Background
Methods
Ethical approval
Study population
Missing value imputation
Baseline statistics
Regularization models
The elastic net
Glinternet
The lasso projection
High-dimensional inference
Machine learning models
Random forests
Gradient boosting machine
Unsupervised learning
Survival and risk analysis
Survival analysis
Risk analysis
Results
Baseline characteristics of the study population
Case (n = 312) | Control (n = 898) | P value | |
---|---|---|---|
Diabetes study | |||
Age (years) | 50.99 ± 10.33 | 39.01 ± 12.13 | 8.60 × 10−55 |
Chloride (mmol/L) | 99.44 ± 2.61 | 101.18 ± 1.99 | 8.60 × 10−24 |
Magnesium (mmol/L) | 0.79 ± 0.08 | 0.84 ± 0.66 | 3.50 × 10−23 |
Triglycerides (mmol/L) | 1.83 ± 0.96 | 1.39 ±1.00 | 2.03 × 10−11 |
Albumin (g/L) | 44.25 ± 2.85 | 45.47 ± 2.86 | 1.07 × 10−10 |
BMI | 31.39 ± 5.87 | 29.11 ± 6.00 | 8.00 × 10−09 |
Free triiodothyronine (pmol/L) | 4.31 ± 0.69 | 4.57 ± 0.62 | 1.50 × 10−08 |
Vitamin D (ng/L) | 21.69 ± 9.65 | 18.17 ± 9.40 | 1.93 × 10−08 |
Sodium (mmol/L) | 139.38 ± 2.54 | 140.30 ± 2.25 | 2.17 × 10−08 |
High density lipoprotein (mmol/L) | 1.21 ± 0.33 | 1.34 ± 0.36 | 5.25 × 10−08 |
Case (n = 508) | Control (n = 224) | P value | |
---|---|---|---|
Obesity study | |||
Albumin (g/L) | 44.07 ± 2.76 | 46.58 ± 2.61 | 1.95 × 10−28 |
Age (years) | 45.36 ± 11.77 | 35.02 ± 12.68 | 6.94 × 10−25 |
C-peptide of insulin (ng/L) | 3.43 ± 2.07 | 2.17 ± 1.39 | 1.43 × 10−25 |
Triglycerides (mmol/L) | 1.61 ± 1.10 | 1.10 ± 0.62 | 5.19 × 10−15 |
HBA1C% | 6.53 ± 1.65 | 5.71 ± 1.26 | 6.87 × 10−13 |
Insulin (mcunit/mL) | 22.77 ± 38.35 | 10.59 ± 10.95 | 1.54 × 10−10 |
High density lipoprotein (mmol/L) | 1.27 ± 0.33 | 1.45 ± 0.36 | 3.24 × 10−08 |
Magnesium (mmol/L) | 0.81 ± 0.07 | 0.84 ± 0.06 | 3.61 × 10−08 |
Uric acid (umol/L) | 304.39 ± 80.52 | 272.01 ± 68.71 | 4.25 × 10−08 |
Total blirubin (umol/L) | 6.19 ± 3.76 | 8.23 ± 4.94 | 7.18 × 10−08 |
Regularization models
Elastic net | Glinternet | Lasso proj | hdi | |
---|---|---|---|---|
Coefficient (β) | Coefficient (β) | P value | P value | |
Diabetes study | ||||
Magnesium | − 1.01 ×10−00 | − 2.82 ×10−00 | 3.35 × 10−10 | 2.34 × 10−09 |
Calcium | 1.33 × 10−01 | − 3.07 × 10−02 | 5.61 × 10−02 | |
High density lipoprotein | − 1.19 × 10−01 | − 5.16 × 10−01 | 3.73 × 10−03 | 6.96 × 10−01 |
Phosphorus | 6.47 × 10 −02 | − 8.15 × 10−03 | 4.71 × 10−01 | |
Chloride | − 3.48 ×10−02 | − 1.66 × 10−02 | 2.99 × 10−09 | 7.43 × 10−11 |
Free triiodothyronine | − 3.05 × 10−02 | − 1.08 × 10−01 | 2.58 × 10−03 | |
Albumin | − 1.08 × 10−03 | 1.29 × 10−03 | 2.09 × 10−01 | |
Insulin | 9.95 × 10−04 | 2.93 × 10−04 | 1.88 × 10−04 | 9.36 × 10−02 |
Uric acid | − 5.40 ×10−04 | − 3.32 × 10−03 | 1.31 × 10−05 | 4.05 × 10−04 |
Obesity study | ||||
Magnesium | − 2.00 × 10−01 | − 2.79 × 10−02 | 6.55 × 10−01 | |
High density lipoprotein | − 8.10 × 10−02 | 4.49 × 10−01 | 7.46 × 10−03 | |
Albumin | −3.00 × 10−02 | − 7.36 × 10−02 | 1.11 × 10−05 | 2.40 × 10−09 |
Calcium | − 2.65 × 10−02 | − 2.06 × 10−01 | ||
C-peptide of insulin | 1.74 × 10−02 | − 5.30 × 10−02 | 1.18 × 10−01 | 3.27 × 10−01 |
Cholesterol | 1.11 × 10−02 | 1.59 × 10−02 | 4.83 × 10−01 | |
Total bilirubin | − 3.30× 10−03 | 4.52 × 10−02 | ||
Vitamin D | − 3.16 × 10−03 | − 2.72 × 10−02 | 1.03 × 10−03 | 1.09 × 10−01 |
Triglycerides | 2.51 × 10−03 | − 1.01 × 10−01 | ||
Uric acid | 5.87 × 10−04 | − 4.61 × 10−03 | 1.22 × 10−07 | 1.52 × 10−03 |
Vitamin B12 | − 1.28 × 10−04 | −2.14 × 10−02 | 1.64 × 10−02 |
Machine learning models
Survival and risk analysis
Survival analysis
Risk analysis
Variable |
β
| HR (95% CI for HR) | Wald test | P value |
---|---|---|---|---|
Hemoglobin | 1.7 × 10−1 | 1.2 (1.1–1.3) | 20.0 | 9.0 × 10−6 |
Albumin | 9.9 × 10−2 | 1.1 (1.1–1.2) | 18.0 | 1.9 × 10−5 |
ALT (GPT) | 1.5 × 10−02 | 1.0 (1.0–1.0) | 15.0 | 8.7 × 10−5 |
HDLC | − 7.2 × 10−1 | 0.48 (0.33–0.71) | 14.0 | 2.1 × 10−4 |
Gender | − 4.5 × 10−1 | 0.64 (0.5–0.81) | 13.0 | 3.5 × 10−4 |
Total bilirubin | 5.8 × 10−02 | 1.1 (1.0–1.1) | 8.7 | 3.2 × 10−3 |
GGT | 4.0 × 10−03 | 1.0 (1.0−1.0) | 7.2 | 7.3 × 10−3 |
Free triiodothyronine | 1.9 × 10−01 | 1.2 (1.0–1.4) | 6.9 | 8.6 × 10−3 |
AST (GOT) | 1.6 × 10−01 | 1.0 (1.0−1.3) | 6.2 | 1.3 × 10−2 |
LDLC | 1.6 × 10−01 | 1.2 (1.0–1.3) | 6.0 | 1.4 × 10−2 |
Triglycerides | 1.5× 10−01 | 1.2 (1.0–1.3) | 5.3 | 2.1 × 10−2 |
Calcium | 1.4 × 10+0 | 4.1 (1.1–16.0) | 4.2 | 4.1 × 10−2 |
ALP | − 5.9 × 10−03 | 0.99 (0.99–1.0) | 3.9 | 4.7 × 10−2 |
Magnesium | 1.5 × 10+0 | 4.3 (1.0–18.0) | 3.9 | 4.8 × 10−2 |