Prediction model for high glycated hemoglobin concentration among ethnic Chinese in Taiwan

This cross-sectional study involved 25,452 adult subjects who participated in the health checkup program at the Health Management Center of one tertiary hospital, from January 2003 to December 2006. The sampling strategy for the study population, including inclusion and exclusion criteria, is shown in Additional file 1, Figure S1. After excluding subjects with a history of diabetes with medication, cardiovascular disease, cancer, missing or duplicated data, and age less than 30 years, a total of 17,773 participants were recruited into the study. The study protocol has been described previously [20, 21]. Briefly, details of socio-economic status, along with medical and medication histories were collected by questionnaires, and standardized clinical measure procedures were undertaken. The protocol was approved by the hospital's Institutional Research Board. Standardized physical examination procedures, such as anthropometric measures and blood pressure, were also performed [22, 23]. Blood pressure was measured in a resting position by trained medical assistants, while body mass index (BMI) was calculated as weight (in kilograms)/square of height (in meters), and waist circumference was measured midline between the low costal margin and superior posterior iliac crest.

The procedures for blood sampling and analytic methods have been described in previous studies [22, 24]. Briefly, blood samples were collected from each participant after fasting for at least 12 hours. Serum total cholesterol levels were measured using the CHOD-PAP method (Boehringer Mannheim, Germany). HDL cholesterol was measured following precipitation of apolipoprotein B-containing lipoproteins with phosphotungstic acid and magnesium ions (Boehringer Mannheim, Germany). Triglyceride concentrations were measured by the GPO-DAOS method (Wako Co., Japan). The aforementioned lipids were measured using a Hitachi 7450 automated analyzer (Hitachi, Japan). LDL-C concentrations were calculated using the Friedewald formula. CRP was measured by automated nephelometric immunoassay using a Beckman Array instrument (Beckman Array 360 system, Canada). All of the measurements were carried out in a single hospital with a coefficient of variation of 5%. HbA1c levels were measured by automatic high-performance liquid chromatography using a Bio-Rad HbA1c kit (Bio-Rad Diagnostic Group, Hercules, CA, USA) in the central laboratory of the hospital. Standardization using mass spectroscopy and capillary electrophoresis was used, and prepared mixtures of purified HbA1c and HbA0 were used as calibrators [25]. With regards to the cutoff level of HbA1c, abnormally high HbA1c levels were defined as 6.7% according to the sensitivity and specificity of diabetes diagnosis and diabetic retinopathy in one cross-sectional study [26]. In addition, a study by the UK Prospective Diabetes Study Group demonstrated that over 10 years, the mean HbA1c level in their intensive treatment group was 7.0% [1]. Moreover, an HbA1 level of 7.3% or greater is considered the cutoff value for screening diabetes in Pima Indians [27]. Therefore, we set the threshold for abnormally high HbA1c at 7%.

The basic demographic, anthropometric measurements, lifestyle factors, and biochemical measures were described according to a high HbA1c concentration, defined as HbA1c ≥ 7%. The constructed model for HbA1c ≥ 6.5% was similar so that we reported the findings about HbA1c ≥ 7%. Missing waist circumference data in the first year (2003) were imputed with the mean values of waist circumference due to the specific HbA1c status to improve the power of the prediction model. The study population was divided randomly into two parts, with 80% as the derivation data and 20% as the validation data.

Multivariate logistic models were used to predict the risk of a high HbA1c level in the derivation data. First, the Cambridge model [28], including variables of age, BMI, anti-hypertensive medication, family history, and smoking status was used to construct the model [6, 19]. Second, an additional anthropometric measurement (waist circumference) and systolic blood pressure were incorporated into the model. History of hypertension medication was excluded due to non-significance in the model. This second prediction model was called the clinical model. Third, important biochemical indicators, including C-reactive protein (CRP), HDL cholesterol, and triglyceride concentrations were added into the model to construct the full biochemical model [29]. Fasting glucose was not included in the model to prevent over-correction by glucose concentration.

Based on results of the multivariate logistic models from the derivation data, two strategies for constructing the prediction model were applied. First, the coefficients for the prediction model from the derivation data were used directly, which is a common strategy in the literature [18, 30‐32]. By directly calculating the coefficients and individual variables, the individual risk was derived in the validation data. We provided the nomogram using Harrell's method [33]. Second, a point-based chart was constructed from the derivation data according to the strategy suggested by Sullivan and colleagues [34]. This strategy was as follows: continuous variables were organized into meaningful categories and the reference values for each variable were determined. We assigned a 5-year increase in age as the referent risk, and points associated with each of the categories of the risk factors were calculated by comparing with the referent risk. Therefore, an individual's risk was constructed from the validation data by the following formula: Risk = 1/[1 + exp(-βX)] where βX is the sum of the reference risk and the product of the 5-year risk constant and the individual points [34].

Performance of the proposed coefficient-based and point-based prediction models were compared with the Cambridge model [6, 19, 28]. The area under the receiver operating characteristic curve (AUC) was used to compare the discriminatory capability among the models. A receiver operating characteristic curve is a graph of sensitivity versus 1-specificity (or false-positive rate) for various cut-off definitions of a positive diagnostic test result [35]. Statistical differences in the AUCs were compared using the method of DeLong et al [36].

Furthermore, the goodness-of-fit for all models was assessed based on the Hosmer-Lemeshow test [37]. The global summary statistics included the Brier score [38], twice the forecast-outcome-covariance (a measure of how accurately the forecast corresponds to the outcome, similar to R² in linear regression) [39], and discrimination (c statistic), which is the same as the AUC [40].

The simple points model was compared with other models using net reclassification improvement (NRI) and integrated discrimination improvement (IDI) statistics [41]. NRI was based on the reclassification tables and was calculated from a sum of differences between the "upward" movement in categories for event subjects and the "downward" movement of non-event subjects [41]. The NRI was presented according to the presumed risk categories of high HbA1c according to quartiles (0.6%, 1.2%, and 2.6%). The IDI was viewed as the difference between improvement in average sensitivity and any potential increase in average "one minus specificity". The statistic was a difference in Yates discrimination slopes between the new and old models [38, 42].

All of the statistical tests were two-sided with a type I error of 0.05, and P values < 0.05 were considered statistically significant. Analyses were performed with SAS version 9.1 (SAS Institute, Cary, NC), Stata version 9.1 (Stata Corporation, College Station, Texas) and R http://​www.​R-project.​org.

Among the study participants, 323 cases (1.8%) had an HbA1c level ≥ 7%. Table 1 shows the basic demographic, clinical, lifestyle, socio-economic status and biochemical measures of the study participants. Participants with higher HbA1c levels were likely to be older, male, have a higher body mass index (BMI), waist circumference, blood pressure, cholesterol, triglycerides, CRP, and white blood cell count, and lower HDL cholesterol level. In addition, participants with higher HbA1c values were likely to take anti-hypertensive medication, have a higher rate of a positive family history of diabetes and current smoking status. The distribution of socio-economic information, such as martial status and job, was similar between participants with and without abnormal HbA1c levels. The distributions of most continuous and categorical variables were consistent in each gender, and there was no differential effect.

The results of the multivariate logistic regression models are listed in Table 2. Hypertension medication was not statistically significant and was excluded in further analyses. Waist circumference and BMI were both associated with abnormal HbA1c levels in the clinical model. Age, family history of diabetes, waist circumference, systolic blood pressure, and biochemical measures, including CRP and triglycerides, were significantly associated with higher HbA1c levels. HDL cholesterol was borderline inversely associated with higher HbA1c.

Regression coefficient-based and point-based prediction models based on the clinical and biochemical models were developed. A nomogram based on the clinical and biochemical models was constructed (Figure 1). Table 3 shows the point-based clinical model to estimate high HbA1c risk using the points system, derived from the coefficients of the clinical model: age (8 points), sex (1 point), family history (3 points), BMI (2 points), waist circumference (4 points), and systolic blood pressure (3 points). This approach allowed for the manual estimation of the risk of developing a higher HbA1c level for each individual (Table 3). The waist circumference-related point-based biochemical model, additionally including HDL cholesterol (3 points) and triglycerides (2 points), is shown in Additional file 1, Table S1. A cutoff point of 7 had a sensitivity of 0.76 to 0.96 and a specificity of 0.39 to 0.63 for both clinical and biochemical prediction models.

The performance of the prediction models, including the Cambridge (Additional file 1, Table S2), coefficient-based and point-based clinical, and biochemical models were compared using different measures (Table 4). The clinical models had a fair discrimination ability with an AUC of 0.712 (95% confidence interval [CI] 0.664-0.760), and 0.723 (95% CI, 0.677-0.769) in the coefficient-based and point-based models, respectively. Adding biochemical measures improved the prediction (AUC of 0.773 [95% CI, 0.726-0.821] and 0.770 [95% CI, 0.723-0.817] for the coefficient-based and point-based models, respectively). Moreover, in the biochemical models, the AUCs were the highest and the Brier scores were the lowest, and they were likely to have a smaller Hosmer-Lemeshow chi-square and high P values, indicating a good calibration ability for a high HbA1c level. Figure 2 shows the AUCs of the various prediction models in the validation data. The Hosmer-Lemeshow chi-square values indicated a goodness-of-fit for these prediction models.

The performance ability between the various prediction models was tested using NRI and IDI statistics (Table 5). The clinical coefficient-based model was compatible with the Cambridge model (Set 1), and the biochemical models outperformed the Cambridge models due to a significant increase in IDI and NRI values (Set 2). The biochemical coefficient-based model had a better performance than the clinical coefficient-based clinical model by NRI value (Set 3). In addition, the clinical point-based model and clinical coefficient-based model had similar performance measures (Set 4). Finally, the biochemical coefficient-based model outperformed the biochemical point-based model (Set 5), and the clinical and biochemical point-based models had a similar performance (Set 6). The sensitivity, specificity and cutoff values for the clinical and biochemical models were listed in Additional file 1, Table S3. Our findings support that the clinical and biochemical point-based models were excellent models for identifying individuals with a high HbA1c value.