The study population was derived from a prospective observational study PRECOMIN (NCT01400295) database between January 2010 and December 2013. The PRECOMIN study aimed at identifying the optimal contrast volume to prevent contrast-induced nephropathy among 3237 consecutive patients undergoing PCI/CAG, [6]. Patients who had previous PCI or previous MI, CABG, acute MI, or emergent PCI and those who lack total cholesterol (CHO) or high-density lipoprotein cholesterol (HDL-C) data were excluded (Additional file 1: Figure S1).

A total of 1262 patients without known CAD undergoing elective CAG were included in the analysis. The Institutional Ethics Research Committee approved the study, and all patients provided written informed consent.

CAG or PCI was performed according to the interventional cardiologist’s preference, which is guided by institutional policy and practice. Baseline data, angiographic characteristics, and medication data were prospectively defined and have been reported in a previous study [6]. During CAG, the highest percent stenosis value within each major coronary artery or their branches was recorded. High-sensitivity C reactive protein was tested with a Beckman Coulter Immage immunobiochemistry system (USA) using nephelometry (unit: mg/L). Left ventricular ejection fraction was calculated by using the biplane modified Simpson’s rule by Two-Dimensional Echocardiography.

The primary endpoint of our study was OCAD, which was defined as (≥50% stenosis by diameter in at least one major coronary vessel based on CAG) [2]. Anemia was defined according to the World Health Organization criteria, i.e., baseline hematocrit value < 39% for men and < 36% for women [7]. Hypertension was definite present if the participant was under treatment with antihypertensive medication or systolic≥140 mmHg or diastolic ≥90 mmHg [3].

Continuous variables were compared with the t-test, and categorical variables were compared with the chi-square test or Fisher exact test, as appropriate. A logistic regression model was developed to predict OCAD in the PRECOMIN substudy. Significant predictors from the univariate analysis and non-significant variables with potential clinical relevance, including traditional Framingham risk factors, were evaluated as candidate factors (age, sex, smoking status, diabetes, CHO, high-density lipoprotein cholesterol [HDL-C], hypertension, baseline systolic blood pressure, and diastolic blood pressure, high-sensitivity C reactive protein [hs-CRP],left ventricular ejection fraction [LVEF], anemia, weight, serum creatinine, serum albumin, uric acid,HbA1c, Lp(a), blood urea nitrogen,) to determine their association with OCAD in a multivariable model [3]. Collinearity and interaction between variables were also evaluated. Backward elimination approach was employed to create a reduced model by successively removing non-significant covariates until all the remaining predictors (age, sex, CHO and HDL-C, hypertension, smoke, anemia, hs-CRP and LVEF) are statistically significant (P < 0.1). Then, we manually investigated the contribution of the remaining predictors to find out the final predictors including age, sex, CHO and HDL-C, hypertension, anemia, hs-CRP, LVEF. We used regression coefficients from the model to generate point scores for predicting the probability of OCAD [8, 9]. The final prediction model was assessed using the area under the receiver operating characteristic (ROC) curve and concordance c-statistic for discriminative ability, and the Hosmer–Lemeshow goodness-of-fit statistic for calibration using fifths of the fitted risk values [10]. Moreover, the final model was tested by bootstrapping method (1000 times) to evaluate the stability of the c-statistics. We assumed that missing data occurred randomly, depending on the clinical variables and the CAG results. We performed multiple imputations using Markov chain Monte Carlo (MCMC) and fully conditional specification (FCS) [11‐13]. Comparisons of baseline characteristics and OCAD incidence between patients with and those without missing values were performed [14, 15]. A P value < 0.05 was considered statistically significant in all tests. All analyses were performed using SAS version 9.3 (SAS Institute, Cary, NC).

The final modified Framingham prediction model consisted of the following: anemia (odds ratio [OR], 1.556; P = 0.0053), hs-CRP (OR, 1.029; P = 0.0006), LVEF (OR, 0.979; P = 0.075), and five Framingham factors (age, sex, CHO and HDL-C, hypertension), and our model equation was “F(y) = − 0.0468 + 0.0204(age) + 1.0961(gender) + 0.5444(hypertension) + 0.0055(CHO)-0.0257(HDL-C)-0.022(LVEF) + 0.5677(anemia) + 0.0254(hs-CRP)”(Table 2).

In the entire cohort, the independent OCAD predictors were anemia, hs-CRP, and LVEF, while the Framingham risk factors were age, sex, CHO and HDL-C, and hypertension. Model fitting performed on the validation cohort showed that the MFS model performed better than the traditional Framingham model (Table 3).

Additionally, individual scores were subsequently calculated for patients in the validation cohort, and the results were expressed as a function of CAD presence. Consequently, a bimodal score distribution was found (Fig. 1), with higher OCAD prevalence in patients with higher scores and lower OCAD prevalence in those with lower scores. Moreover, a bimodal distribution of OCAD score was noted in the validation set (n = 683), with preponderance of patients with significant CAD with higher scores (positive: subjects with at least 1 coronary stenosis ≥50%; negative: subjects without coronary stenosis ≥50%).

Bootstrap method (1000 times) revealed that the model demonstrated a good discriminative power (c-statistic, 0.729 ± 0.0225; 95% CI, 0.69–0.77).

In addition, the MFS provided adequate goodness of fit (P = 0.43). For the operating characteristics of the OCAD algorithm across various scores, the MFS model had a higher area under the ROC curve than the Framingham score (c-statistic, 0.703 vs. 0.521; P < 0.001); similarly, the modified Framingham risk factors model had a higher area under the ROC curve than the Framingham risk factors model (c-statistic, 0.719 vs. 0.693; P = 0.059) (Table 3; Fig. 2).

Moreover, the score was divided into four categories according to predicted risk (low risk score, ≤17; moderate risk score, 18–26; high risk score, 27–41; and very high risk score, ≥42), which allowed identifying patients with high risk for OCAD (risk score ≥ 27) with ≥70% predictive value in 68.8% of subjects (range, 37.2–87.3% for a low [≤17] and very high [≥41] risk score) (Fig. 3). The predicted risk of CIN in the validation set is presented in parallel to the observed OCAD prevalence in each risk group (Fig. 4).

Most of the baseline characteristics were similar between patients with missing data (n = 579) and those with complete data (n = 683). The missing data in the final model included gender, hypertension, smoking, CHO and HDL-C, and LVEF. Patients with missing data were younger and had lower hs-CRP level, systolic BP, and rate of anemia than patients with complete data. No significant difference in OCAD incidence (73.40 vs. 76.13%; P = 0.2648) was noted (Additional file 2: Table S1).

We performed imputations of clinical variables and CAG results for 100 times using MCMC and FCS. Multivariate logistic regression and ROC curve were analyzed for the final modified Framingham model using complete and imputation data, and we found similar results, including ORs for predictor models and c-statistic by ROC analysis (0.719, 0.712, 0.711) (Additional file 3: Table S2 and Additional file 4: Table S3).

Our study has several limitations. First, our study adds significant information to the current literature on pretest probability of OCAD for stable patients without known CAD; however, this is a single-center prospective observational study with a limited sample size. Second, angina types (e.g., classification of chest pain symptoms: typical, atypical, or non-specific) were not considered; thus, the accuracy of the OCAD risk model may have been affected. Thirdly, some bias in patient selection especially in CAG possibly existed; cardiologists tended to recruit patients with more baseline risk factors but with a stable condition for elective CAG. Thus, our findings may not be applicable to patients with low risk for OCAD or with emergent conditions. Fourthly, our study only focused on the anatomical result of angiography without kind of plaque evaluated with imaging (OCTs or IVUS), such as culprit plaque rupture (CPR) and thin-cap fibro-atheroma (TCFA), which could trigger acute coronary syndrome (ACS). Lastly, the high loss of follow-up rate possibly affected the quality of long-term prognosis and the predictive value of the modified Framingham score.