This cohort study was conducted using data from the CHARLS from 2011 to 2018 (18). BMI was the independent variable, and the outcome variable was incident stroke (dichotomous variables: stroke, non-stroke).

The CHARLS, an ongoing population-based, longitudinal cohort research that is now being conducted nationally to evaluate economic, social, and health status, provided the data for this study (18, 19). The CHARLS sample was obtained from 450 communities in 150 districts and 28 provinces through multi-stage probability sampling, with 10,257 households participating in the baseline survey and 17,708 participants. The sample was drawn from the Chinese population aged 45 or older at baseline (June 2011 to March 2012) (18, 19). All participants were assessed by one-on-one interviews using a standardized questionnaire. Participants underwent in-person follow-up every two years (18). The Biomedical Ethics Review Board of Peking University, China, approved the CHARLS study (IRB00001052-11015), and all participants provided written informed consent (18). This study’s data and related information can be downloaded from the CHARLS project website (http://charls.pku.edu.cn/).

Our study used data from four CHARLS waves (2011, 2013, 2015, and 2018). 17,708 participants were included in the baseline survey in 2011-2012. Firstly, we excluded participants with less than two years of follow-up (n=1,717). Secondly, we excluded participants who had a stroke at baseline (n=612) and who lacked information on stroke (n=187) or who were treated for stroke in wave 2011 (n=2). In addition, participants with missing weight data (n=2,900) and missing information on height (n= 64) and extreme values of BMI (BMI<15kg/m² and BMI>50kg/m², n=65) were also excluded (20). Finally, a total of 12,161 participants were included in the final analysis. The procedure for choosing participants is shown in Figure 1 .

The means and standard deviations were reported for continuous variables with Gaussian distributions. Medians were reported for skewed distributions, while frequencies and percentages were reported for categorical variables. To examine if certain BMI groups differed from one another, we employed the Kruskal-Wallis H test (skewed distribution), the One-Way ANOVA test (normal distribution), or the χ2 test (categorical variables).

Three distinct models were constructed using univariate and multivariate Cox proportional hazards regression models to examine the association between BMI and the risk of stroke in males, females, and all participants. These models included: (i) crude model: no covariates were adjusted; (ii) Model I: adjusted for age, sex, and drinking, smoking; and Model II: adjusted for age, sex, CRP, HGB, LDL-c, HDL-c, TG, HBA1c, FPG, HCT, HBA1c, hypertension, diabetes, SBP, diabetes, CKD, CHD, mental disease, CLD. The calculated effect sizes were reported with 95% confidence intervals (95%CI). Adjustments for confounding variables were made based on clinical knowledge and published reports (12, 27–29). Note that in the male and female subgroups, neither Model I nor Model II included sex among the variables that were adjusted for. In addition, the final multivariate Cox proportional hazards regression equation did not include TC due to its collinearity with other variables ( Supplementary Table S1 ).

We also examined the non-linear relationship between BMI and stroke risk in men, women, and all participants using Cox proportional hazards regression with cubic spline function and smoothed curve fitting. We first utilized a recursive technique to locate the inflection point if a non-linear relationship was discovered. A two-piecewise Cox proportional hazards regression model was then constructed on both sides of the inflection point. The best model to explain the connection between BMI and the risk of stroke was ultimately selected using a log-likelihood ratio test. In addition, we performed subgroup analyses. We converted age into categorical variables (age: <60, 60 to <70, ≥70 years) and used Cox proportional hazards regression with cubic spline functions and smooth curve fitting to identify the non-linear relationship between BMI and stroke risk in different age subgroups.

To assess the validity of our findings, we conducted multiple sensitivity analyses. According to the definition provided by the Chinese Obesity Task Force, we transformed BMI into a categorical variable. We calculated P for the trend to validate the finding of BMI as a continuous variable and to explore the possibility of a non-linear association between BMI and stroke risk. Since smoking, hypertension, and diabetes are strongly associated with stroke (30–33), We explored the association between BMI and stroke in men, women, and the entire sample by excluding smokers, hypertensive patients, or diabetic patients, respectively, from sensitivity analyses. Furthermore, we investigated potential unobserved confounders between BMI and stroke risk by calculating E-values (34).

All of the results were made in line with the STROBE statement (35). R statistical software tools (http://www.r-project.org, The R Foundation) and Empower Stats (X&Y Solutions, Inc., Boston, MA, http://www.empowerstats.com) were used for all analyses. The statistical significance was set at P values lower than 0.05(two-sided).

The demographic and clinical characteristics of the participants in the study are detailed in Table 1 . There were 12,161 participants in the final analysis, and 46.20% were males. Of these, 1,335 participants had a stroke, with a cumulative incidence of 10.98%. BMI presented a normal distribution, with a mean of 23.45kg/m² ( Figure 2 ). We divided participants into four subgroups according to the definition proposed by the Chinese Obesity Task Force. In comparison to the underweight group, PLT, TC, FPG, TG, CPR, LDL-c, HBA1C, UA, HCT, HGB, SBP, and DBP increased significantly in the obese group, while the inverse was true for age, HDL-c, BUN, and Scr. In addition, the proportion of never-smokers, women, CHD, malignant tumors, and diabetes was greater in the obese group.

To investigate the connection between BMI and stroke risk across all individuals, three models were constructed using Cox proportional hazards regression models( Table 2 ). 1 kg/m² rise in BMI was linked to a 5.8% increase in the risk of stroke in the crude model (HR=1.058, 95% CI 1.045-1.072). The incidence of stroke increased by 6.6% for every kg/m² rise in BMI in Model I (HR=1.066, 95% CI 1.053-1.079, P0.001). Each extra kg/m² of BMI in Model II was associated with a 2.5% increase in stroke risk(HR=1.025, 95%CI 1.010-1.040).

Besides, we reintroduced the categorically transformed BMI into the model after converting it from a continuous variable to a categorical variable. Using underweight participants as a reference, the multivariate-adjusted model’s findings revealed an HR of 1.261 (95% CI: 0.959-1.658) for participants with normal weight, 1.434 (95% CI: 1.079-1.907) for overweight participants, and 1.546(95% CI: 1.137- 2.103) for obese participants ( Table 2 ).

We also used Cox proportional hazards regression models to construct three models to examine the relationship between BMI and stroke risk in men and women. According to the multivariate-adjusted model’s findings, a 1 kg/m² rise in BMI was linked to a 5.8% higher risk of stroke in male participants (HR=1.032, 95% CI 1.007-1.057). Using underweight participants as a reference, the HR was 1.277 (95% CI: 0.838-1.947) for normal BMI participants, 1.576 (95% CI: 1.011-2.456) for overweight participants, and 1.425 (95% CI 0.865- 2.350) for obese participants ( Table 2 ).

In female participants, results from multivariate-adjusted models showed that a 1 kg/m² increase in BMI was associated with a 2.1% increase in stroke risk (HR=1.021, 95% CI 1.002-1.040, p=0.03). Using underweight participants as a reference, the HR was 1.269 (95% CI: 0.884-1.821) for normal BMI participants, 1.365 (95% CI: 0.940-1.983) for overweight participants, and 1.614 (95% CI 1.086-2.399) for obese participants ( Table 2 ).

Multivariate adjusted models based on all participants showed no significant difference in the risk of stroke in normal-weight participants compared to underweight participants (p>0.05). In contrast, overweight and obese participants had a significantly increased risk of stroke and had similar HR values. These results suggest that there may be a non-linear association between BMI and stroke.

Using Cox proportional hazards regression with cubic spline functions and smooth curve fitting, we discovered that the association between BMI and stroke incidence was non-linear ( Figure 3 ), with a log-likelihood ratio test of P less than 0.05. We adjusted for variables including age, sex, CRP, HGB, LDL-c, HDL-c, TG, FPG, HCT, HBA1c, hypertension, diabetes SBP, CKD, CHD, mental illness, CLD, drinking status, and smoking status. Using a recursive technique, we first identified a BMI inflection point of 26.63 kg/m². Then we used a two-slice Cox proportional-hazards regression model to determine effect sizes and confidence intervals for the left and right sides of the inflection point. Each 1 kg/m² increase in BMI was linked to a 4.4% increase in the incidence of stroke on the left side of the inflection point (HR=1.044, 95% CI 1.019-1.069, p=0.002). The HR and 95% CI on the right side of the inflection point were 0.998 and 0.967,1.030, respectively, but there was no significant difference ( Table 3 ).

We discovered that the association between BMI and stroke risk in men was non-linear ( Figure 4 , log-likelihood ratio test P<0.05). The inflection point for BMI was 25.94 kg/m2, and each 1 kg/m2 increase in BMI was associated with a 7.6% increase in the risk of stroke on the right before the inflection point (HR=1.076, 95% CI: 1.034-1.119, P<0.001). Their relationship on the left side of the inflection point was not statistically significant in men. In contrast, the non-linear association between BMI and stroke risk did not exist in females (log-likelihood ratio test P > 0.05) ( Table 3 ).

Using the same method, we found that the association between BMI and stroke risk was non-linear in all age subgroups (log-likelihood ratio test P<0.05). Adjusted variables included age, sex, CRP, HGB, LDL-c, HDL-c, TG, FPG, HCT, HBA1c, hypertension, diabetes, SBP, CKD, CHD, mental illness, CLD, drinking status, and smoking status. On the less-than-inflection point side, the HRs for BMI and stroke risk were 1.065 (1.027, 1.104), 1.057 (1.023, 1.092), and 0.643 (0.449, 0.920) for the age <60, 60 to <70, and ≥70 subgroups, respectively. Their relationship on the side greater than the inflection point was not statistically significant in all age subgroups. ( Supplementary Table S3 ).

We conducted sensitivity analyses on participants without diabetes (n=11,510). After adjusting for confounding variables (including age, sex, CRP, HGB, LDL-c, HDL-c, TG, FPG, HCT, HBA1c, hypertension, SBP, CKD, CHD, mental disease, CLD), two-stage linear regression model analysis revealed a non-linear relationship between BMI and stroke risk, while in women participants, there was no non-linear relationship between them. Besides, we also excluded participants with hypertension (n=9,419). After adjusting for confounding variables (including age, sex, CRP, HGB, LDL-c, HDL-c, TG, HBA1c, FPG, HCT, diabetes, SBP, CKD, CHD, mental disease, CLD), similar results were obtained, that is, the relationship between BMI and stroke risk was non-linear in male participants and their relationship was not statistically significant in female participants. In addition, we also excluded participants with CKD (n=11,398) for sensitivity analysis and found that their relationship remained non-linear in male participants and linear in females (adjusted age, sex, CRP, HGB, LDL-c, HDL-c, TG, HBA1c, FPG, HCT, HBA1c, hypertension, SBP, CKD, CHD, mental disease, CLD) ( Table 4 ). To evaluate the sensitivity to unmeasured confounders, an E-value was also calculated. The E-value (1.31) was higher than the relative risk of BMI and unmeasured confounders (1.27), suggesting that unknown or unmeasured factors may not have significantly affected the link between BMI and stroke risk. It is obvious that our results are reliable based on all sensitivity assessments.

We enumerated the following strengths of our study. First, the independent variables in our study employed both categorical and continuous BMI to evaluate its association with the risk of stroke, reducing information loss and quantifying their relationship. Second, Missing data were handled using multiple imputations. This approach can enhance statistical power and reduce potential bias brought on by the absence of covariate information. Third, our study is a significant improvement compared to previous studies regarding the nonlinearity addressing; for the first time, we found a non-linear association between BMI and stroke risk in men. In addition, we ran a battery of sensitivity analyses to ensure the stability of our finding (reanalyzing the non-linear association between BMI and stroke incidence after excluding participants with diabetes, hypertension, and CKD and calculating E-values to investigate the possibility of unmeasured confounding variables).

Potential limitations should be noted. First, the population included in this study was middle-aged and elderly Chinese; therefore, the generalizability of these results to younger populations and other ethnicities needs further validation. In the future, we will collaborate with researchers from outside of China to confirm the associations in populations with distinct genetic backgrounds. Second, BMI was only assessed once, at baseline, and not again thereafter. Their changes over time were disregarded; in addition, certain indicators associated with stroke were missing from the original data, including waist-to-hip ratio, medications, and genetic history of stroke. We can also consider structuring our studies or collaborating with other researchers to collect as many data points as possible, such as information on how BMI varies during participants’ follow-up. Third, stroke diagnosis relies on self-reported stroke history, and the subtypes and stages of stroke are unclear. In the future, we will need to combine medical history information and imaging findings to diagnose stroke. Fourth, as with all observational research, uncontrolled or unmeasured confounders may still exist even if known potential confounders are adjusted for. However, we estimated E-values to assess the possible influence of unmeasured confounders and discovered that they were unlikely to explain and influence our study’s results. Finally, this is an observational study that does not prove a causal relationship between BMI and stroke risk; rather, it only establishes an association between them.