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

Abstract

Background: Standardized β-coefficients (stBs) are traditional indices that enable the estimation of covariates that more strongly influence outcomes. However, in studies possessing many categorical covariates, stBs are often difficult to calculate. In contrast, Wald Chi-squared (WCS) values, calculated in logistic regression analysis, represent the magnitude of a covariate’s statistical significance. To date, many machine-learning algorithms have been used to evaluate the feature importance (FI), which is used to predict the order of precedence of covariates’ contributions to outcomes. Therefore, the relationships between WCS values and both stBs and FI were investigated using several existing clinical databases.

Methods: We investigated the correlations between WCS values and both stBs in logistic regression analysis and FI calculated using machine learning and the data from 615,077 and 90,053 middle-aged people in our previous studies (including one study that used a generalized linear model) and two studies using open data obtained from 86,151 medical students and 100,000 children. The covariates were standardized, and StBs were obtained using logistic regression analysis.

Results: Overall, WCS values were more highly correlated with FI (Spearman correlation, ρ = 0.79 - 0.94) than with stBs (ρ = 0.73 - 0.85) and were very highly correlated with stBs (ρ = 0.83 - 0.99) in five studies.

Conclusions: These results suggest that WCS values likely represent covariates’ statistical significances and the magnitudes of covariates’ influences on outcomes, which is consistent with the very high correlation between WCSs and stBs. However, because these results were obtained using limited data, they must be verified through further study.