The NHANES was conducted under the oversight of the NCHS Research Ethics Review Board. This investigation utilized data from the 2013–2018 NHANES, encompassing a cohort of 29,400 participants. The study’s methodology is depicted in Figure 1 . The exclusion criteria were rigorously applied as follows: (1) 14451 male participants were excluded; (2) 10,625 individuals beyond the age of 45 years or younger than 18 years were omitted; (3) those without available AIP values were excluded (N=2,574); (4) subjects with incomplete fertility data were removed (N=194); (5) participants missing either the outcome of interest or necessary covariate information were also excluded (N=234). Following this meticulous screening process, a cohort of 1,322 eligible subjects was retained for subsequent analysis.

Using self-reports and the reproductive health questionnaire, infertility was characterized. Individuals who affirmed experiencing infertility were classified into the infertility group; otherwise, they were categorized as not having infertility. To maintain the integrity and precision of the study’s outcomes, participants who either abstained from answering or expressed uncertainty about their fertility status were systematically removed from the analysis. This approach ensured that the analysis was conducted with the most accurate and reliable data available.

The formula for calculating AIP which is an exposure variable, is log [TG (mg/dL)/HDL-C(mg/dL)]. Utilizing subsequent definitions of the quartiles, subjects were divided into different categories relying on their AIP values: Q1 (AIP < -0.077), Q2 (AIP -0.077 to <0.127), Q3 (AIP -0.127 to < 0.348), and Q4 (AIP ≥ 0.348) (27).

All waist circumference is taken at the mobile examination center (MEC). HOMA-IR is equal to fasting insulin (µU/mL) ×fasting glucose (mmol/L)/22.5 (28).

In this study, covariates were meticulously selected to encompass both continuous variables, such as age and poverty income ratio (PIR), and categorical variables. The categorical variables included race, smoking status, education level, BMI status, CVD, leisure time physical activity (LTPA), daily sitting time, history of treatment for pelvic inflammatory disease (PID), usage of female hormones, and history of taking birth control pills in accordance with prior characterized or clinical expertise (21–23).

The categorizations of participants’ responses regarding PID, whether they have ever used birth control pills, and whether they have ever used female hormones are straightforwardly determined based on participants’ responses, categorized as either “yes” or “no”. CVD encompassed conditions that were clinically diagnosed, including coronary heart disease, congestive heart failure, stroke, and angina. Self-reported data on daily sitting time and weekly LTPA were collected through respondent-level interviews. Based on their sedentary time, participants were classified into four groups (29). For physical activity levels, participants were divided into three categories: inactive (individuals not engaging in any LTPA), insufficiently active (0 - 150 min LTPA/week), and sufficiently active (>150 min LTPA/week) (30).

The statistical analyses were conducted using R 4.4.2 software and EmpowerStats. The threshold for determining statistical significance was established at P < 0.05. Characteristics across groups were contrasted utilizing t-tests and chi-square tests in Table 1 . Levels of AIP were stratified into four groups for analysis. This analysis involved the calculation of odds ratios (ORs) and 95% confidence intervals (CIs) to quantify the strength and precision of these associations. No factor was altered by Model 1. Model 2 brought into aspects including age, racial background, levels of education, and PIR. Model 3 was adjusted for smoked status, pelvic infection, ever taken birth control pills, ever use female hormones, CVD, daily sitting time, LTPA, building upon the adjustments made in Model 2. Subsequently, the effects of AIP on infertility were evaluated through subgroup analyses and interaction tests, focusing on groups characterized by age, smoked status, daily sitting time, history of pelvic infection, usage of female hormones, history of taking birth control pills, CVD and LTPA.

In addition, the non-linear connections between AIP and infertility were researched utilizing a Generalized Additive Model (GAM). Furthermore, mediation analysis was carried out to investigate whether waist circumference mediated the relation between AIP and infertility in reproductive-aged women.

There were 1,163 controls and 159 infertile participants among the 1,322 participants. Table 1 reveals the features of the subjects categorized by AIP quartiles. AIP levels failed to indicate any meaningful correlations with CVD, daily sitting duration, history of pelvic infection, usage of female hormones, or history of taking birth control pills (P > 0.05). In contrast, AIP were correlations with to age, race, education level, PIR, WC, smokers, LTPA and individuals with infertility (all P-values < 0.05). Participants with increased AIP tended to be older with a larger WC, lower PIR, and education levels compared to those in the lower AIP quartile groups.

The results demonstrated a considerably greater likelihood of WC and elevated AIP among infertile women in the US, across all models, regardless of adjustments for confounding factors in Table 2 . After adjusting for all confounding variables (model 3), each 1-unit increase in AIP was linked with an 94% increase in the odds of infertility. Furthermore, in Model 3, which adjusted for all relevant covariates, participants in the highest AIP quartile had an OR of 1.97(95% CI: 1.13–3.44), indicating an 97% higher likelihood of infertility in comparison with others in the lower AIP quartile groups.

The smooth curve fitting demonstrated a non-linear link between AIP and infertile participants ( Figure 2 ). Further calculations determined the inflection point to be 0.16 ( Table 3 ). AIP and female infertility exhibited an intensely favorable relationship before the inflection point, with an OR of 11.13(95% CI: 2.83–43.72). This indicates a strong relationship between higher AIP levels and increased infertility risk up to the inflection point. However, beyond the inflection point, the link between AIP and female infertile participants was not significant, with an OR of 0.71(95% CI: 0.28–1.78), indicating a significant threshold effect of AIP and infertility.

To further investigate the factors influencing the link between AIP and the likelihood of female infertility, we conducted stratified analyses and interaction tests based on age, smoked status, daily sitting time, history of pelvic infection, usage of female hormones, history of taking birth control pills, CVD and LTPA ( Table 4 ). Significant interactions were detected for age, smoked status, daily sitting time, history of pelvic infection, ever taken birth control pills, ever use female hormones, CVD and LTPA, with all P-values for interaction being < 0.05. A positive link between AIP and female infertile participants persisted in specific subgroups, including women aged 35 years or younger, smokers, people whether have CVD, those without a history of pelvic infections, users of female hormones, and individuals who have ever taken birth control pills. Notably, the subgroup analysis indicated that even among women aged 35 years or younger with no history of cardiovascular disease, pelvic infections, or use of female hormones, an elevated AIP still correlates with the gradually relative odds of infertility.

All of the models in Table 5 demonstrated an important positive correlation between WC and female infertility [model 1: OR (95% CI) =1.020(1.011–1.028); model 2: OR (95% CI) = 1.017(1.008–1.027); model 3: OR (95% CI) = 1.018 (1.009–1.028)].

An increased AIP level was associated with an elevated risk of WC across all models [model 1: β (95% CI) = 16.14(20.38–26.02); model 2: β (95% CI) = 16.37(20.56–26.15); model 3: β (95% CI) = 5.60 (19.79–25.48)] as shown in Table 6 . In Model 3, the WC of the highest quartile was 14.6cm higher than that of the lowest quartile.

As depicted in Figure 3 , WC demonstrated a strong link with infertility [total effect (95% CI, P): 0.030(0.009,0.051), 0.012]. Additionally, there was a substantial moderating effect for WC in the link between AIP and infertility [mediation effect (95% CI, P): 0.016(0.005–0.026), 0.004], accounting for 54.49% of the association. While there was no direct correlation between AIP and infertility [direct effect (95% CI, P): 0.014 (-0.011, 0.037), 0.337]. These findings indicate that WC served as a significant complete mediator in the link between AIP and infertility.

The results of the ROC curves were presented in Table 7 ; Figure 4 . Regarding infertility, the AUCs of AIP, WC and the HOMA-IR index were 0.642 (95% CI: 0.599, 0.683) vs. 0.658 (95% CI: 0.618, 0.705) vs. 0.637 (95% CI: 0.593, 0.686). Although the AUC of WC was higher, there was no statistically significant difference between the AUCs of the diverse surrogates (P > 0.05). It appears that the various IR surrogates did not demonstrate variability in their predictive ability for infertility.