A new mathematical model for diagnosing chronic diseases (kidney failure) using ANN

Figures & data

Table 1. Classification of CKD defined by KDOQI

Stage	State of kidney function	Classification by severity by $GFR$
1	Kidney damage with normal or increasing in GFR	$GFR\ge 90$
2	Kidney damage with mild decreasing in GFR	$GFR$ of $60-89$
3	Moderate with decreasing in GFR	$GFR$ of $30-59$
4	Severe with decreasing in GFR	$GFR$ of $15-29$
5	Kidney failure	$GFR<15$ (or dialysis)

Figure 1. Back-propagation neural network method (BPNN).

Figure 2. Nodes hidden layer-ridge basis function.

Table 2. Training data for kidney failure

Data	Unit
Sex	0 or 1
Age	Numeric
Creatinine	Numeric
Weight	Numeric
Glucose (GLU)	Numeric
Systolic pressure (SP)	Numeric
Hematuria	Numeric
Blood urea nitrogen	Numeric
Protein in urine (UP)	0 or 1,2,3,…
(BUN) GFR	0 or 1,2,3,4,5

Table 3. The influence factors in the GFR formula

Factors	Description	Mean	Max	Mini
Sex	0 female, 1 male	–	–	–
Age	Integer	64.6	94	22
Creatinine	Real	0.45	4.36	0.36
Weight	Real	61.4	94	47

Table 4. Neural network influence factors for CKD detection

Factors	Description	Mean	Max	Mini
Creatinine	Real	0.45	4.36	0.36
Glucose (GLU)	Real	107.93	269	80
Systolic pressure (SP)	Real	137.34	196	89
Hematuria	Real	–	–	–
Blood urea nitrogen	Real	16.20	81.10	5.30
Protein in urine (UP)	0 negative 1,2,3,…,trace	–	–	–
(BUN) GFR	0 negative 1,2,3,4,5 Positive measured in levels	–	–	–

Table 5. Data distribution for model training, testing, and cross verification

Input data for modeling	Number of records	Number of desired output
Training data	670	300 negative 370 positive
Testing data	380	180 negative 200 positive
Cross verification data	100	40 negative 60 positive

Figure 3. The BPNN model for kidney failure.

Figure 4. Training least-squares error for the (BPNN) model.

Table 6. Training and testing data least-squares error for the (BPNN) model

No. of neurons in hidinglayers	Epochs	Training Least-squares error	Testing data Least-squares error
2	5000	${10}^{-5}$	0.4367
5	2009	${10}^{-7}$	0.1739
10	405	${10}^{-11}$	0.0832
20	15	${10}^{-15}$	0.0164
30	82	${10}^{-20}$	0.0085
50	7	${10}^{-25}$	0.0012
100	6	${10}^{-25}$	0.0012