HT 3 and 12

WorkJ Exact 30447,1 WorkJ = MaxPower *

Time * 0.5

Time,
MaxPower

12

BC Exact 15,6 BC = BF * BV BF, BV 12

Oxygen
pulse

Estimated 10,29 Linear regression O2plus 0 and 3

and 12