Comparison between multiple logistic regression and machine learning methods in prediction of abnormal thallium scans in type 2 diabetes

Table 1 Participant demographics

Variables	mean ± SD	N
Age	67.38 ± 9.69	556
Body mass index	26.16 ± 3.9	556
Duration of diabetes	13.69 ± 7.94	556
Systolic blood pressure	131.14 ± 15.42	493
Diastolic blood pressure	73.32 ± 10.15	493
Hemoglobin	12.92 ± 1.68	444
Triglyceride	153.74 ± 45.85	539
Glycated hemoglobin	7.79 ± 1.36	538
High density lipoprotein cholesterol	122.65 ± 74.34	535
Low density lipoprotein cholesterol	49.65 ± 14.75	498
Alanine aminotransferase	23.87 ± 13.94	537
Creatinine	1.16 ± 1	536
Microalbumin creatinine ratio	194.18 ± 733.73	526
Homeostasis assessment-insulin resistance	0.63 ± 0.34	366
Homeostasis assessment-insulin secretion	1.71 ± 0.37	366

Table 2 Participant demographics – sex, smoking and sum stressed score

	N (%)	N
Sex		556
0	287 (51.62)
1	269 (48.38)
Smoking		310
0	202 (65.16)
1	108 (34.84)
Sum stressed score		556
0	180 (32.37)
1	376 (67.63)

Table 3 Summary of the values of the hyperparameters for the best random forest, classification and regression tree, Naïve Byer’s classifier, eXtreme gradient boosting

Methods	Hyperparameters	Best value	Meaning
RF	Mtry	8	The number of random features used in each tree
	Ntree	500	The number of trees in forest
CART	Minispilt	20	The minimum number of observations required to attempt a split in a node
	Minibucket	7	The minimum number of observations in a terminal node
	Maxdepth	10	The maximum depth of any node in the final tree
	Xval	10	Number of cross-validations
	Cp	0.03588	Complexity parameter: The minimum improvement required in the model at each node
XGBoost	Nrounds	100	The number of tree model iterations
	Max_depth	3	The maximum depth of a tree
	Eta	0.4	Shrinkage coefficient of tree
	Gamma	0	The minimum loss reduction
	Subsample	0.75	Subsample ratio of columns when building each tree
	Colsample_bytree	0.8	Subsample ratio of columns when constructing each tree
	Rate_drop	0.5	Rate of trees dropped
	Skip_drop	0.05	Probability of skipping the dropout procedure during a boosting iteration
	Min_child_weight	1	The minimum sum of instance weight
NB	Fl	0	Adjustment of Laplace smoother
	Usekernel	TRUE	Using kernel density estimate for continuous variable versus a Gaussian density estimate
	Adjust	1	Adjust the bandwidth of the kernel density

CART: Classification and regression tree; RF: random forest; XGBoost: eXtreme gradient boosting; NB: Naïve Byes.

Table 4 The average performance of the LR, random forest, stellate ganglion block, classification and regression tree, and eXtreme gradient boosting methods

	Accuracy	Sensitivity	Specificity	AUC
LGR	0.685 ± 0.072	0.687 ± 0.152	0.683 ± 0.114	0.703 ± 0.057
CART	0.541 ± 0.074	0.546 ± 0.078	0.529 ± 0.670	0.540 ± 0.070
RF	0.707 ± 0.047	0.711 ± 0.100	0.678 ± 0.099	0.707 ± 0.037
XGBoost	0.712 ± 0.072	0.727 ± 0.139	0.674 ± 0.088	0.719 ± 0.062
NB	0.692 ± 0.059	0.702 ± 0.116	0.669 ± 0.090	0.704 ± 0.056

AUC: Area under the curve; LGR: Logistic regression; CART: Classification and regression tree; RF: Random forest; XGBoost: eXtreme gradient boosting; NB: Naïve Byes.

Table 5 The variable importance and rank of the importance of the risk factors derived from machine learning methods

Variables	RF	XGBoost	NB	Average	Rank
Sex	100.0 ± 0	100.0 ± 0	100.0 ± 0	100.0	1.0
Body mass index	54.2 ± 6.6	61.1 ± 14.7	86.2 ± 6.8	67.1	2.0
Age	13.1 ± 7.6	78.3 ± 13.2	67.9 ± 6.5	53.1	3.0
Low density lipoprotein cholesterol	30.4 ± 3.1	8.4 ± 12.8	71.0 ± 7.8	36.6	4.0
Glycated hemoglobin	15.4 ± 5.9	12.8 ± 11.9	48.0 ± 8.3	25.4	5.0
Smoking	12.2 ± 2.7	28.8 ± 9.2	34.5 ± 6.6	25.2	6.0
Creatinine	10.1 ± 2.3	5.3 ± 9.12	53.1 ± 7.3	22.8	7.0
Duration	6.3 ± 4.61	41.5 ± 8.6	10.1 ± 8.9	19.3	8.0
Hemoglobin	8.0 ± 4.16	16.6 ± 8.9	17.0 ± 5.7	13.8	9.0
Blood urine nitrogen	9.0 ± 8.15	6.5 ± 6.79	17.3 ± 9.6	11.0	10.0
Systolic blood pressure	4.2 ± 1.03	21.6 ± 5.1	6.4 ± 2.88	10.7	11.0
Triglyceride	5.4 ± 17.5	15.0 ± 4.4	11.1 ± 12.3	10.5	12.0
Microalbumin	4.3 ± 2.23	3.6 ± 3.83	22.7 ± 6.9	10.2	13.0
Diastolic blood pressure	2.5 ± 5.91	18.9 ± 3.7	5.6 ± 9.33	9.0	14.0
Alainine aminotransferase	3.2 ± 5.96	6.9 ± 3.90	13.0 ± 12.6	7.7	15.0
High density lipoprotein cholesterol	1.3 ± 3.60	9.8 ± 3.29	7.3 ± 8.41	6.1	16.0
HOMA-IR	5.7 ± 2.85	2.2 ± 2.52	10.2 ± 8.1	6.0	17.0
HOMA-B	4.3 ± 2.22	0.0 ± 0.00	7.4 ± 8.831	3.9	18.0

The most important sixth rank. RF: Random forest; XGBoost: eXtreme gradient boosting; NB: Naïve Byes; HOMA-IR: Homeostasis assessment insulin resistance; HOMA-B: homeostasis model assessment of beta-cell function.