Prediction of graft outcomes after kidney transplantation: When standard statistics compare to machine learning techniques

Table 1 Clinical characteristics of kidney donors

Donor feature	Summary statistics, mean ± SD (range)	Completeness (%)
Sex	Female: 40.9%; male: 59.1%	94
Age (years)	42.6 ± 14.6 (4-73)	98
Weight (kg)	74.5 ± 17.3 (15-180)	19
Height (cm)	166.7 ± 10.8 (97-190)	19
Body mass index (kg/m2)	26.6 ± 4.8 (16-56)	19
Cause of death	Hemorrhagic stroke: 39.2%, trauma: 33.4%, ischemic stroke: 11.7%, other: 11.0%, anoxia: 4.7%	100
Extended criteria donor (ECD)	Yes: 16.8%, no: 83.2%	100
Blood type	O: 55.8%, A: 31.8%, B: 11.4%, AB: 1.1%	98
Hypertension	Yes: 22.9%, no: 77.1%	83
Diabetes mellitus	Type 1 0.8%, type 2 4.4%, no: 94.8%	80
Serum creatinine (mg/dL)	0.88 ± 0.37 (0.20-2.82)	89
Mean blood pressure (mmHg)	83.9 ± 13.1 (50-120)	57
Diuresis (mL/hour)	154.6 ± 123.6 (0-700)	56

ECD: Extended criteria donor.

Table 2 Clinical characteristics of kidney transplants

Transplant feature	Summary statistics, mean ± SD (range)	Completeness (%)
Origin of the kidney	Local: 38.6%, national: 61.4%	83
Cold ischemia time (hours)	18.99 ± 6.05 (3.50, 40.15)	93
Warm ischemia time (minutes)	39.49 ± 11.57 (10, 90)	71

Table 3 Clinical characteristics of kidney recipients

Recipient feature	Summary statistics, mean ± SD (range)	Completeness (%)
Recipient characteristics
Sex	Female: 45.7%, male: 54.3%	100
Age (years)	46.4 ± 12.9 (2-76)	98
Weight (kg)	66.0 ± 11.8 (28.2-115)	92
Height (m)	1.63 ± 0.09 (1.00-1.87)	74
Body mass index (m/kg2)	24.6 ± 3.1 (16.6-38.9)	74
Blood type	O: 53.0%, A: 32.1%, B: 12.3%, AB: 2.51%	99
Number of transplants (n)	1: 83.5%, 2: 15%, 3: 1.5%	51
Time on the waiting list (months)	40.2 ± 31.7 (1-191)	57
Pre-transplant dialysis time (months)	69.3 ± 44.2 (0-384)	95
Residual diuresis (mL/day)	324.3 ± 491.5 (0-2500)	63
Comorbidities
Hypertension	Yes: 84.9%, no: 15.1%	94
Coronary artery disease	Yes: 5.9%, no: 94.1%	90
Congestive heart failure	Yes: 3.2%, no: 96.8%	90
Arrhythmias	Yes: 2.6%, no: 97.4%	90
Peripheral vascular disease	Symptomatic: 2.8%, asymptomatic: 0.6%, no: 96.6%	89
DM	Yes: 9.7%, no: 90.3%	91
DM type	Type 1: 16.2%, type 2: 82.4%	90
Cancer	Yes: 2.3%, no: 97.7%	90
Uropathy	Yes: 2.6%, no: 97.4%	90
HIV	Yes: 1.7%, no: 98.3%	90
Other physical	Yes: 5.0%, no: 95.0%	90
Other psychiatric	Yes: 2.6%, no: 97.4%	90
Charlson score	2.92 ± 1.23 (2-10)	42
Clinical history
Transfusions	Yes: 30.3%, no: 69.7%	64
Previous organ transplant	Yes: 0.56%, no: 99.44%	70
Tobacco use	Yes: 47.5%, no: 52.5%	69
Alcohol use	Yes: 26.1%, no: 73.9%	72
Other drugs	Yes: 0.2%, no: 99.8%	72
Cause of chronic kidney disease	Unknown: 44.5%, non-diabetes mellitus glomerulopathy: 27.1%, congenital and cystic: 8.0%, diabetic kidney disease: 6.9%, other: 6.8%, hypertensive or vascular: 3.8%, tubulointerstitial: 3.0%	99
Dialysis	Yes: 99.7%, no: 0.3%	97
Dialysis type	HD: 91.0%, PD: 5.1%, combination: 3.9%	90

DM: Diabetes mellitus; HIV: Human immunodeficiency virus; HD: Hemo dialysis; PD: Peritoneal dialysis.

Table 4 Laboratory features of kidney recipients

Laboratory feature of the recipient	Summary statistics, mean ± SD (range)	Completeness (%)
Serum creatinine (mg/dL)	8.5 ± 2.6 (1.04-18.7)	55
Proteinuria (g)	12.5 ± 36.6 (0-148)	4
Cholesterol (mg/dL)	182.0 ± 44.0 (100-320)	11
Phosphorus (mg/dL)	5.0 ± 1.6 (1.4-9.9)	48
Calcium (mg/dL)	9.1 ± 1.0 (5.1-12.0)	48
PTH (pg/mL)	387.1 ± 371.5 (2.5-2292)	43
Albumin (g/dL)	4.3 ± 0.3 (3.1-5.5)	38
Hb (g/dL)	10.9 ± 1.6 (5.9-17.0)	37
CMV	Positive: 78.5%, negative: 21.5%	60
Chagas	Positive: 2.8%, negative: 97.2%	61
Toxoplasma	Positive: 31.9%, negative: 68.1%	61
HTLV-1	Positive: 23.1%, negative: 76.9%	2
PPD	Positive: 43.2%, negative: 56.8%	5

PTH: Parathyroid hormone; Hb: Hemoglobin; CMV: Cytomegalovirus; HTLV-1: Human T-lymphotropic virus 1; PPD: Purified protein derivative.

Table 5 The area under the receiving operating curve and Accuracy metrics for the different delayed graft function classification models and different combinations of predictor variables

Metric	AUC-ROC				Accuracy
Model and data	D	DT	DR	DTR	D	DT	DR	DTR
LR	0.49	0.68	0.53	0.67	0.51	0.58	0.58	0.62
SVM	0.35	0.62	0.51	0.51	0.57	0.57	0.53	0.53
DET	0.67	0.45	0.58	0.51	0.58	0.49	0.58	0.48
RF	0.78	0.71	0.57	0.52	0.70	0.70	0.58	0.50
GB	0.81	0.70	0.67	0.62	0.63	0.63	0.56	0.60
XGB	0.75	0.66	0.60	0.62	0.60	0.63	0.58	0.61
MLP	0.68	0.70	0.50	0.47	0.61	0.61	0.53	0.49

AUC-ROC: Area under the receiving operating curve; D: Donor data; DT: Donor and transplant data; DR: Donor and recipient data; DTR: Donor, transplant and recipient date; LR: Logistic regression; SVM: Support vector machine; DET: Decision trees; RF: Random forest; GB: Gradient boost; XGB: Extreme gradient boost; MLP: Multilayer perceptron.

Table 6 Sensitivity and specificity metrics for the different delayed graft function classification models and different combinations of predictor variables

Metric	Sensitivity				Specificity
Model and data	D	DT	DR	DTR	D	DT	DR	DTR
LR	0.33	0.44	0.18	0.56	0.67	0.71	0.95	0.67
SVM	0	0	0	0	1	1	0.93	0.93
DET	0.44	0.29	0.38	0.50	0.69	0.64	0.73	0.47
RF	0.44	0.50	0.32	0.52	0.89	0.84	0.78	0.49
GB	0.21	0.50	0	0.47	0.96	0.73	0.98	0.69
XGB	0.09	0.50	0.41	0.61	0.98	0.73	0.71	0.64
MLP	0.53	0.56	0.56	0.44	0.67	0.64	0.51	0.53

D: Donor data; DT: Donor and transplant data; DR: Donor and recipient data; DTR: Donor, transplant and recipient date; LR: Logistic regression; SVM: Support vector machine; DET: Decision trees; RF: Random forest; GB: Gradient boost; XGB: Extreme gradient boost; MLP: Multilayer perceptron.

Table 7 Kruskal-Wallis P-values when comparing logistic regression to each Machine learning model independently

Comparison	AUC-ROC P value	Accuracy P value	Sensitivity P value	Specificity P value
LR vs SVM	0.2454	0.2396	0.0139	0.0778
LR vs DET	0.4678	0.2186	0.8845	0.3836
LR vs RF	0.3865	0.5516	0.6631	0.7715
LR vs GB	0.1913	0.2425	0.7728	0.1465
LR vs XGB	0.5637	0.2367	0.7728	0.6612
LR vs MLP	0.8845	0.7702	0.1804	0.0384

LR: Logistic regression; SVM: Support vector machine; DET: Decision trees; RF: Random forest; GB: Gradient boost; XGB: Extreme gradient boost; MLP: Multilayer perceptron.

Table 8 Statistically significant variables at the 95% significance level from multivariate logistic regressions

Data	Variable	Odds ratio	P value
DTR
Donor (D)	Age	82.4	< 0.01
Transplant (T)	Cold ischemia time (hours)	30.8	0.001
Recipient (R)	Residual diuresis (mL/day)	0.1	0.006
	Smoking (BV1 = no smoking)	15.5	0.02
DR
Recipient (R)	Residual diuresis (mL/day)	0.1	0.008
	Smoking (BV1 = no smoking)	10.4	0.02
DT
Transplant (T)	Cold ischemia time (hours)	28.9	0.001
Donor (D)	Age	60.8	< 0.01
D
Donor (D)	Age	35.9	< 0.01

¹Indicates the base value of the categorical predictor in the model.

D: Donor data; DT: Donor and transplant data; DR: Donor and recipient data; DTR: Donor, transplant and recipient date.

Table 9 Most important features according to permutation feature importance and Shapley additive explanations methods

Model and data	Relevant predictors and the data set from which they come	Mean of error increase (from PFI)	Standard deviation of error increase (from PFI)	Mean and direction of SHAP values
GB with D	Creatinine (D)	0.05	0.02	0.07 (+ -)
	Age (D)	0.03	0.01	0.09 (+)
	Stroke death (D)	0.02	0.01	0.03 (+)
	ECD (D)	0.02	0.02	0.03 (+)
	MBP (D)	0.01	0.01	0.01 (-)
RF with DT	Age (D)	0.06	0.02	0.03 (+)
	MBP (D)	0.04	0.01	0.02 (-)
	Cold ischemia time (T)	0.03	0.04	0.05 (+)
	Creatinine (D)	0.01	0.01	0.02 (+ -)
	Warm ischemia time (T)	0.01	0.02	0.05 (+)
GB with DR	Age (D)	0.04	0.01	0.03 (+)
	Smoking (R)	0.03	0.02	0.02 (+)
	MBP (D)	0.02	0.01	0.01 (-)
	Creatinine (D)	0.02	0.01	0.01 (+ -)

SHAP: Shapley values; ECD: Extended criteria donor; MBP: Mean blood pressure; D: Donor data; DT: Donor and transplant data; DR: Donor and recipient data; RF: Random forest; GB: Gradient boost; PFI: Permutation feature importance.