Based on the 2007–2018 NHANES, the survey utilized a cross-sectional design. It involves collecting data from a sample of persons who are not in institutions, chosen to reflect a larger population using a specific research design that includes multistage, cross-sectional, subgroup stratified, and probability sampling. Every 2 years, a survey is conducted [21].NCHS Ethics Review Committee approved the NHANES research proposal. Every single participant in the research study supplied a written agreement after being fully informed. Check out at www.cdc.gov/nchs/nhanes/irba98.htm for a more comprehensive overview. The data were analyzed throughout the period from April 1 to April 30, 2024. Detailed information on NCHS IRB/ERB Protocol Number can be found in Supplementary Material.

59,842 individuals were included in the sample for this cross-sectional study during six consecutive periods (2007–2009, 2009–2010, 2011–2012, 2013–2014, 2015–2016, 2017–2018). Due to the absence of BMD data in the 2011–2012 NHANES and 2015–2016 NHANES, we have chosen to exclude the data from these two years from our analysis. The exclusion criteria were patients age < 20 (n = 961) or with missing AIP data (n = 8,356), BMD data including total femur (TF), femoral neck (FN), Lumbar spine (LS) BMD (n = 25,779). As a result of the study, 5,019 participants were included with complete data. (Fig. 1)

Flow chart of participants selection from the NHANES 2007–2018

AIP is a variable indicative of exposure determined by the mathematical formula lg[TG(mg/dL)/HDL-C(mg/dL)]. Based on their AIP quartiles, the subjects were further partitioned into four groups: Q1 (-0.79, 0.09), Q2 (0.09, 0.30), Q3 (0.30, 0.53), and Q4 (0.53, 2.15).

TF, FN, and LS BMD were included as outcome variables. The NHANES website provides additional information.

The following criteria were used to evaluate the Covariables in this study: [1] data related to the characteristics of the population being studied; [2] factors that have been identified in previous research as influencing AIP and BMD; [3] adherence to the STROBE statement guidelines, which suggest that the basic model should show a change of more than 10% when additional variables are introduced [22]. Thus, we incorporated the subsequent covariables that align with the aforementioned guidelines: age, degree of education, income, sex, race, average daily alcohol consumption in the past 12 months, have been told to suffer from osteoporosis/bone fragility (Yes/No), alanine aminotransferase (ALT, U/L), aspartate transaminase (AST, U/L), serum creatinine (SCr, mg/dL), Total calcium (Tc, mg/dL).

The classification of race/ethnicity included the categories Other Hispanic, Mexican, Non-Hispanic Black, American, Non-Hispanic White, and Other. Three education categories were classified: senior high school or below, above high school, and unknown. The quantity of alcohol consumed is contingent upon the mean number of alcoholic beverages ingested by individuals throughout the previous 12-month period. Additional comprehensive information on covariables may be found in Supplementary Table S1.

The study employed appropriate weighting methodology to consider the intricate sample design, ensuring that the results are representative at a national level, as advised by the NHANES Guidelines [23]. The AIP levels were categorized into Q1-Q4. Counts and percentages (%) were used to represent categorical variables, while means and SD or medians were used to describe continuous variables. Discrepancies among continuous variables were examined using weighted linear regression. Categorical variables were analyzed with Chi-square tests.

According to the STROBE statement [24], the present study utilized three models. Model 1 involved a univariate logistic regression analysis. Model 2 was adjusted for sex, race, and age. Model 3 included additional adjustments for age, degree of education, sex, income, race, alcohol consumption, and information on osteoporosis, ALT, AST, SCr, and TC.

The relationship between AIP and BMD was analyzed using three weighted multivariable linear regression models. We employed three different logistic regression models, each with a weighted factor, to assess the relationships between AIP and BMD. Following that, subgroup analysis was conducted to examine potential interactions and account for confounding categorical characteristics. The subgroup analysis using weighted multivariable logistic regression. Results of the different strata can be considered valid if the interaction P-value is not statistically significant. The presence of a distinctive population, however, is suggested by a significant interaction P-value.

We analyzed the non-linear associations between AIP and BMD using a generalized additive model (GAM) that employed smooth curve fitting(SCF). The significant inflection points between AIP and BMD were calculated using a recursive algorithm upon detecting non-linearity. The two-part logistic regression model was compared with the logistic regression model with a threshold effect analysis.

The statistical analysis was conducted using EmpowerStats (V2.0.0, www.empowerstats.com) and R (V3.4.3, http://www.R-project.org). A two-sided P-value < 0.05 was considered statistically significant.