The study received approval from the Ethics Committee of the Affiliated Kunshan Hospital of Jiangsu University, Suzhou, China (approval No. 2021–06-015-K01), and adhered to the principles outlined in the Declaration of Helsinki. The patients’ identities were concealed to ensure an unbiased investigation. All patients provided written informed consent.

In the present study, a retrospective cross-sectional analysis was performed using patient data collected from January 2017 to July 2022. The medical information of the patients was obtained from Kunshan Hospital, affiliated with Jiangsu University, Suzhou, China. The study involved a cohort of 3,558 patients with OPF who underwent surgical procedures or required hospitalization. All participants received blood tests while they were hospitalized. The diagnosis of OP was established based on the following criteria: (1) The existence of bone instability and fractures without any accompanying metabolic bone disorders, coupled with a standard bone mineral density (BMD) (T-score); (2) verification of osteoporosis (OP) using a T-score of −2.5 or below, even in the absence of a prevailing bone fracture (27). The exclusion criteria were as follows: (1) Missing or incomplete records; (2) Multiple or pathological hip fractures; (3) Diagnosed with other diseases that interfere with bone metabolism (such as thyroid diseases, parathyroid-related diseases, diabetes, gonadal diseases); (4) Presence of an autoimmune disease such as systemic lupus erythematosus; (5) Long-term use of drugs that affect bone metabolism; (6) SIRI>15 (28).

Levels of SIRI, β-CTX, and P1NP were assessed in a cohort of 732 individuals. The complete blood counts of the patients were determined and the SIRI was computed as the exposure variable. Neutrophils, monocytes, and lymphocytes were measured using flow cytometry with nuclear staining on the Sysmex XN-10 (B4) hematology analyzer. The outcome variables investigated were the levels of β-CTX and P1NP. The β-CTX and P1NP levels in patients were measured using automated electrochemiluminescence immunoassays (ECLIA) from Roche Diagnostics in (Mannheim, Germany). All measurements were collected using the same instrument and the same experienced operator following standardized protocols.

The covariate variables including age, sex, body mass index (BMI), high-density lipoprotein (HDL), total cholesterol (TC), hypertension, diabetes, calcium, platelet count, smoking status, alcohol consumption, and the Charlson comorbidity index (CCI) (29) were measured and recorded. Calcium levels were measured using a Beckman AU5800 automated biochemistry analyzer, employing the Arsenazo III method. Platelet counts were determined by flow cytometry with impedance on a Sysmex XN-10 (B4) hematology analyzer, while HDL was measured on the Beckman AU5800 automated biochemistry analyzer employing the direct approach. All clinical indicators were assessed within three days of admission.

The data related to demographics, laboratory tests, and clinical outcomes are presented as either the median with the interquartile range (the 25th and 75th percentiles) or the mean ± standard deviation (SD). The data are presented in the form of frequencies (expressed as percentages) for each category. Categorical data were analyzed using either Pearson’s chi-square test or Fisher’s exact test for univariate analysis. Independent-sample tests were used to compare normally distributed continuous data, while the Mann–Whitney U test was used for non-normally distributed continuous data. The association between the attributes of OPFs and the BTMs, β-CTX, and P1NP, was also investigated using univariate analysis.

The Generalized Estimating Equation (GEE) and Generalized Additive Model (GAM) are two common statistical modeling approaches. GEE models the average response and correlations by specifying a working correlation structure, suitable for handling correlated data such as longitudinal or clustered data. In contrast, the GAM employs flexible nonparametric smoothing functions to explore complex nonlinear relationships between the response and predictors, without assuming parametric forms. Both require specifying the response distribution, formulating the mean model, and using iterative algorithms to estimate parameters. Researchers can then evaluate model fit and perform statistical inference.

The GEE was employed for appropriate adjustment of covariates and investigation of the independent relationship between SIRI levels and β-CTX and P1NP in OPFs. The models that were developed included unadjusted and slightly adjusted models, referred to as Model 1 and Model 2, respectively, as well as the fully adjusted model, termed Model 3. Firstly, a variance inflation factor (VIF) analysis was conducted to detect any collinearity among the covariates. Subsequently, decisions were taken to modify these elements based on the following criteria: (1) A modification in the matched odds ratio (OR) by ≥10% was observed upon the addition or removal of covariates in the basic or full model, respectively; (2) Variables that satisfied criterion 1 or had a p-value less than 0.1 in the univariate model (30). Model 3 employed both criteria 1 and 2 to adjust for covariates. This resulted in the development of three models, namely, Model 1, which was left unadjusted, and Model 2 (minimally adjusted model), which included covariate adjustments for age, sex, BMI, smoking status, alcohol consumption, hypertension, and diabetes CCI levels, and Model 3, which additionally included covariates such as calcium, HDL, total cholesterol, and the platelet count.

The GAM was used to detect possible non-linear associations. After the identification of these correlations, a two-piecewise linear regression model was used to determine the threshold effects in the resulting smoothing curves. A recursive approach was used to independently determine the inflection point, employing a maximum-likelihood model when the curves exhibited a clear ratio (31). The robustness of the studies and changes among patient subgroups were assessed by conducting subgroup analyses, stratifying patients based on specific covariates. Subgroup interactions and modifications were analyzed using the likelihood ratio test (LRT).

The R packages from The R Foundation¹ and Empower Stats from X&Y Solutions, Inc., MA, USA² were utilized for all analyses. A significance criterion of p < 0.05, using a two-tailed test, was employed.

According to the eligibility criteria depicted in Figure 1, a total of 732 patients were treated between January 1, 2017, to July 27, 2022, were ultimately included in the analysis. Table 1 summarizes the baseline characteristics of the hospitalized patients (n = 732), of whom 33.61% were male and 66.39% female, with a mean age of 69.04 ± 11.02 years.

The subjects in this study exhibited a mean Systemic Immune-Inflammation Index (SIRI) value of 2.40 ± 2.18, a mean β-CTX value of 0.53 ± 0.28 ng/mL, and a mean P1Np value of 57.72 ± 30.72 μg/L. Observations were conducted to identify variations in the co-variate variables among the patient cohort.

A univariate analysis was performed to investigate the relation between β-CTX and P1NP with covariate variables (Table 2). No significant relationships were found between the investigated variables and β-CTX or P1NP in the patients with OPF.

Three models were used in the subsequent phase to analyze the correlation between SIRI and both BTMs (β-CTX and P1NP) in participants with OP (Table 3). In the unadjusted Model 1, there was a significant correlation between SIRI and β-CTX (β = −0.03, 95% CI: −0.04 to −0.02, p < 0.001) (β is the regression coefficient in the linear regression model, representing the magnitude and direction of the association between SIRI and BTMs). Similarly, a significant correlation was found between SIRI and P1NP (β = −2.87, 95% CI: −3.70 to −1.70, p < 0.001). After adjusting for variables including age, sex, BMI, smoking status, alcohol intake, CCI, hypertension, and diabetes in Model 2, the observed relationships were consistent. The SIRI remained significantly associated with both β-CTX (β = −0.03, 95% CI: −0.04 to −0.02, p < 0.001) and P1NP (β = −2.83, 95% CI: −4.02 to −1.64, p < 0.001). Expanding on Model 2, Model 3 included further adjustments for HDL, TC, calcium, and platelet count, and consistently showed a negative correlation. The SIRI remained significantly associated with β-CTX (β = −0.04, 95% CI: −0.05 to −0.03, p < 0.001) and P1NP (β = −3.77, 95% CI: −5.07 to −2.47, p < 0.001).

Additional subgroup analysis was conducted to assess the robustness of Model 3 by categorizing patients with OPF according to various characteristics such as age, sex, BMI, smoking status, alcohol consumption, CCI, hypertension, diabetes, HDL, TC, calcium, and platelet count. Adjustment was established for those covariates that were not utilized for stratification. The studies showed consistent patterns in the results, with no detected interactions due to stratification (all p < 0.05, Table 4).

The link between SIRI β-CTX and P1NP was then evaluated using graphical techniques to determine if it was linear or nonlinear (Figure 2). The GAM estimation revealed that, after accounting for covariate variables, there were distinct nonlinear relationships between SIRI and BTMs in the OPF population in the study. These associations were modeled using segmented linear regression, with the identified breakpoints (K-values) being 1.41 and 1.63, respectively (Table 5). To the left of the thresholds, there was a stronger negative correlation between SIRI and β-CTX, as well as with P1NP.

In the threshold studies for SIRI and β-CTX, the effect size on the left side of the threshold was −0.13 (95% CI: −0.20 to −0.06, p = 0.002). The effect size on the right side of the threshold was −0.03 (95% CI: −0.04 to −0.02, p < 0.001). Regarding the SIRI and P1NP thresholds, the effect size on the left side of the threshold was −13.64 (95% CI: −20.17 to −7.11, p < 0.001). The effect size on the right side of the threshold was −2.35 (95% CI: −3.94 to −0.77, p = 0.003) (Figure 3).