Cardiovascular risk prediction: a comparative study of Framingham and quantum neural network based approach

Figures & data

Table 1 Risk levels for total cholesterol

Total cholesterol	Risk
Less than 200 mg/dL (5.17 mmol/L)	Desirable
200–239 mg/dL (5.17–6.18 mmol/L)	Borderline high risk
240 and over (6.2 mmol/L)	High risk

Table 2 Risk levels for high density lipoprotein

High density lipoprotein	Risk
Less than 40 mg/dL (men) (1.03 mmol/L)	Increased risk of heart disease
Less than 50 mg/dL (women) (1.29 mmol/L)	Increased risk of heart disease
Greater than 60 mg/dL (1.55 mmol/L)	Some protection against heart disease

Table 3 Blood pressure range according to age

Age group	Lower limita	Average limita	Upper limita
15–19	105/73	117/77	120/81
20–24	108/75	120/79	132/83
25–29	109/76	121/80	133/84
30–34	110/77	122/81	134/85
35–39	111/78	123/82	135/86
40–44	112/79	125/83	137/87
45–49	115/80	127/84	139/88
50–54	116/81	129/85	142/89
55–59	118/82	131/86	144/90
60–64	121/83	134/87	147/91
65–69	122/84	136/88	149/92
≥70	123/85	138/89	151/93

Note:

a Systolic/diastolic blood pressure range (mmHg).

Table 4 BMI range

Category	BMI range, kg/m^2
Severely underweight	<16.5
Underweight	16.5 to 18.5
Normal	18.5 to 25
Overweight	25 to 30
Obese	>30

Abbreviation: BMI, body mass index.

Figure 1 Activity diagram of proposed system.

Abbreviations: QNN, quantum neural network; CHD, coronary heart disease; CVD, cardiovascular disease.

Table 5 Forecast of number of cases (both male and female) of CVD in India

Year/age group	20–29	30–39	40–49	50–59	60–69	Total
2000	4,511,192	5,619,470	5,909,011	7,334,040	5,349,313	28,723,024
2005	6,150,408	7,566,792	7,659,859	10,308,145	6,894,266	38,579,471
2010	8,317,184	9,608,484	9,682,192	13,981,687	9,137,258	50,726,804
2015	10,492,011	13,134,021	12,628,644	18,230,363	11,884,240	66,369,279

Abbreviation: CVD, cardiovascular disease.

Table 6 Input parameters

Serial number	Parameters
1	Age
2	Sex
3	Tobacco smoke
4	High density lipoprotein
5	Systolic blood pressure
6	Total cholesterol
7	Medication

Figure 2 Architecture of quantum neural network.

Notes: n_i denotes the input to the input layer; O_j and O_k denote the output of hidden and output layer, respectively. The weights between input and hidden layers are denoted by W_ij and the weights between hidden and output layers are denoted by W_kj.

Figure 3 Flowchart of quantum neural network for heart disease prediction system.

Notes: θ^r denotes quantum interval between sub-states, with the difference of quantum level r. n_s denotes the number of grades or excitation levels, η is learning rate, δ_k is error rate of output layer, and δ_j error rate of hidden layer. n_i denotes the input to the input layer. O_j and O_k denote the output of hidden and output layer, respectively. The weights between input and hidden layers are denoted by W_ij and the weights between hidden and output layers are denoted by W_kj. t denotes target value.

Table 7 Data partition set

Data partition set	Records	Percentage
Training set	189	27.44
Validation set	250	36.28
Test set	250	36.28
Total	689	100.00

Table 8 Percentage level of risk categories

Risk category	Percentage
Normal (under baseline risk)	<26
Low risk range	26–51
Intermediate risk range	51–76
Highest risk range	≥76

Table 9 Baseline value of parameters

Serial no	Age	Sex	TC (mg/dL)	SBP (mmHg)	HDL (mg/dL)
1	20	Male	172	120	60
2	25	Male	174	121	60
3	30	Male	174	122	60
4	35	Male	174	123	60
5	40	Male	174	125	60
6	45	Male	175	127	60
7	50	Male	178	129	60
8	55	Male	182	131	60
9	60	Male	182	134	60
10	65	Male	182	136	60
11	70	Male	182	138	60
12	20	Female	165	120	70
13	25	Female	167	121	70
14	30	Female	167	122	70
15	40	Female	167	123	70
16	45	Female	169	125	70
17	35	Female	172	127	70
18	50	Female	172	129	70
19	55	Female	182	131	70
20	60	Female	182	134	70
21	65	Female	182	136	70
22	70	Female	182	138	70

Abbreviations: TC, total cholesterol; HDL, high density lipoprotein; SBP, systolic blood pressure.

Table 10 Percentage-wise patient distribution for various risk factors

Risk factors	Percentage-wise patient distribution
	Lower	Average	High
Blood pressure	8%	29%	63%
Total cholesterol	6%	12%	82%
High density lipoprotein	73%	N/A	27%

Abbreviation: N/A, not applicable.

Table 11 Percentage-wise patient distribution for smoking and being on medication

Risk factors	Percentage-wise patient distribution
	Yes	No
Smoker	24.35%	75.65%
Medication	85.50%	14.50%

Table 12 Comparison of the results of the proposed algorithm with similar algorithms

Method	Accuracy
Proposed algorithm with quantum neural network	98.57%
Fuzzy-evidential based theories^Citation3	91.58%
Neural network^Citation4	84%
Bayesian classification and neural network^Citation5	80%
Probability theory (logistic regression)^Citation6	77%
Framingham risk score^Citation41	19.22%

Figure 4 Graph showing accuracy of proposed system and Framingham risk score (FRS).

Abbreviation: QNN, quantum neural network.

Table 13 Data showing comparison of the proposed system and FRS of random testing on different experimental values

Parameters used for comparison of proposed system and FRS (patient record)							Manually equated/calculated desired result		Desired result based on doctor’s diagnosis	Result and accuracy of proposed QNN based system		% accuracy QNN	Accuracy group-wise	Result FRS	% accuracy FRS	Accuracy group-wise
Age (Years)	Sex	TC (mmol/L)	HDL (mmol/L)	Smoker	SBP (mmHg)	Medication	Output	Risk category		Output	Risk category
40	Male	4.20	2.20	No	117	Yes	18.75%	Normal	Normal	18.71%	Normal	99.79	99.94	0.99	5.28	19.60
35	Female	5.00	1.81	No	121	Yes	37.50%	Low risk	Low risk	37.50%	Low risk	100.00		0.77	2.04
55	Female	5.28	1.68	No	132	Yes	43.75%	Low risk	Low risk	43.75%	Low risk	100.00		6.32	14.44
45	Male	5.28	1.68	Yes	126	Yes	43.75%	Low risk	Low risk	43.70%	Low risk	99.89		9.45	21.60
70	Male	5.83	1.42	No	140	Yes	56.25%	Intermediate risk	Intermediate risk	56.22%	Intermediate risk	99.95		27.71	49.26
65	Female	4.74	1.94	No	135	Yes	31.25%	Low risk	Low risk	31.24%	Low risk	99.97		8.34	26.70
45	Male	7.17	0.78	No	190	Yes	87.50%	Highest risk	Highest risk	87.50%	Highest risk	100.00		15.64	17.87
60	Male	5.28	1.68	No	132	Yes	43.75%	Low risk	Low risk	43.70%	Low risk	99.89	99.96	13.49	30.83	20.49
50	Male	6.37	1.17	Yes	134	Yes	68.75%	Intermediate risk	Intermediate risk	68.76%	Intermediate risk	100.01		23.37	33.99
60	Female	4.20	2.20	No	130	Yes	18.75%	Normal	Normal	18.76%	Normal	100.05		4.50	24.00
25	Male	6.37	1.17	Yes	126	Yes	68.75%	Intermediate risk	Intermediate risk	68.76%	Intermediate risk	100.01		1.68	2.44
60	Male	4.20	2.20	No	126	Yes	18.75%	Normal	Normal	18.71%	Normal	99.79		7.43	39.60
20	Female	7.74	0.65	No	160	No	93.75%	Highest risk	Highest risk	93.75%	Highest risk	100.00		0.92	0.99
35	Male	6.63	1.04	Yes	129	Yes	75.00%	Intermediate risk	Intermediate risk	75.00%	Intermediate risk	100.00		8.67	11.57
60	Male	8.29	0.52	No	190	Yes	100.00%	Highest risk	Highest risk	100.00%	Highest risk	100.00	99.97	46.52	46.52	30.57
60	Female	7.74	0.65	No	180	Yes	93.75%	Highest risk	Highest risk	93.75%	Highest risk	100.00		31.23	33.32
25	Female	8.29	0.52	No	165	Yes	100.00%	Highest risk	Highest risk	100.00%	Highest risk	100.00		3.65	3.65
25	Male	5.83	1.42	Yes	123	Yes	56.25%	Intermediate risk	Intermediate risk	56.22%	Intermediate risk	99.95		1.00	1.79
45	Male	5.83	1.42	No	129	No	56.25%	Intermediate risk	Intermediate risk	56.22%	Intermediate risk	99.95		6.26	11.13
65	Female	7.74	0.65	No	170	Yes	93.75%	Highest risk	Highest risk	93.75%	Highest risk	100.00		35.44	37.81
70	Male	5.28	1.68	Yes	136	Yes	43.75%	Low risk	Low risk	43.70%	Low risk	99.89		34.89	79.74
40	Female	4.74	1.94	No	125	Yes	31.25%	Low risk	Low risk	31.25%	Low risk	100.00	99.97	1.26	4.04	15.77
65	Female	6.37	1.17	No	145	Yes	68.75%	Intermediate risk	Intermediate risk	68.76%	Intermediate risk	100.01		20.08	29.20
45	Female	5.00	1.81	No	122	Yes	37.50%	Low risk	Low risk	37.50%	Low risk	100.00		2.16	5.75
25	Male	5.28	1.68	No	120	Yes	43.75%	Low risk	Low risk	43.70%	Low risk	99.89		0.17	0.39
40	Female	6.09	1.30	No	125	Yes	62.50%	Intermediate risk	Intermediate risk	62.50%	Intermediate risk	100.00		3.08	4.93
40	Male	7.74	0.65	Yes	160	No	93.75%	Highest risk	Highest risk	93.73%	Highest risk	99.98		24.33	25.96
65	Male	5.28	1.68	No	134	Yes	43.75%	Low risk	Low risk	43.70%	Low risk	99.89		17.55	40.10
65	Male	3.65	2.46	Yes	124	Yes	6.25%	Normal	Normal	6.25%	Normal	100.00	99.90	14.53	23.25	31.00
55	Male	6.09	1.30	Yes	134	Yes	62.50%	Intermediate risk	Intermediate risk	62.50%	Intermediate risk	100.00		26.34	42.15
65	Female	5.54	1.55	No	140	Yes	50.00%	Low risk	Low risk	49.80%	Low risk	99.60		13.11	26.21
55	Male	4.20	2.20	No	123	No	18.75%	Normal	Normal	18.71%	Normal	99.79		5.00	26.67
55	Male	6.92	0.91	No	139	Yes	81.25%	Highest risk	Highest risk	81.26%	Highest risk	100.01		23.89	29.40
45	Male	8.29	0.52	Yes	170	No	100.00%	Highest risk	Highest risk	100.00%	Highest risk	100.00		38.31	38.31
20	Male	8.29	0.52	No	160	Yes	100.00%	Highest risk	Highest risk	100.00%	Highest risk	100.00	98.36	1.10	1.10	13.96
35	Male	8.29	0.52	Yes	175	Yes	100.00%	Highest risk	Highest risk	99.96%	Highest risk	99.96		21.32	21.32
55	Female	5.83	1.42	No	135	Yes	56.25%	Intermediate risk	Intermediate risk	50.75%	Low risk	90.22		8.85	15.74
30	Female	4.74	1.94	No	115	No	31.25%	Low risk	Low risk	31.25%	Low risk	100.00		0.24	0.78
50	Male	7.74	0.65	Yes	175	No	93.75%	Highest risk	Highest risk	93.73%	Highest risk	99.98		40.08	42.75
35	Female	5.28	1.68	No	120	Yes	43.75%	Low risk	Low risk	43.75%	Low risk	100.00		0.91	2.07
60	Female	4.45	2.07	No	130	Yes	25.00%	Normal	Normal	25.01%	Normal	100.04	99.99	5.17	20.69	17.02
55	Female	3.91	2.33	No	125	Yes	12.50%	Normal	Normal	12.50%	Normal	100.00		2.52	20.14
60	Male	6.92	0.91	Yes	160	Yes	81.25%	Highest risk	Highest risk	81.26%	Highest risk	100.01		44.34	54.57
40	Male	4.74	1.94	No	120	Yes	31.25%	Low risk	Low risk	31.21%	Low risk	99.87		1.57	5.02
50	Male	4.45	2.07	No	123	Yes	25.00%	Normal	Normal	25.00%	Normal	100.00		3.93	15.71
35	Female	3.65	2.46	No	110	Yes	6.25%	Normal	Normal	6.25%	Normal	100.00		0.17	2.75
25	Female	4.20	2.20	No	110	Yes	18.75%	Normal	Normal	18.75%	Normal	100.00		0.04	0.24
20	Female	4.20	2.20	No	110	Yes	18.75%	Normal	Normal	18.75%	Normal	100.00	99.28	0.01	0.06	13.85
50	Female	4.45	2.07	No	125	Yes	25.00%	Normal	Normal	24.01%	Normal	96.04		2.47	9.90
40	Female	6.37	1.17	No	129	Yes	68.75%	Intermediate risk	Intermediate risk	68.75%	Intermediate risk	100.00		4.10	5.97
65	Male	6.92	0.91	No	175	No	81.25%	Highest risk	Highest risk	81.26%	Highest risk	100.01		36.06	44.38
55	Male	3.91	2.33	No	121	Yes	12.50%	Normal	Normal	12.50%	Normal	100.00		4.10	32.78
25	Female	6.37	1.17	No	125	Yes	68.75%	Intermediate risk	Intermediate risk	68.00%	Intermediate risk	98.91		0.60	0.87
40	Female	4.45	2.07	No	115	Yes	25.00%	Normal	Normal	25.00%	Normal	100.00		0.75	2.99
30	Female	5.83	1.42	No	120	Yes	56.25%	Intermediate risk	Intermediate risk	56.25%	Intermediate risk	100.00	99.97	0.71	1.26	14.90
60	Male	5.54	1.55	No	134	Yes	50.00%	Low risk	Low risk	50.00%	Low risk	100.00		15.57	31.14
50	Male	6.92	0.91	Yes	190	Yes	81.25%	Highest risk	Highest risk	81.26%	Highest risk	100.01		30.24	37.22
50	Female	6.63	1.04	No	180	Yes	75.00%	Intermediate risk	Intermediate risk	75.00%	Intermediate risk	100.00		11.20	14.94
35	Male	4.20	2.20	No	116	Yes	18.75%	Normal	Normal	18.71%	Normal	99.79		0.46	2.46
55	Female	4.45	2.07	No	124	Yes	25.00%	Normal	Normal	25.00%	Normal	100.00		3.36	13.46
35	Female	6.63	1.04	No	160	Yes	75.00%	Intermediate risk	Intermediate risk	75.00%	Intermediate risk	100.00		2.87	3.82
20	Male	5.83	1.42	Yes	122	Yes	56.25%	Intermediate risk	Intermediate risk	56.22%	Intermediate risk	99.95	99.98	0.28	0.49	15.05
55	Female	6.63	1.04	No	140	No	75.00%	Intermediate risk	Intermediate risk	75.00%	Intermediate risk	100.00		14.64	19.52
70	Male	6.92	0.91	Yes	180	Yes	81.25%	Highest risk	Highest risk	81.26%	Highest risk	100.01		56.33	69.33
40	Female	5.54	1.55	No	126	Yes	50.00%	Low risk	Low risk	50.00%	Low risk	100.00		2.21	4.42
45	Female	4.74	1.94	No	120	Yes	31.25%	Low risk	Low risk	31.23%	Low risk	99.94		1.72	5.50
25	Female	4.74	1.94	No	115	Yes	31.25%	Low risk	Low risk	31.25%	Low risk	100.00		0.09	0.30
30	Male	3.65	2.46	Yes	112	No	6.25%	Normal	Normal	6.25%	Normal	100.00		0.36	5.75

Abbreviations: TC, total cholesterol; HDL, high density lipoprotein; SBP, systolic blood pressure; QNN, quantum neural network; FRS, Framingham risk score.

Table 14 Validation based on the dataset from the Framingham study of 5,209 American CVD patients

Out of 5,209 CVD patients	Very high riska	Intermediate riska	Low riska	Normala
Deaths recorded due to myocardial infarction =378	32.93%	41.46%	25.61%	Nil
Deaths recorded due to coronary heart disease =605	37.17%	43.77%	19.06%	Nil

Note:

a Predicted by the proposed system.

Abbreviation: CVD, cardiovascular disease.

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