All the data analyzed in this study were obtained from The DATADRYAD database (http://www.Datadryad.org/). The raw data could be freely download from the dryad data package (Okamura, Takuro et al. (2019)) (23).

This study was a cohort study that included 15,464 subjects in Japan. All the participants come from the NAGALA (NAfld in the Gifu Area, Population-based Longitudinal Analysis) database, which aimed to investigate risk factors for chronic diseases. All inclusion and exclusion criteria are detailed in the literature of the data source (23). The exclusion criteria for the study of raw data included: 1) T2DM at baseline or fasting plasma glucose ≥ 6.1 mmol/L; 2) missing data; 3) known liver disease; 4) ethanol consumption (> 60 g/day for men and 40 g/day for women); medication usage (23). The study was approved by the Ethics Committee of Murakami Memorial Hospital in Japan. Informed consent was obtained from participants in the study (23).

BMI = weight (kg) divided by height²(m). TyG = Ln [(FPG (mg/dL)/2) × TG (mg/dL)] (8). TyG-BMI = BMI × TyG (8). The study exposure was ByG. The formula for calculating the index: ByG = Ln [1/2 BMI (kg/m²) × FPG (mg/dL)].

The sociodemographic characteristics included age, sex, habit of exercise, alcohol consumption (non, light, moderate, heavy), and smoking status (never, past, current). The laboratory results were as follows: BMI, waist circumference (WC), alanine aminotransferase (ALT), aspartate aminotransferase (AST), gamma-glutamyl transferase (GGT), total cholesterol (TC), triglycerides (TG), high-density lipoprotein cholesterol (HDL), FPG, glycosylated haemoglobin (HbA1c), systolic blood pressure (SBP), and diastolic blood pressure (DBP). Criteria for fatty liver diagnosis by abdominal ultrasonography were as follows: hepatorenal echo contrast, liver brightness, deep attenuation, and vascular blurring (23).

Newly developed T2DM was either diagnosed following the American Diabetes Association criteria [FPG ≥ 7 mmol/l or HbA1c ≥ 6.5%] (24) or was based on self-report (25).

The total cohort was divided into the normoglycemia (defined as FPG < 100mg/dL or HbA1c < 5.7%) group and the prediabetes (defined as FPG≥100mg/dL or HbA1c level of 5.7% to 6.4%) group (26). For normally distributed continuous variables, one-way analysis of variance was used to analyze the differences among groups, expressed as mean ± standard deviation. For non-normally distributed continuous variables, differences across groups were analyzed using Kruskal-Wallis test and expressed as median with interquartile ranges. Categorical variables were compared by the chi-square test and expressed as proportions.

Characteristics of participants were described by ByG tertiles. Then, a univariate analysis model was applied to explore the relation between the baseline characteristics and T2DM. Moreover, Cox proportional hazards models and restricted cubic spline (RCS) analysis were conducted to assess the association of the levels of ByG with T2DM. Additionally, we performed receiver operating characteristic (ROC) curve analysis and informativeness analysis (27) to examine the potential diagnostic value of ByG in T2DM. Finally, a stratified study and interaction analysis between ByG and T2DM were identified in different subgroups by grouping sex, fatty liver, smoking status (never, past, current), alcohol consumption (non, light, moderate, heavy), and habit of exercise. All statistical analyses in our study were executed by EmpowerStats (www.empowerstats.com, X&Y solutions, Inc., Boston MA) and R statistical software (http://www.R-project.org).

A total of 15,464 participants were included in the cohort study. There were 11,806 participants in the normoglycemia cohort and 3,658 participants in the prediabetes cohort. Table 1 presented the characteristics of the study stratified by ByG tertiles in all populations. Compared with subjects in the lowest tertile of ByG, those in the highest tertile were more likely to be older, male, smoking (past or current), drinking (light or moderate or heavy), have fatty liver, have no habit of exercise, have higher BMI, WC, ALT, AST, GGT, TC, TG, HbA1c, FPG, SBP, DBP and lower HDL. Additionally, the ByG highest tertile group had the highest T2DM incidence, with 9.75 cases per 1000 person-years in all populations, 2.26 cases per 1000 person-years among the normoglycemia cohort and 22.26 cases per 1000 person-years among the prediabetes cohort ( Figure 1 ).

The results of univariate Cox proportional hazards models between baseline variables and T2DM were presented in Table 2 . We found that male, age, BMI, WC, ALT, AST, GGT, TC, TG, HbA1c, FPG, SBP, DBP, fatty liver, smoking status (past or current) and alcohol consumption (heavy) (P < 0.05) were positively correlated with the risk of T2DM, and that HDL (P < 0.0001) was negatively correlated with the risk of T2DM.

The results of the multiple Cox proportional hazards models are shown in Table 3 . With the lowest tertile as a reference, unadjusted, minimally adjusted (adjusted for age and sex) and fully adjusted (adjusted for age, sex, ALT, GGT, TC, fatty liver, smoking status, alcohol consumption and habit of exercise) Cox regression analysis showed that the hazard ratios (HRs) for T2DM significantly increased as the tertiles of ByG increased. Moreover, multiple Cox regression analysis demonstrated that ByG per-SD change was positively correlated with the risk of T2DM (HR:2.57 in all populations; HR:1.97 in the normoglycemia cohort; HR:1.50 in the prediabetes cohort; all P < 0.0001).

We further assessed the potential nonlinear relationship between ByG and new-onset T2DM. The RCS analysis ( Figure 2 ) showed a linear relationship between ByG and T2DM in all populations, normoglycemia and prediabetes (all P for nonlinearity > 0.05).

ROC curve analysis was done to assess the effectiveness of ByG in predicting T2DM risk in all populations ( Figure 3 ). The result showed that ByG (AUC 0.807) had the strongest predictive performance for T2DM compared with BMI (AUC 0.733), TyG (AUC 0.750) and TyG-WC (AUC 0.774). Consistent with this result, ByG was almost 1.23 times more informative about the risk of T2DM than TyG and TyG-BMI ( Table 4 ).

For each SD increase of ByG, the HRs for T2DM were 2.59 in females and 2.54 in males; 2.53 in non-fatty liver and 2.51 in fatty liver; 2.78 in never smokers, 1.99 in previous smokers and 2.69 in current smokers; 2.61 in never drinkers, 2.29 in light drinkers and 2.45 in moderate drinkers;2.48 in persons without habit of exercise and 3.68 in persons with habit of exercise in Table 5 . No interaction between ByG and T2DM was observed between subgroups by grouping sex, fatty liver, smoking status (never, past, current), alcohol consumption (non, light, moderate, heavy), and habit of exercise in Table 5 (all P _interaction > 0.05 or close to 0.05).

Here, we provided for the first time evidence that ByG was independently positively associated with T2DM in Japan. Moreover, these associations were independent of age, sex, ALT, GGT, TC, fatty liver, smoking status, alcohol consumption and habit of exercises. The present study may suggest that ByG was a better predictor of T2DM than BMI, TyG and TyG-BMI.

Several screening indicators that predict high risk of future T2DM have been previously reported. Given the high cost of time and money, oral glucose tolerance test is seldom used for routine testing. A Swedish case-referent study showed that the combination of HbA1c, FPG and BMI was effective in screening for individuals at risk of future clinical diagnosis of T2DM (28). Both Japanese and Chinese studies suggested that the combined measurement of FPG and HbA1c was effective for predicting T2DM (29, 30). A study in the Finnish population revealed that these individuals can be identified early by knowledge of FPG, BMI, and family history of diabetes (31). The American Diabetes Association diabetes risk test, as a simple and inexpensive tool to identify individuals at high risk for T2DM, had highlighted the importance of BMI in predicting the risk of T2DM (32). Different from previous studies, our study was the first to demonstrate a positive association between the combination of BMI and FPG and T2DM and suggested that ByG may be used to identify people who were at high risk for developing T2DM.

IR was one of the important factors affecting various metabolic diseases. Thus, identifying IR was critically important for early diagnosis, prevention, and personalized therapy. The TyG was a new and economical index for IR evaluation. In recent years, the role of TyG in the evaluation of diabetes, non-alcoholic fatty liver disease and other common clinical diseases has been confirmed to a certain extent (33–35), which has become a new research direction. A meta-analysis in 2020 demonstrated that TyG was a predictor of T2DM development (17). Another meta-analysis in 2021 assessed the dose-response relationship between TyG and the incidence of T2DM (36). It has been found that a high TyG was associated with the incidence of T2DM and the relationship between them was non-linear (36). Other studies on IR and diabetes indicated that the combined application of BMI with TyG (TyG-BMI) showed a significant increase in the area under the curve and its discrimination accuracy was higher than TyG (19, 20). This meant that BMI was essentially important to predict diabetes risk. Given that TG levels were affected by race and steroid hormones (37), we created a new index - ByG, which linked together BMI and FPG. Importantly, ByG was much easier to compute and utilize than TyG-BMI. Compared with TyG and TyG-BMI, ByG showed a better performance in identifying T2DM. More future studies are needed to gain more insights about ByG.

Many studies have pointed to a strong relationship between obesity and diabetes (5, 38, 39). Also, obesity was closely related to high blood sugar (40). Moreover, reactive oxygen species, mainly derived from adipose tissue, may cause multiple metabolic disorders, including obesity-related IR and T2DM (41). BMI, calculated from weight and height, represented general obesity. In addition to obesity, elevated FPG levels have also been shown to be an independent risk factor for the development of T2DM (42). Our results showed that ByG, the combination of obesity and FPG, was a predictor of diabetes. The dominance of ByG may be due to the well-verified roles of FPG and obesity in the development of IR and diabetes. Elevated glucose concentrations have a toxic effect upon beta cells by increasing reactive oxygen species (43). Altogether, these results suggested that glucotoxicity and lipotoxicity played pivotal roles for pathogenesis of diabetes.

Furthermore, BMI was a cheap, easy-to-operate and non-invasive compared to TG. Advantageously, an accurate scale enabled real-time measurement of BMI at home. ByG simplified the calculation of TyG-BMI. Due to its convenience and simplification, ByG was not only suitable for large-scale health assessment, but also for individuals’ evaluation of themselves.

This analysis had important strengths. The large size and long follow-up duration of the two cohort studies strengthened the credibility of the results. More importantly, more confounding factors were adjusted to increase the reliability of the results compared with previous studies. Besides, because the data come from Japan, the results were more instructive to the Japanese. It was interesting to notice that ByG would be a new predictor of diabetes. In addition, ByG can serve as a reference biomarker for T2DM during follow-up.

Several limitations may exist in this study. Firstly, as a single-center cohort study in Japan, the results may not be directly applicable to other regions and ethnicities. The generality of the findings needed to be confirmed across regions and ethnic groups. Then, the prevalence of diabetes may be inaccurate due to the lack of oral glucose tolerance tests. Lastly, because the research data came from an existing database, unmeasured confounding factors may not fully be resolved. We were unable to obtain potentially important information that may influence T2DM, such as family history of diabetes, history of gestational diabetes, therapy and main comorbidities (in particular obesity).