Reply
Authors: Ya Deng, Chun‐Yan Wang, Xiao‐Xia Niu, Dong Ji
Journal: Hepatology (2022)

To the editor, We read with interest the letter by Huang et al. regarding our article which referred to the difference between stepwise regression and regularized linear regression. As we know, regularized linear regression methods are popular in bioinformatics, particularly useful in scenarios with fewer observations than parameters.[1] Although our study contained a large sample size and few parameters, resulting in less sampling error and less probability of overfitting, we performed regularized linear regression including least absolute shrinkage and selection operator (Lasso) and Ridge regression analyses for biochemical nonresolution 6 (BNR‐6) model construction, as Huang suggested. We found that the risk factors screened by Lasso or Ridge regression were completely consistent with the stepwise regression; the AUC values of three methods were approximately equivalent (Lasso, 0.826; Ridge, 0.823; stepwise, 0.824) (Table 1 and Figure 1). Statistical methods serve for clinical practice. Different researchers have different understandings of the same method, so it is difficult to determine which method is the best or better. We can only choose the most appropriate statistical analysis based on the characteristics of the study design. Furthermore, no matter which method is used, the predictive model can only be applied after it is validated. In our study, the clinical applicability of the BNR‐6 model was also validated by an external cohort and 400 times 10‐fold cross‐validation. These results further confirmed that the BNR‐6 model is robust and convincing. TABLE 1 - Different regression analyses for screening risk factors in the internal training cohort Stepwise Lasso Ridge OR (95% CI) p value OR (95% CI) p value OR (95% CI) p value Age (years) 1.019 (1.006, 1.032) 0.003 1.018 (1.005, 1.031) 0.007 1.018 (1.006, 1.031) 0.005 Female sex 1.488 (1.083, 2.045) 0.014 1.434 (1.038, 1.995) 0.030 1.500 (1.094, 2.070) 0.013 AST (U/L) 1.006 (1.005, 1.008) <0.001 1.007 (1.005, 1.009) <0.001 1.006 (1.005, 1.008) <0.001 TBIL (μmol/L) 1.020 (1.015, 1.026) <0.001 1.020 (1.014, 1.025) <0.001 1.020 (1.015, 1.025) <0.001 PT (s) 1.344 (1.219, 1.481) <0.001 1.350 (1.224, 1.492) <0.001 1.353 (1.227, 1.494) <0.001 PLT (109/L) 0.997 (0.995, 0.999) 0.005 0.997 (0.995, 0.999) 0.008 0.997 (0.995, 0.999) 0.004 ALT (U/L) – – 0.999 (0.998, 1.001) 0.241 – – ALP (U/L) – – – – – – GGT (U/L) – – 1.001 (1.000, 1.001) 0.184 1.001 (1.000, 1.001) 0.199 Abbreviations: ALP, alkaline phosphatase; ALT, alanine aminotransferase; AST, aspartate transaminase; GGT, gamma‐glutamyltransferase; Lasso, least absolute shrinkage and selection operator; PLT, platelet; PT, prothrombin time; and TBIL, total bilirubin. FIGURE 1: Receiver operating characteristic for three different regressions for BNR‐6 modelFurthermore, variance inflation factor (VIF) is a good diagnostic tool for multicollinearity. When the VIF is higher than 5, multicollinearity is present.[2] We had considered this issue and evaluated VIF for each variable prior to model inclusion, but had not presented them. Thanks to Huang et al.'s comments, we supplied the results in Table 2. All of the VIF indexes were less than 5, indicating that there was no multicollinearity in our study. TABLE 2 - Evaluation of multicollinearity between covariates using variance inflation factor method VIF df VIF^(1/[2*df]) Age (years) 1.09 1 1.04 Female sex 1.13 1 1.06 ALT (U/L) 2.79 1 1.67 AST (U/L) 1.83 1 1.35 TBIL (μmol/L) 1.22 1 1.11 ALP (U/L) 1.6 1 1.27 GGT (U/L) 1.49 1 1.22 PLT (109/L) 1.19 1 1.09 PT (s) 1.25 1 1.12 Pattern 2.52 2 1.26 HAI ≥ 10 points 1.11 1 1.26 BDI 2.04 1 1.43 Cholestasis 2.12 1 1.46 Abbreviations: BDI, biliary duct injury; HAI, histology activity index; VIF, variance inflation factor. After comparison with advanced regularized linear regression, such as Lasso and Ridge regression, the BNR‐6 model established through the widely used stepwise logistic regression indeed has a good predictive performance. FUNDING INFORMATION Beijing Municipal Science and Technology Commission Z181100001718034. CONFLICT OF INTEREST Nothing to report.