AI in Clinical Medicine, ISSN 0000-0000 online, Open Access
Article copyright, the authors; Journal compilation copyright, AI Clin Med and Elmer Press Inc
Journal website https://aicm.elmerpub.com

Original Article

Volume 1, 2025, e10


Correlations Between Wald Chi-Squared Values and Standardized Beta-Coefficients in Regression Analysis and Feature Importance Calculated Using Machine Learning

Figures

Figure 1.
Figure 1. Scatter plot of the natural logarithm of the WCS values and FI for the outcome of a 10% increase in bodyweight over 10 years. The WCS values of the age, smoking status, sex, TG and HbA1c levels, BMI, pharmacotherapy for hypertension, systolic blood pressure, weekly alcohol consumption, pharmacotherapy for dyslipidemia, habitual exercise status, history of cardiovascular disease, pharmacotherapy for diabetes, and HDL-C level are 5,903, 3,170, 2,414, 800, 701, 293, 221, 83, 71, 50, 22, 8, 2, and 2, respectively. The solid and dotted lines represent the regression line and 95% CI, respectively.
Figure 2.
Figure 2. Scatter plot of the natural logarithm of the WCS values and FI for the outcome of a decrease of 10 mg/dL or more in the HDL-C level over 10 years. The WCS values of the HDL-C and LDL-C levels, BMI, pharmacotherapy for dyslipidemia, TG level, age, smoking status, amount of alcohol consumed per session, GGT level, and weekly alcohol consumption are 2,282, 193, 134, 38, 19, 13, 28, 13, 10, and 1, respectively. The solid and dotted lines represent the regression line and 95% CI, respectively.
Figure 3.
Figure 3. Scatter plot of the natural logarithm of the WCS values and FI for the outcome of a percentage (%) change in bodyweight over 10 years, as analyzed using a GLM. The WCS values of the age, smoking status, HbA1c level, BMI, TG level, systolic blood pressure, sex, pharmacotherapy for hypertension, weekly alcohol consumption, pharmacotherapies for diabetes and dyslipidemia, HDL-C level, habitual exercise status, and history of cardiovascular disease are 12,979, 2,996, 2,835, 1,676, 1,310, 578, 505, 360, 177, 161, 126, 26, 3, and 1, respectively. The solid and dotted lines represent the regression line and 95% CI, respectively.

Tables

Table 1. Correlation of FI With WCS and stB
 
FI
Study 1 (n = 615,077 (R)a)Study 2 (n = 10,189 (R)a)Study 3 (n = 615,077 (R)b)
aMultivariable logistic regression model. bGeneralized linear model. cCorrelation coefficients by Spearman correlation. AUC: area under the curve; FI: feature importance; HDL-C: high-density lipoprotein cholesterol; stB: standardized β-coefficient; WCS: Wald Chi-squared.
Outcome10% body weight increase (dichotomized variable)Decrease of HDL-C ≥ 10 mg/dL (dichotomized variable)Body weight increase (%) (continuous variable)
Number of explanatory factors141014
AUC, %68.5%68.4%-
WCS
  Correlation coefficientsc0.840.940.87
  P values0.0002< 0.0001< 0.0001
stB
  Correlation coefficientsc0.800.730.85
  P values0.00060.0160.0001

 

Table 2. Results of Logistic Regression Analysis After Standardization of Covariates and FI by Machine Learning
 
stBAbsolute stBWCS valueFI
The factors are listed in descending order according the value of WCS. aObesity; BMI ≥ 30 kg/m2, non-obesity; BMI < 30 kg/m2. AUC: area under the curve; FI: feature importance; HbA1c: glycated hemoglobin; stB: standardized β-coefficient; WCS: Wald Chi-squared. Genetic information was excluded due to large standardized β in the study 5.
Study 4: Medical students (Outcome: high systolic blood pressure ≥ 130 mm Hg)
  Heart rate0.03160.03167.75610.0102
  Cholesterol-0.02530.02534.9940.0113
  Sex (men 1, women 2)0.02180.02183.70340.0090
  Obesity (obesity 1, non-obesity 0)a-0.02110.02113.36960.0101
  Smoking (smoker 1, non-smoker 0)0.01970.01973.10510.0057
  Age-0.00930.00930.66820.0095
  Diabetes (diabetes 1, non-diabetes 0)-0.00230.00230.04000.0055
  AUC, %51.654.2
Study 5: Permanent neonatal diabetes mellitus (Outcome: permanent neonatal diabetes mellitus)
  Age-1.76781.76784269.67240.1280
  Birth weight-0.68180.68181674.72980.0721
  Family history (yes 1, no 0)0.02620.02622.83330.0082
  HbA1c0.01910.01911.46340.0067
  Insulin level0.01050.01050.44500.0086
  Development delay (yes 1, no 0)0.00700.00700.19710.0056
  AUC, %87.570.2