Explainable machine learning model for predicting minor amputation in diabetic foot ulcers

Table 1 Comparison of basic information between the two groups, n (%)/mean ± SD/median (interquartile range)

Variables	Non-amputation group (n = 370)	Minor amputation group (n = 315)	P value
Gender
Male	259 (70)	243 (77)	0.043
Female	111 (30)	72 (23)
Smoking
No	187 (51)	171 (54)	0.367
Yes	183 (49)	144 (46)
Alcohol
No	239 (65)	202 (64)	0.962
Yes	131 (35)	113 (36)
Hypertension
No	122 (33)	96 (30)	0.537
Yes	248 (67)	219 (70)
CAD
No	265 (72)	224 (71)	0.950
Yes	105 (28)	91 (29)
ABI
Abnormal	256 (69)	206 (65)	0.330
Normal	114 (31)	109 (35)
CVD
No	277 (75)	239 (76)	0.829
Yes	93 (25)	76 (24)
PVC
No	164 (44)	93 (30)	< 0.001
Yes	206 (56)	222 (70)
Age (years)	62.5 (54, 70)	63 (55, 70)	0.534
DM duration (years)	17 (10, 21)	19 (10, 23)	0.313
DFU duration (months)	1.50 (0.70, 4.00)	1.00 (0.70, 3.00)	0.480
Diabetic peripheral vascular disease	355 (96)	299 (95)	0.646
PAD	107 (29)	198 (64)	< 0.001
DKD	167 (45)	173 (55)	0.013
DR	185 (50)	176 (56)	0.145
Wagner grade > 3	292 (78)	271 (85)	0.020
Wound size			0.109
Small	167 (45)	126 (40)
Medium	111 (30)	88 (28)
Large	92 (25)	101 (32)
Ulcer site			0.484
Forefoot	342 (93)	283 (90)
Midfoot	24 (6)	27 (9)
Hindfoot/lower leg	0 (0)	3 (0.9)
Multiple sites	4 (1)	2 (0.6)
WBC (109/L)	7.00 (5.78, 8.81)	8.60 (6.78, 11.29)	< 0.001
RBC (109/L)	3.99 ± 0.67	3.77 ± 0.64	< 0.001
Hb (g/L)	117.19 ± 18.96	110.16 ± 19.60	< 0.001
PLT (109/L)	260.50 (211.00, 327.50)	315.00 (246.00, 406.50)	< 0.001
NEUT (109/L)	4.60 (3.50, 6.18)	6.20 (4.60, 8.84)	< 0.001
MONO (109/L)	0.47 (0.36, 0.60)	0.57 (0.44, 0.73)	< 0.001
LYM (109/L)	1.65 (1.25, 2.05)	1.49 (1.17, 1.92)	0.004
CRP (mg/L)	9.00 (2.39, 27.64)	34.60 (11.57, 76.26)	< 0.001
HbA1c (%)	8.50 (7.30, 9.85)	9.10 (7.80, 10.60)	< 0.001
FPG (mmol/L)	8.15 (6.10, 10.70)	8.10 (6.20, 11.00)	0.464
BUN (mmol/L)	6.40 (4.90, 8.50)	6.20 (4.70, 8.10)	0.152
Scr (µmol/L)	71.00 (58.05, 94.00)	72.30 (59.00, 96.85)	0.592
TC (mmol/L)	3.78 (3.17, 4.37)	3.66 (2.96, 4.31)	0.074
TG (mmol/L)	1.30 (1.02, 1.83)	1.24 (0.99, 1.69)	0.169
HDL-C (mmol/L)	0.92 (0.79, 1.09)	0.83 (0.72, 0.95)	< 0.001
LDL-C (mmol/L)	2.12 (1.64, 2.62)	2.14 (1.65, 2.67)	0.840
ALB (g/L)	38.40 (35.44, 41.48)	35.20 (32.15, 38.95)	< 0.001
Ca (mmol/L)	2.22 (2.12, 2.32)	2.19 (2.08, 2.30)	< 0.001
BUA (µmol/L)	318.00 (250.25, 378.75)	285.00 (227.00, 364.50)	0.002
FIB (g/L)	4.26 (3.63, 4.89)	5.03 (4.40, 5.53)	< 0.001
BMI (kg/m2)	24.18 (22.22, 26.76)	24.24 (22.31, 26.65)	0.678
Neutrophil percentage	66.90 (59.15, 73.60)	72.70 (66.40, 79.05)	< 0.001
Lymphocyte percentage	23.00 (17.02, 30.10)	17.80 (12.35, 23.30)	< 0.001
NLR	2.90 (1.96, 4.25)	4.05 (2.86, 6.34)	< 0.001
NPR	0.02 (0.01, 0.02)	0.02 (0.02, 0.03)	< 0.001
PLR	159.26 (118.39, 216.67)	210 (151.86, 285.21)	< 0.001
MHR	0.49 (0.36, 0.71)	0.67 (0.50, 0.90)	< 0.001
NHR	4.96 (3.64, 7.33)	7.55 (5.20, 10.36)	< 0.001
SIRI	0.86 (0.47, 1.73)	1.48 (0.80, 3.27)	< 0.001
CALLY	0.74 (0.20, 3.37)	0.17 (0.07, 0.56)	< 0.001
SII	757.04 (464.92, 1204.66)	1302.39 (747.74, 2186.72)	< 0.001

ALB: Albumin; BMI: Body mass index; BUA: Blood uric acid; BUN: Blood urea nitrogen; Ca: Serum calcium; CAD: Coronary artery disease; CALLY: C-reactive protein-albumin-lymphocyte; CRP: C-reactive protein; CVD: Cerebrovascular disease; DKD: Diabetic kidney disease; FIB: Fibrinogen; FPG: Fasting plasma glucose; Hb: Hemoglobin; HbA1c: Hemoglobin A1c; HDL-C: High-density lipoprotein cholesterol; LDL-C: Low-density lipoprotein cholesterol; LYM: Lymphocyte count; MHR: Monocyte-high-density lipoprotein cholesterol ratio; MONO: Monocyte count; NEUT: Neutrophil count; NHR: Neutrophil-high-density lipoprotein cholesterol ratio; NLR: Neutrophil-lymphocyte ratio; NPR: Neutrophil-platelet ratio; PLR: Platelet-lymphocyte ratio; PLT: Platelet count; PVC: Pedal vessel calcification; RBC: Red blood cell count; Scr: Serum creatinine; SII: Systemic immune-inflammation index; SIRI: Systemic inflammation response index; TC: Total cholesterol; TG: Triglycerides; WBC: White blood cell count; PAD: Peripheral arterial disease; DR: Diabetic retinopathy; DM: Diabetes mellitus; DFU: Diabetic foot ulcer; ABI: Ankle-brachial index.

Table 2 Multivariable logistic regression analysis

Variables	B	P value	OR (95%CI)
PVC
No	Ref	Ref	Ref
Yes	0.486	0.009	1.626 (1.131-2.336)
PLT	0.001	0.356	1.001 (0.999-1.003)
MONO	0.792	0.111	2.208 (0.835-5.837)
SII	0.000	0.216	1.000 (1.000-1.000)
CALLY	-0.088	0.019	0.915 (0.850-0.986)
Lymph percentage	0.006	0.732	1.006 (0.971-1.042)
CRP	0.002	0.554	1.002 (0.996-1.008)
HDL-C	-0.700	0.093	0.496 (0.219-1.126)
ALB	-0.043	0.028	0.958 (0.921-0.996)
FIB	0.407	0.001	1.503 (1.176-1.920)
BUA	-0.002	0.089	0.998 (0.997-1.000)

ALB: Albumin; B: Regression coefficient; BUA: Blood uric acid; CALLY: C-reactive protein-albumin-lymphocyte; CRP: C-reactive protein; FIB: Fibrinogen; HDL-C: High-density lipoprotein cholesterol; MONO: Monocyte count; OR: Odds ratio; PLT: Platelet count; PVC: Pedal vessel calcification; Ref: Reference category; SII: Systemic immune-inflammation index.

Table 3 Hyperparameter optimization for predictive models

Model	Hyperparameter	Hyperparameter search space	Optimal hyperparameters
RF	Trees	200-500	300
	Mtry	2-10	2
	Min_n	20-50	30
KNN	Neighbors	3-11	11
XGBoost	Mtry	2-8	2
	Min_n	5-20	20
	Tree_depth	1-3	3
	Learn_rate	0.001-0.1	0.001
	Loss_reduction	0.001-1	0.001
	Sample_size	0.8-1	0.8
LR	Penalty	0.001-1	0.001
MLP	Hidden_units	15-24	15
	Penalty	0.001-1	1
	Epochs	50-150	50
SVM	Cost	0.00001-100000	0.031
	Rbf_sigma	0.0001-0.1	0.003

Cost: Regularization parameter controlling the margin error trade-off; Epochs: Number of complete passes through the training dataset; Hidden_units: Number of neurons in the hidden layer; KNN: K-nearest neighbors; Learn_rate: Learning rate shrinking weights to prevent overfitting; Loss_reduction: Minimum loss reduction required to split a leaf node; LR: Logistic regression; Min_n: Minimum number of data points required in a node to split further; MLP: Multilayer perceptron; Mtry: Number of predictors randomly sampled at each split; Neighbors: Number of nearest neighbors; Penalty: Regularization penalty term; Rbf_sigma: Kernel coefficient for the radial basis function; RF: Random forest; Sample_size: Subsample ratio of the training instances; SVM: Support vector machine; Trees: Total number of decision trees in an ensemble; XGBoost: Extreme gradient boosting.

Table 4 Predictive performance comparison of six machine learning models

Dataset	Model	AUC (95%CI)	Sensitivity (95%CI)	Specificity (95%CI)	F1 score (95%CI)1
Train	RF	0.844 (0.810-0.878)	0.747 (0.689-0.803)	0.761 (0.708-0.811)	0.737 (0.690-0.782)
	KNN	0.785 (0.744-0.824)	0.719 (0.658-0.778)	0.714 (0.658-0.769)	0.700 (0.650-0.748)
	XGBoost	0.757 (0.714-0.799)	0.693 (0.632-0.752)	0.672 (0.614-0.730)	0.667 (0.615-0.714)
	LR	0.754 (0.710-0.795)	0.669 (0.608-0.730)	0.718 (0.663-0.772)	0.669 (0.616-0.718)
	MLP	0.754 (0.711-0.797)	0.683 (0.623-0.745)	0.722 (0.667-0.776)	0.680 (0.629-0.729)
	SVM	0.753 (0.708-0.795)	0.832 (0.780-0.880)	0.476 (0.413-0.537)	0.680 (0.633-0.725)
Validation	RF	0.766 (0.700-0.828)	0.628 (0.529-0.722)	0.703 (0.618-0.788)	0.633 (0.551-0.710)
	KNN	0.734 (0.665-0.800)	0.659 (0.560-0.755)	0.668 (0.582-0.755)	0.641 (0.557-0.718)
	XGBoost	0.749 (0.682-0.814)	0.638 (0.538-0.732)	0.731 (0.648-0.813)	0.651 (0.570-0.727)
	LR	0.755 (0.689-0.817)	0.617 (0.519-0.713)	0.704 (0.614-0.789)	0.626 (0.540-0.704)
	MLP	0.756 (0.685-0.816)	0.649 (0.553-0.743)	0.695 (0.607-0.780)	0.644 (0.562-0.717)
	SVM	0.753 (0.684-0.815)	0.831 (0.750-0.905)	0.505 (0.410-0.595)	0.687 (0.615-0.753)

¹The F1 score represents the harmonic mean of precision and recall, calculated as 2 × (precision × recall)/(precision + recall). This metric evaluates binary classification performance and fits data with mild imbalance between two groups.

AUC: Area under the receiver operating characteristic curve; KNN: K-nearest neighbors; LR: Logistic regression; MLP: Multilayer perceptron; RF: Random forest; SVM: Support vector machine; F1 score: F-measure (harmonic mean of precision and recall); XGBoost: Extreme gradient boosting.

Table 5 Predictive performance evaluation of the random forest model

Model	Dataset	AUC (95%CI)	Sensitivity (95%CI)	Specificity (95%CI)	F1 score (95%CI)1
RF	Train	0.844 (0.810-0.878)	0.747 (0.689-0.803)	0.761 (0.708-0.811)	0.737 (0.690-0.782)
	Validation	0.766 (0.700-0.828)	0.628 (0.529-0.722)	0.703 (0.618-0.788)	0.633 (0.551-0.710)

¹The F1 score represents the harmonic mean of precision and recall, calculated as 2 × (precision × recall)/(precision + recall). This metric evaluates binary classification performance and fits data with mild imbalance between two groups.

AUC: Area under the receiver operating characteristic curve; F1 score: F-measure (harmonic mean of precision and recall); RF: Random forest.