The National Health and Nutrition Examination Survey (NHANES) is a comprehensive national survey conducted by the Centers for Disease Control and Prevention (CDC) to evaluate the health and nutritional status of the U.S. population. Due to its use of probability sampling, NHANES data is considered highly credible and valuable for academic research. The 2017-2020 NHANES serves as the primary data source for this analysis. The National Center for Health Statistics (NCHS) Ethics Review Board has approved all study protocols for NHANES, and each participant has provided written informed consent. Detailed NHANES study designs and data are publicly available at http://www.cdc.gov/nchs/nhanes/.

Initially, 15,560 participants from the 2017-2020 NHANES were enrolled. In order to select the most eligible subjects for the current study, the researchers further evaluated these individuals. First, they excluded 7,839 male subjects and female subjects younger than 20 years (n = 3,086) or older than 45 years (n = 2,796). Second, participants with missing data on self-reported infertility (n = 282) and body mass index (n = 55) were excluded. Participants who had both ovaries removed (n = 35), underwent hysterectomy (n = 54), or were pregnant at the time of examination (n = 68) were also excluded. Ultimately, 1,463 eligible women participated in the study ( Figure 1 ).

The exposure factor was BRI, which was calculated using the formula: B R I = 364.2 − 365.5 × 1 − W C ( m ) / 2 π 2 0.5 × H e i g h t ( m ) 2 (8, 9). The height and waist circumference data were obtained from the participants’ physical examination documents. Body measurements were taken by professionally trained health technicians at the Mobile Health Screening Center and were recorded with the corresponding person to ensure accuracy. Participants were asked to remove their clothes and shoes before the measurements were taken. Height was measured while standing, and waist circumference was measured at the midpoint between the lower ribs and the upper part of the hips in a standing position.

The outcome indicator is self-reported female infertility, which was obtained from the Reproductive Health Questionnaire. The questionnaire was administered by professionally trained interviewers using the Ministry of Education’s computer-assisted personal interview system. Participants were asked about their pregnancy history with the question, “Have you been trying to get pregnant for one year?” Women who answered “yes” were categorized as having infertility, and those who answered “no” were categorized as not having infertility (Questionnaire variable name: RHQ074).

Covariates in this study included age, race, education level, marital status, poverty-to-income ratio (PIR), smoking status, hypertension, diabetes mellitus, regular menstruation, sex hormone use, history of treatment for pelvic infection, waist circumference, and BMI. In our analyses, we used the questionnaire “Your doctor told you that you have diabetes” to determine if participants had diabetes. Those who answered “yes” were categorized as diabetic. Similar questionnaires were used to identify patients with hypertension and other conditions. Additionally, we used the questionnaire “Have you smoked at least 100 cigarettes in your life” to determine smoking status, categorizing those who answered “yes” as smokers. The above covariates were determined professionally after reviewing existing studies. All data collection and measurement procedures for these covariates are available on the NCHC website. Moreover, measurement procedures for these covariates are available on the NCHC website.

Questions about missing data, after data processing, the only variable with missing values was the poverty-to-income ratio (PIR), with a missing data percentage of 10.2% (168/1463). The missing values were estimated using the continuous iterative imputation method, which is based on the conditional distribution of other variables. This approach improves the accuracy and reliability of subsequent analysis.

Statistical analyses were performed using Empower Stats software (X&Y et al., USA) and the R package (version 3.4.3). p < 0.05 was considered statistically significant. Data were obtained from NHANES 2017-2020. The NHANES study employed a sophisticated multi-stage probability sampling design to collect data, which was taken into account in our analysis. To ensure representativeness of the sample, we performed weighted multivariate logistic regression analyses. Demographic and measurement indicators were descriptively analyzed for the study population. These indicators were categorized into two groups according to the presence or absence of infertility. Continuous variables were expressed as Mean ± Standard Error (Mean ± S.E.), and a t-test was used to compare groups. Categorical variables were expressed as frequencies (constitutive ratios) [n (%)], and comparisons between groups were made using the chi-square test. Multivariate regression models were used to examine the association between BRI and infertility. In model 1, the covariates were not adjusted. In model 2, adjustments were made for age and race. Model 3 was adjusted for the following factors: age, race, marital status, education level, household income, poverty rate, smoking at least 100 cigarettes, diabetes, hypertension, previous use of female hormones, previous treatment for pelvic infection, and regularity of menstruation in the past 12 months. Model 3 also used the RCS curve to assess the association between BRI and infertility. In addition, subgroup analyses and interaction tests were performed according to age, marital status, smoking status, diabetes, and regularity of menstruation. We aim to identify possible impact modifiers and understand the differences in results among various groups and circumstances. The sensitivity of BRI and BMI in predicting infertility was assessed by examining the receiver operating characteristic curve (ROC) and calculating the area under the curve (AUC).

In Table 1 , we can see the characteristics of participants aged 20 to 45 years based on whether they had infertility. Out of 1463 participants, 172 (11.76%) were found to be infertile. The research showed that older women who lived with a partner who smoked at least 100 cigarettes, had diabetes mellitus, irregular menstruation, higher waist circumference, body mass index, and body roundness index reported a higher prevalence of infertility.

In Table 2 , it is evident that there is a positive association between BRI and the prevalence of infertility. This positive correlation remained consistent in model 3 (OR 1.19; 95% CI 1.05-1.34), indicating that each unit increase in BRI raises the risk of infertility by 19%. For sensitivity analysis, we converted BRI from a continuous variable to a categorical variable (quartile). The likelihood of infertility in Q4 was 83% higher compared to Q1. However, the difference between Q2 and Q1 was not statistically significant (OR 1.17; 95% CI 0.68-2.02), nor was the difference between Q3 and Q1 (OR 1.52; 95% CI 0.89-2.59). Additionally, we used smoothed curve fitting based on model 3 to investigate the relationship between BRI and infertility, revealing a positive nonlinear relationship ( Figure 2 ).

Subgroup analyses and interaction tests were performed using different variables to investigate the stability of the association between BRI and female infertility across subgroups. Subgroup analyses were stratified by age, marital status, diabetes, smoking status, and menstrual pattern. In all subgroups, BRI values were generally and consistently positively associated with the risk of infertility. The smoking group showed a significant interaction effect (P for interaction=0.0027), suggesting that smoking or not smoking may have a differential effect on the relationship between BRI and infertility ( Figure 3 ).

In this study, we initially calculated the sensitivity and specificity at varying thresholds, subsequently employing the Youden index to assess the performance of BRI and BMI at distinct thresholds. Youden’s index = sensitivity + specificity - 1.We identified the optimal cut-off point through the selection of a threshold that maximized the Youden index. This process ensured an optimal balance between positive and negative predictions. The results demonstrate that BRI exhibits a Youden index of 14.48%, an optimal threshold of 6.2945, an AUC of 0.5773, a sensitivity of 43.60%, and a specificity of 70.95%. The Youden index for BMI is 12.77%, with an optimal threshold of 3.345 and an AUC of 0.5681. The sensitivity is 41.28%, while the specificity is 71.49%. BRI demonstrated superior performance relative to BMI. Furthermore, a receiver operating characteristic (ROC) curve was plotted. The receiver operating characteristic (ROC) curve illustrates the correlation between sensitivity and the false positive rate (1-specificity) at varying thresholds. The optimal inflection point is defined as the point on the receiver operating characteristic (ROC) curve that is furthest from the diagonal line ( Table 3 , Figure 4 ).