both deteriorated insulin sensitivity ( si ) and impaired insulin secretion are recognized as 2 of the foremost forms of pathophysiology for type 2 diabetes ( t2 dm ) [ 1 , 2 ] . in the natural course of developing diabetes , the plasma glucose does not rise until the decompensation of the -cell function to insulin resistance ( ir ) occurs . moreover , the impaired -cell function is a more critical factor than decreased si to determine the development of t2 dm , especially in asian people [ 3 , 4 ] . two phases of insulin secretion are widely known : the first - phase insulin secretion ( fpis ) and the second - phase insulin secretion ( spis ) . the fpis is normally secreted by the -cells within 10  min after being exposed to an acute rise in plasma glucose levels to reduce their emission , whereas the spis is the newly secreted insulin from -cells after the fpis . a better fpis results in longer maintenance of normal glucose homeostasis before the occurrence of diabetes . the fpis is a sensitive indicator for the deterioration of insulin sensitivity [ 6 , 7 ] because it decreases rapidly even in prediabetes stage ( predm ) . numerous studies have documented the link between metabolic syndrome ( mets ) , the clustering of hyperglycemia , hypertension , obesity , and dyslipidemia , and an elevated risk of developing cardiovascular disease and diabetes [ 9 , 10 ] . components such as the body mass index ( bmi ) , triglyceride ( tg ) , high - density lipoprotein cholesterol ( hdl - c ) , and fasting plasma glucose ( fpg ) levels were all shown to be related to insulin secretion [ 11 , 16 ] . although , as mentioned , the fpis is important , no readily available accurate method exists for measuring the first isec . in this study , we built an equation to estimate the fpis by using routine clinical variables and mets components . either they were self - referred or health professionals had referred them for diabetes screening . they had no history of diabetes and , therefore , they took no diabetes medications at the time of the study . they were defined as having a normal glucose tolerance ( ngt ) , predm , and t2 dm according to the criteria published by the american diabetes association in 2012 . otherwise , none of the participants had a remarkable medical or surgical history . in total , 51 participants had ngt , 40 had predm , and 95 had t2 dm . before participating in the study , they were instructed by physicians and dietitians not to receive any medication known to affect glucose or lipid metabolism and to remain on a stable diet for at least 1  wk before the study . on the day of the first study , an entire routine workout was completed by participants to exclude those with significant cardiovascular , endocrine , renal , hepatic , and respiratory disorders . the study protocol had been approved by the hospital 's institutional review board and ethics committee ; all participants provided written informed consent prior to participating . to validate our equation , 75% of the participants this equation was subsequently used to calculate the fpis among the remaining 25% , who constituted the external validation group . frequently sampled intravenous glucose tolerance test ( fsigt ) : all tests were performed at the clinical research center . on the day of the study visit , after a 12  h overnight fast , one catheter was placed on both arms of each participant . a bolus of 10% glucose water ( 0.3  g / kg ) was given . another bolus of regular human insulin ( novo nordisk pharmaceutical , princeton ) 0.05 units / kg was injected 20  min after the glucose load . blood samples for plasma glucose and insulin levels were collected at 0  min , 2  min , 4  min , 8  min , 19  min , 22  min , 30  min , 40  min , 50  min , 70  min , 100  min , and 180  min . the data were inputted into a bergman minimal model , and then the si , glucose effectiveness ( ge ) , and acute insulin response after the glucose load ( airg ) were obtained . the airg was considered the fpis , and the product of the si and the calculations of homa - ir and homa- ( homeostasis model assessment of insulin resistance and the -cell function ) were performed according to matthew 's equation . plasma was separated within 1  h of blood withdrawal and stored at 30c until the analysis . plasma glucose was measured using a glucose analyzer by employing an oxidase method ( ysi model 203 , scientific division , yellow spring instrument company , inc . , yellow spring , oh , usa ) . plasma insulin was assayed using a commercial solid phase radioimmunoassay technique ( coat - a - count insulin kit , diagnostic products corporation , los angeles , ca , usa ) with intra- and interassay coefficients of variance of 3.3% and 2.5% , respectively . serum tg was measured using the fuji dri - chem 3000 analyzer ( fuji photo film corporation , minato - ku , tokyo , japan ) by employing the dry multilayer analytical slide method . the serum hdl - c concentration was determined using the enzymatic cholesterol assay method after dextran sulfate precipitation . the data were tested for normal distribution by using the kolmogorov - smirnov test and for the homogeneity of variances by using the levene test . continuous variables were expressed as mean  standard deviation . among the data , fpis , fpi , si , and di were not normally distributed and were logarithmically transformed . an independent t - test was used to evaluate the demographic data , the clinical characteristics , and the parameters derived from the fsigt between the 2 groups ( a study and external validation group ) . to build the equation to estimate the fpis , we used the stepwise method in multiple regression analysis . we adopted sex , age , and the mets components as independent variables and the fpis as the dependent variable . although fpi is not a component of mets , it was found to be strongly related to fpis ; another equation with the fpi as the independent variable was also built . these equations were subsequently used to calculate the fpis among the remaining 25% of participants . the correlation between the calculated fpis and measured fpis was measured using pearson 's r correlation coefficient . all statistical analyses were performed using the spss software system , version 13.0 ( spss inc . , in the study , 140 and 46 participants were classified into the study group and the external validation group , respectively . table 1 shows the demographic data , fpg and fpi , plasma lipids , and variables derived from the fsigt of these two groups . there was no significant difference in these measurements between the two groups . the demographic data of ngt , predm , and t2 dm are shown in table 2 . the participants in the t2 dm group were older and had a higher fpg compared to the ngt group . log  ( fpis ) , log  ( di ) , and log  ( ge ) were significantly lower in the dm group . to identify the parameters that contribute most to the fpis , the correlations between the fpis and different parameters were evaluated ; the results are shown in table 3 . the fpis was significantly correlated to age ( r = 0.398 , p = 0.000 ) , bmi ( r = 0.264 , p = 0.002 ) , fpg ( r = 0.475 , p = 0.000 ) , hdl - c ( r = 0.190 , p = 0.034 ) , and log  ( fpi ) ( r = 0.382 , p = 0.000 ) . three of them were selected from regression analysis , and the equation was built and is shown as log  ( fpis ) = 1.477  0.119  fpg + 0.079  bmi  0.523  hdl - c ( standard coefficients are shown in table 4 ) . subsequently , as mentioned , this equation was used to calculate the fpis of the external validation group . the correlation between calculated log  ( fpis ) and the measured log  ( fpis ) was assessed , and the results are shown in figure 1 . the r value was 0.671 , and p was 0.000 . because the fpi is also considered a surrogate for the fpis , it was also added to multiple linear regression analysis to build a second equation and , unlike the first , 4 factors were selected , and the following equation was formulated : log  ( fpis ) = 1.532  0.127  fpg + 0.059  bmi  0.511  hdl - c + 0.375  log  ( fpi ) . the difference of predicting power of fpis between the first and the second equation was determined using hierarchical multiple regression method . the r increased significantly in both of the study ( p = 0.000 ) and external validation groups ( p = 0.049 ) after adding log  ( fpi ) into fpg , bmi , and hdl - c . the correlation between the calculated fpis and the measured fpis in the external group was also evaluated , and the results are shown in figure 2 . the calculated log  ( fpis ) determined the measured log  ( fpis ) with good accuracy in the external validation group ( r = 0.722 , p = 0.000 ) . compared to homa- , both equations showed a better predictive accuracy for the fpis ( r = 0.551 , p = 0.000 ) . the standardized coefficient between the associated factors and the fpis is shown in table 4 . in this study , we built an equation by using routine clinical measurements and mets components to predict the fpis in participants with different levels of glucose tolerance . because of the tight correlation between fpi and fpis , fpi was also added into analysis to build a second equation to improve predictive accuracy . to verify our results , external validation was also performed . although previous studies have been done to predict the fpis , most of them enrolled only nondiabetic participants [ 3 , 11 , 1921 ] . because we believe that our study results are informative and reliable , they could be applied widely to the public health domain and in clinical settings . the most widely used standardized methods for measuring the fpis are the hyperglycemic clamp and the fsigt . by using the hyperglycemic clamp , chiu et al . reported that the combination of ethnicity and bmi could be used to predict 16.6% of the variance of the fpis in ngt participants . similarly to this study , van haeften et al . found that a combination of sex , bmi , and the family history of t2 dm ( fh ) could predict the fpis in the ngt and predm participants with similar accuracy ( r = 0.152 , p < 0.0001 and 0.250 , p < by using the fsigt , alford et al . showed the best prediction accuracy among these 3 studies ( r = 0.27 ) . in our study , by using only the mets component , r was as elevated as 0.45 , which is a substantially superior result compared to those of the mentioned studies . after adding the fpi into the model , r could have been improved to 0.521 in the external validation group . in our study , the fpg , bmi , hdl - c , and fpi were selected among all other factors and inputted into multiple linear regression analysis . because the predominant function of -cells is to maintain glucose in homeostasis , the fpg provides the most substantial contribution in the regression model . our results are in line with earlier studies which showed that the fpis deteriorated as the fpg levels increased from ngt to diabetic range , which suggested that the fpg level is the most critical determinant for assessing the deterioration of -cell function . following the fpg , the bmi was the second most critical factor inputted in the model . the results were not surprising because the evidence has shown that people with a higher bmi would have a better -cell function because of the larger amount of -cell mass [ 11 , 19 , 21 , 23 ] . van haeften et al . reported that the bmi is a critical contributor to the fpis in the ngt and the predm participants ( r = 0.096 and 0.090 , resp . ) . in agreement with their findings , our study also demonstrated that the bmi explained a similar level of variance for the fpis in participants across the spectrum of glucose tolerance ( r = 0.107 , data not shown ) . it could be questioned that waist circumference was not added into analysis in the study as it is the key component of mets . however , waist circumference was not measured in the study , so we could not estimate fpis using waist circumference . evidence showed that bmi was highly correlated with waist circumference ( r = 0.900 in men and r = 0.889 in women ) in chinese . moreover , chiu et al . demonstrated that bmi is better marker than waist - hip ratio to predict first insulin secretion . because the lower hdl - c is associated with ir [ 11 , 16 ] , we postulate that a negative correlation between hdl - c and the fpis should exist . both hanley et al . and gower et al . have supported this hypothesis [ 11 , 16 ] . this study also produced similar findings ( r = 0.190 , p = 0.034 ) . however , the bardini study results demonstrated that there was no significant correlation between hdl - c and early - phase insulin secretion in ngt subjects but there was positive correlation between hdl - c and early - phase insulin secretion in impaired glucose tolerance subjects , which do not match ours . first , ethnic differences might be the reason for the discrepancies between studies [ 16 , 21 ] . second , the fpis was measured in the current study by using the fsigt , which was identical with the hanley and gower studies . in addition , early - phase insulin secretion in the bardini study was assessed using only a surrogate marker derived from the oral glucose tolerance test ( ogtt ) , which is a less accurate method compared to the fsigt . third , in the bardini study , the participants with t2 dm were not enrolled . these differences could have a profound effect on the relationship between the fpis and the hdl - c . the fpi , which is not a routinely used measurement , is associated with -cell function [ 7 , 11 , 18 , 26 ] . , showed a significant association between the fpi level and the first isec ( r = 0.361 , p = 0.000 ) . after combining the fpi and the mets components into the equation , the predictive accuracy improved further ( r increase from 0.450 to 0.521 in the external validation group ) . this finding might also imply that the fpi and mets could have affected the fpis via different pathways because the improvement of r is substantial . the -cell function declines as age increases , even in participants with ngt [ 21 , 27 ] . earlier study has shown that this negative influence of aging on the -cell function might be attributed to the gradual loss of the abilities of both proinsulin converted to insulin and the decreased baseline proliferative activity of -cell compared with younger adults [ 28 , 29 ] . moreover , evidence also showed that aging positively correlated with enhanced glucose - induced -cell apoptosis in vitro . in our study , we demonstrated that age was negatively correlated with the fpis ( r = 0.398 , p = 0.000 ) . the finding might be attributed to the strong correlation between age and either fpg , bmi , or fpi which could reduce the impact of age on fpis . in other words , the effect of age was masked by other stronger relationships between the fpis and the mets components . to the best of our knowledge , the current study is the first to formulate an equation for estimating the fpis by using the mets components and the fpi level . first , the body fat content and its distribution , which were known to be associated with ir and the -cell function , were not measured in the study . measuring these factors in the study might help further improve predictive power of the equation . second , fh was not assessed in the study . it has been established that participants with an fh of t2 dm have a reduced -cell function and a decreased -cell response to ir compared to those without . thus , the application of our results to other ethnic groups should be exercised with caution . finally , this study is only a cross - sectional study . in future studies , using a baseline that incorporates mets components to estimate the fpis would be more valuable . however , even with these limitations , we still believe that our finding could be easily and widely used in clinical settings . in conclusion , by using the mets components , the fpis could be predicted with reliable accuracy ( r = 0.671 ) . after adding the fpi to the equation , the predictive power increases further ( r = 0.722 ) . these equations could be widely used in daily practice .
aims . there are two phases of insulin secretion , the first ( fpis ) and second phase ( spis ) . in this study , we built equations to predict fpis with metabolic syndrome ( mets ) components and fasting plasma insulin ( fpi ) . methods . totally , 186 participants were enrolled . 
 75% of participants were randomly selected as the study group to build equations . 
 the remaining 25% of participants were selected as the external validation group . 
 all participants received a frequently sampled intravenous glucose tolerance test , and acute insulin response after the glucose load ( airg ) was obtained . 
 the airg was considered as fpis 
 . results . 
 when mets components were only used , the following equation was built : log ( fpis ) = 1.477  0.119  fasting plasma glucose ( fpg ) + 0.079  body mass index ( bmi )  0.523  high - density lipoprotein cholesterol ( hdl - c ) . 
 after fpi was added , the second equation was formulated : log ( fpis ) = 1.532  0.127  fpg + 0.059  bmi - 0.511  hdl - c + 0.375  log ( fpi ) , which provided a better accuracy than the first one 
 . conclusions . using mets components , the fpis could be estimated accurately . after adding fpi into the equation , 
 the predictive power increased further . 
 we hope that these equations could be widely used in daily practice .