Prediction of the Risk of Bone Mineral Density Decrease in Type 2 Diabetes Mellitus Patients Based on Traditional Multivariate Logistic Regression and Machine Learning: A Preliminary Study

Figures & data

Figure 1 Workflow of the study.

Abbreviations: T2DM, type 2 diabetes mellitus; LASSO, least absolute shrinkage and selection operator; ROC, receiver operating characteristic; DCA, decision curve analysis.

Table 1 Baseline Characteristics of the Study Population

Variable	Decreased BMD Group (n=305)	Normal BMD Group (n=145)	P value
Sex, male (%)	155.0 (50.8%)	97.0 (66.9%)	0.001
Age (years)	63.0 (56.0, 71.0)	57.0 (53.0, 64.0)	<0.001
Diabetes duration (months)	120.0 (36.0, 168.0)	96.0 (30.0, 162.0)	0.568
Smoking, n (%)	39.0 (26.9%)	74.0 (24.3%)	0.547
Drinking, n (%)	43.0 (14.1%)	42.0 (29.0%)	<0.001
SBP (mmHg)	138.0 (126.0, 150.0)	136.0 (122.5, 148.0)	0.197
DBP (mmHg)	80.0 (75.0, 88.0)	82.0 (75.0, 89.0)	0.305
ALT (U/L)	16.1 (11.7, 24.5)	18.6 (14.1, 28.4)	0.008
AST (U/L)	18.0 (14.9, 23.5)	18.6 (16.0, 23.2)	0.251
TBIL (μmol/L)	11.1 (8.4, 14.7)	11.3 (8.4, 14.8)	0.826
ALP (U/L)	80.0 (64.0, 91.5)	70.0 (57.0, 81.0)	<0.001
UA (μmol/L)	293.0 (236.3, 353.1)	336.2 (282.5, 393.8)	<0.001
Ca (mmol/L)	2.29 ± 0.11	2.32 ± 0.13	0.007
TC (mmol/L)	4.5 (3.9, 5.2)	4.5 (3.9, 5.3)	0.836
TG (mmol/L)	1.5 (1.1, 2.2)	1.8 (1.2, 2.5)	0.024
HDL (mmol/L)	1.1 (0.9, 1.2)	1.0 (0.8, 1.2)	0.028
LDL (mmol/L)	2.6 (2.2, 3.2)	2.6 (2.1, 3.1)	0.188
TG/HDL	1.5 (0.9, 2.3)	1.8 (1.1, 2.8)	0.013
FT3 (pmol/L)	4.3 (3.9, 4.7)	4.3 (4.0, 4.8)	0.650
FT4 (pmol/L)	16.7 (15.2, 18.2)	17.3 (15.7, 18.5)	0.210
TSH (uIU/mL)	1.9 (1.3, 2.7)	2.1 (1.5, 3.0)	0.113
HbA1c (%)	9.1 (7.6, 11.1)	8.6 (7.4, 10.6)	0.224
FCP (mmol/L)	530.6 (384.5, 746.7)	595.5 (425.5, 830.0)	0.057
FPG (mmol/L)	8.1 (6.4, 10.8)	8.1 (6.3, 10.2)	0.856
HOMA-IR	3.2 (2.5, 4.0)	3.3 (2.7, 4.0)	0.183
HOMA-islet	29.8 (17.7, 52.9)	36.2 (19.8, 55.3)	0.147
TyG index	0.5 (0.3, 0.8)	0.5 (0.3, 0.7)	0.541
PINP (ng/mL)	40.3 (30.1, 55.7)	33.0 (24.7, 42.1)	<0.001
CTX (pg/mL)	431.0 (308.8, 624.1)	298.7 (224.0, 451.7)	<0.001
PTH (pg/mL)	38.6 (29.5, 46.4)	35.6 (25.7, 46.8)	0.192
eGFR (mL/min/1.73 min^2)	97.8 (86.4, 108.2)	100.0 (86.4, 109.1)	0.567
DN, n (%)	99.0 (32.5%)	40.0 (27.6%)	0.296
DR, n (%)	61.0 (20.0%)	34.0 (23.4%)	0.402
CVD, n (%)	212.0 (69.5%)	76.0 (52.4%)	<0.001
DPN, n (%)	169.0 (55.4%)	69.0 (47.6%)	0.120
ASMI (kg/m^2)	6.7 (6.0, 7.4)	7.4 (6.8, 7.9)	<0.001
PFFM	0.71 ± 0.08	0.71 ± 0.08	0.989
PSMM	0.39 ± 0.05	0.39 ± 0.05	0.564
TBW (kg)	32.9 (27.8, 37.0)	37.3 (33.2, 41.0)	<0.001
ICW (kg)	20.0 (17.0, 22.7)	23.0 (20.3, 25.4)	<0.001
ECW (kg)	12.6 (10.8, 14.4)	14.3 (12.9, 15.7)	<0.001
BFM (kg)	17.8 (14.5, 21.6)	20.4 (15.9, 24.3)	<0.001
FFM (kg)	44.5 (37.7, 49.9)	50.8 (45.1, 55.7)	<0.001
SMM (kg)	24.1 (20.2, 27.5)	28.0 (24.5, 31.1)	<0.001
BMI (kg/m^2)	23.2 (21.4, 25.2)	24.8 (22.9, 26.8)	<0.001
PBF (%)	28.8 ± 7.8	28.9 ± 7.3	0.827
Inbody Score	71.0 (66.0, 74.0)	70.0 (65.0, 73.0)	0.341
BMR	1331.0 (1185.0, 1449.0)	1468.0 (1343.5, 1573.5)	<0.001
WHR	0.91 ± 0.06	0.94 ± 0.06	<0.001
TBW/FFM	73.62 ± 0.24	73.63 ± 0.26	0.852
FFMI (kg/m^2)	16.4 (15.3, 17.7)	17.5 (16.4, 18.8)	<0.001
FMI (kg/m^2)	6.7 (5.2, 8.2)	7.2 (5.7, 8.8)	0.040
PhA	4.8 (4.5, 5.3)	5.2 (4.8, 5.7)	<0.001

Notes: Bold values represented a P value less than 0.05 with statistical significance.

Abbreviations: BMD, bone mineral density; SBP, systolic blood pressure; DBP, diastolic blood pressure; ALT, alanine transaminase; AST, aspartate aminotransferase; TBIL, total bilirubin; ALP, alkaline phosphatase; UA, uric acid; Ca, calcium; TC, total cholesterol; TG, triglyceride; HDL, high-density lipoprotein; LDL, low-density lipoprotein; FT3, free triiodothyronine; FT4, free thyroxine; TSH, thyroid stimulating hormone; HbA1c, glycated hemoglobin A1c; FCP, fasting C-peptide; FPG, fasting plasma glucose; HOMA-IR, homeostasis model assessment for insulin resistance; HOMA-islet, homeostasis model assessment for islet beta-cell function; TyG index, triglyceride-glucose index; PINP, N-terminal propeptide of type I procollagen; CTX, C-terminal telopeptide of type I collagen; PTH, parathyroid hormone; eGFR, estimated glomerular filtration rate; DN, diabetic nephropathy; DR, diabetic retinopathy; CVD, cardiovascular disease; DPN, diabetic peripheral neuropathy; ASMI, appendicular skeletal muscle mass index; PFFM, percentage of fat-free mass; PSMM, percentage of skeletal muscle mass; TBW, total body water; ICW, intracellular water; ECW, extracellular water; BFM, body fat mass; FFM, fat-free mass; SMM, skeletal muscle mass; BMI, body mass index; PBF, percentage of body fat; BMR, basal metabolic rate; WHR, waist-to-hip ratio; FFMI, fat-free mass index; FMI, fat mass index; PhA, phase angle.

Table 2 Univariate and Multivariate Analysis of Factors Associated with a BMD Decrease in Total Study Population

Variable	Univariate Logistic Regression		Multivariate Logistic Regression
	OR (95% CI)	P value	OR (95% CI)	P value
Age	1.070 (1.043, 1.098)	<0.001	1.088 (1.051, 1.126)	<0.001
Diabetes duration	1.001 (0.999, 1.003)	0.427
Smoking	0.871 (0.555, 1.367)	0.547
Drinking	0.402 (0.248, 0.652)	<0.001
SBP	1.007 (0.996, 1.018)	0.235
DBP	0.991 (0.973, 1.008)	0.296
ALT	0.990 (0.979, 1.002)	0.104
AST	0.996 (0.978, 1.014)	0.634
TBIL	1.007 (0.967, 1.049)	0.727
ALP	1.023 (1.013, 1.033)	<0.001	1.021 (1.008, 1.033)	0.001
UA	0.995 (0.992, 0.997)	<0.001	0.996 (0.993, 0.999)	0.003
Ca	0.099 (0.018, 0.541)	0.008	0.044 (0.005, 0.362)	0.004
TC	1.022 (0.859, 1.215)	0.807
TG	0.907 (0.818, 1.004)	0.060
HDL	1.100 (0.640, 1.890)	0.730
LDL	1.182 (0.939, 1.487)	0.154
TG/HDL	0.974 (0.926, 1.023)	0.292
FT3	0.951 (0.700, 1.292)	0.749
FT4	0.986 (0.956, 1.018)	0.392
TSH	0.940 (0.820, 1.079)	0.380
HbA1c	1.029 (0.946, 1.119)	0.508
FCP	1.000 (0.999, 1.000)	0.150
FPG	1.007 (0.956, 1.061)	0.791
HOMA-IR	0.978 (0.840, 1.138)	0.771
HOMA-islet	0.997 (0.993, 1.001)	0.121
TyG index	1.116 (0.654, 1.903)	0.688
PINP	1.031 (1.017, 1.044)	<0.001
CTX	1.003 (1.002, 1.004)	<0.001	1.002 (1.001, 1.003)	0.005
PTH	1.005 (0.992, 1.018)	0.472
eGFR	0.999 (0.990, 1.009)	0.895
DN	1.262 (0.816, 1.951)	0.296
DR	0.816 (0.507, 1.313)	0.403
CVD	2.070 (1.378, 3.109)	<0.001	1.676 (1.007, 2.790)	0.047
DPN	1.369 (0.921, 2.035)	0.121
ASMI	0.473 (0.373, 0.599)	<0.001	0.495 (0.351, 0.700)	<0.001
PFFM	1.018 (0.087, 11.921)	0.989
BFM	0.944 (0.915, 0.974)	<0.001
BMI	0.864 (0.810, 0.922)	<0.001
PBF	0.998 (0.972, 1.024)	0.878
Inbody Score	1.009 (0.975, 1.044)	0.615
WHR	0.001 (0.000, 0.025)	<0.001	0.003 (0.000, 0.165)	0.005
FFMI	0.723 (0.643, 0.813)	<0.001
PhA	0.563 (0.417, 0.760)	<0.001	1.597 (0.993, 2.569)	0.054

Notes: Bold values suggested a P value less than 0.05 with statistic significance.

Abbreviations: SBP, systolic blood pressure; DBP, diastolic blood pressure; ALT, alanine transaminase; AST, aspartate aminotransferase; TBIL, total bilirubin; ALP, alkaline phosphatase; UA, uric acid; Ca, calcium; TC, total cholesterol; TG, triglyceride; HDL, high-density lipoprotein; LDL, low-density lipoprotein; FT3, free triiodothyronine; FT4, free thyroxine; TSH, thyroid stimulating hormone; HbA1c, glycated hemoglobin A1c; FCP, fasting C-peptide; FPG, fasting plasma glucose; HOMA-IR, homeostasis model assessment for insulin resistance; HOMA-islet, homeostasis model assessment for islet beta-cell function; TyG index, triglyceride-glucose index; PINP, N-terminal propeptide of type I procollagen; CTX, C-terminal telopeptide of type I collagen; PTH, parathyroid hormone; eGFR, estimated glomerular filtration rate; DN, diabetic nephropathy; DR, diabetic retinopathy; CVD, cardiovascular disease; DPN, diabetic peripheral neuropathy; ASMI, appendicular skeletal muscle mass index; PFFM, percentage of fat-free mass; BFM, body fat mass; BMI, body mass index; PBF, percentage of body fat; WHR, waist-to-hip ratio; FFMI, fat-free mass index; PhA, phase angle.

Figure 2 Comparison of ROC curves among different machine learning models.

Notes: (A) Comparison of ROC curves among different machine learning models for the prediction of BMD decreases in male patients. (B) Comparison of ROC curves among different machine learning models for the prediction of BMD decreases in female patients.

Abbreviations: ROC, receiver operating characteristic; BMD, bone mineral density; AUC, area under the curve; LR, logistic regression; RF, random forest; XGBoost, extreme gradient boost; SVM, support vector machine; DT, decision tree; KNN, k-nearest neighbors.

Figure 3 Nomograms to predict the incidence of BMD decreases.

Notes: (A) The nomogram was constructed for male T2DM patients, with drinking, ALP, UA, and ASMI incorporated. (B) The nomogram was constructed for female T2DM patients, with age, PINP, ICW, and PBF incorporated. In the drinking section of the figure, 0 represents non-drinking, and 1 represents drinking.

Abbreviations: BMD, bone mineral density; T2DM, type 2 diabetes mellitus; ALP, alkaline phosphatase; UA, uric acid; ASMI, appendicular skeletal muscle mass index; PINP, N-terminal propeptide of type I procollagen; ICW, intracellular water; PBF, percentage of body fat.

Figure 4 The ROC curves of the nomograms.

Notes: (A) In male patients, the AUCs of the nomogram are 0.784 (95% CI: 0.715–0.854) in the training dataset and 0.722 (95% CI: 0.608–0.835) in the testing dataset, respectively. (B) In female patients, the AUCs of the nomogram are 0.899 (95% CI: 0.842–0.955) in the training dataset and 0.876 (95% CI: 0.774–0.978) in the testing dataset, respectively.

Abbreviations: ROC, receiver operating characteristic; AUC, area under the curve; CI, confidence interval.