GFR计算公式

Modified Glomerular Filtration Rate Estimating Equation for Chinese Patients with Chronic Kidney Disease

Ying-Chun Ma,*Li Zuo,*Jiang-Hua Chen,?Qiong Luo,?Xue-Qing Yu,§Ying Li,?

Jin-Sheng Xu,?Song-Min Huang,**Li-Ning Wang,??Wen Huang,??Mei Wang,*

Guo-Bin Xu,§§and Hai-Yan Wang;*

on behalf of the Chinese eGFR Investigation Collaboration

*Division of Nephrology and Institute of Nephrology,and§§Department of Clinical Laboratory,The First Hospital, Peking University,Beijing,?Department of Nephrology,The First Hospital,ZheJang Medical College,ZheJiang,

?Department of Nephrology,ShenZhen Hospital,Peking University,ShenZhen,§Department of Nephrology,The First Hospital,Sun Yat-sen University,GuangZhou,?Department of Nephrology,The Third Hospital,and?Department of Nephrology,The Fourth Hospital,HeBei Medical University,ShiJia Zhuang,**Department of Nephrology,HuaXi Hospital,SiChuan University,ChengDu,??Department of Nephrology,The First Hospital,China Medical University, ShenYang,and??Department of Nephrology,TongRen Hospital,Capital Medical University,Beijing,China

The Modification of Diet in Renal Disease(MDRD)equations provide a rapid method of assessing GFR in patients with chronic kidney disease(CKD).However,previous research indicated that modification of these equations is necessary for application in Chinese patients with CKD.The objective of this study was to modify MDRD equations on the basis of the data from the Chinese CKD population and compare the diagnostic performance of the modified MDRD equations with that of the original MDRD equations across CKD stages in a multicenter,cross-sectional study of GFR estimation from plasma creatinine, demographic data,and clinical characteristics.A total of684adult patients with CKD,from nine geographic regions of China were selected.A random sample of454of these patients were included in the training sample set,and the remaining230 patients were included in the testing sample set.With the use of the dual plasma sampling99m Tc-DTPA plasma clearance method as a reference for GFR measurement,the original MDRD equations were modified by two methods:First,by adding a racial factor for Chinese in the original MDRD equations,and,second,by applying multiple linear regression to the training sample and modifying the coefficient that is associated with each variable in the original MDRD equations and then validating in the testing sample and comparing it with the original MDRD equations.All modified MDRD equations showed significant performance improvement in bias,precision,and accuracy compared with the original MDRD equations,and the percentage of estimated GFR that did not deviate>30%from the reference GFR was>75%.The modified MDRD equations that were based on the Chinese patients with CKD offered significant advantages in different CKD stages and could be applied in clinical practice,at least in Chinese patients with CKD.

J Am Soc Nephrol17:2937–2944,2006.doi:10.1681/ASN.2006040368

G FR is one of the commonly used indexes for early

detection of chronic kidney disease(CKD).An accu-

rate,convenient,and reproductive GFR estimating method is important for clinical practice.Earlier studies fo-cused on plasma creatinine(Pcr)and creatinine clearance as markers of GFR,but Pcr usually does not increase until GFR has decreased by50%or more,and many patients with normal Pcr levels frequently have lower GFR(1).Also,creatinine clear-ance usually overestimates true GFR(2).

Creatinine-based estimating equations overcame some of these limitations and offered a rapid method for GFR estima-tion.In the Modification of Diet in Renal Disease(MDRD) Study,using renal clearance of125I-iothalamate as a reference GFR(rGFR),Levey et al.(3)published a series of creatinine-based GFR estimating equations(MDRD equations).The ab-breviated MDRD equation,which includes only four vari-ables—Pcr,gender,age,and ethnicity(4)—has been the most widely used in clinical practice,becoming a powerful screening tool for early detection of CKD.It provided an acceptable level of accuracy(at least70%of estimated GFR[eGFR]within a30% deviation from the rGFR)in advanced stages of CKD(5)and was recommended by Kidney Disease Outcome Quality Initia-tive(K/DOQI)clinical practice guidelines(5).

Race is an important determinant of GFR estimation.For example,when the MDRD equations are applied to black indi-viduals,a coefficient should be used(3).In our previous study (6),the performance of MDRD equation7and the abbreviated MDRD equation was tested in a group of Chinese patients with

Received April19,2006.Accepted August2,2006.

Published online ahead of print.Publication date available at https://www.wendangku.net/doc/0118360793.html,.

Address correspondence to:Dr.Li Zuo,Division of Nephrology and Institute of

Nephrology,The First Hospital,Peking University,No.8Xishiku Street,Xicheng

District,Beijing,100034,PR China.Phone:?86-10-66551122ext.2388,?86-10-

66551072;Fax:?86-10-66551055,?86-10-66551072;E-mail:zuoli@https://www.wendangku.net/doc/0118360793.html,

Copyright?2006by the American Society of Nephrology ISSN:1046-6673/1710-2937

CKD.The results showed that both equations underestimated rGFR in near-normal renal function and overestimated rGFR in advanced renal failure.We concluded that careful modification of these equations was necessary to improve their performance when used to identify Chinese patients with CKD.

In our study,an attempt was made to improve the perfor-mance of the original MDRD equations by modifying the orig-inal MDRD equation7and abbreviated MDRD equation.The diagnostic performance of the modified equations was com-pared with the original ones in various stages of CKD. Materials and Methods

Patients and Design

Nine renal institutes of university hospitals located in nine geo-graphic regions of China participated in this study from June2004to September2005.The same inclusion and exclusion criteria were used in all participating renal institutes:Patients who were older than18yr and had CKD were eligible for inclusion.CKD was diagnosed and classified according to K/DOQI clinical practice guideline(5).Patients with acute kidney function deterioration,edema,skeletal muscle atrophy,pleural effusion or ascites,malnutrition,amputation,heart failure,or ketoaci-dosis were excluded.Patients who were taking cimetidine or tri-methoprim or who were on any kind of renal replacement therapy also were excluded.

The nine participating renal institutes used the same data collecting methods and the same data collecting forms.The collected data in-cluded gender,age,body height,body weight,BP,and rGFR.Fasting plasma was taken from selected patients for analysis of creatinine,urea nitrogen,and albumin in a single laboratory at the First Hospital, Peking University.

GFR Measurement

Unlike Pcr,99m Tc-DTPA plasma clearance was measured in the nine participating renal institutes.Efforts had been made to make the inter-institute variance as small as possible,including staff training,99m Tc-DTPA drug selection(radiochemical purity?95%and percentage of 99m Tc-DTPA bound to plasma protein?5%).The identical operational procedures were followed by all nine participating centers,including patients’preparation,intravenous injection,plasma sampling time points and procedure,and radioactivity measurement(6).

rGFR was measured by the dual plasma sampling method(7,8), standardized by body surface area(BSA)(9),and resulted in the rGFR: rGFR(ml/min per1.73m2)?[Dln(P1/P2)/(T2-T1)]exp{[(T1lnP2)?(T2lnP1)]/(T2?T1)}?0.93?1.73/BSA,where D is dosage of drug injected,T1is time of first blood sampling(approximately2h),P1is plasma activity at T1,T2is time of second blood sampling(approxi-mately4h),and P2is plasma activity at T2.The units of measurement were counts per minute per milliliter for D,P1,and P2and minutes for T1and T2.

Pcr Assay and Calibration

Pcr levels were measured in a single laboratory on a Hitachi7600 analyzer using the Jaffe’s kinetic method,which was described else-where(6).To ensure that our Pcr values were calibrated equally to the MDRD study,we randomly selected57fresh-frozen plasma samples (range0.72to12.64mg/dl[64to1118?mol/L]of Jaffe’s kinetic method Pcr values measured in our laboratory)from our specimens and ana-lyzed them in both our laboratory and the Cleveland Clinic Laboratory. The Pcr value that was measured by our laboratory can be calibrated to the Pcr value that was measured by the Cleveland Clinic Laboratory, which used a CX3analyzer(Beckman Coulter Inc.,Fullerton,CA),using a linear regression equation:CX3Pcr(mg/dl)??15.91?1.32?Hitachi Pcr(mg/dl)(R2?0.999;P?0.001).

Other Analyses

Plasma urea was measured by the urease method.The normal ref-erence range was3.20to7.10mmol/L[8.96to19.88mg/dl]blood urea nitrogen(BUN).Plasma albumin was measured using the bromcresol green method.The normal reference range was3.5to5.5g/dl(35to55 g/L).

Estimation of GFR from Original MDRD Equations Calibrated CX3Pcr was put into the MDRD equation7and abbre-viated MDRD equation to estimate GFR(7GFR and aGFR,respec-tively):

7GFR(ml/min per1.73m2)?170?Pcr?0.999?age?0.176

?BUN?0.170?albumin0.318?0.762(if female)(1) aGFR(ml/min per1.73m2)?186?Pcr?1.154

?age?0.203?0.742(if female)(2) where Pcr is in mg/dl,BUN is in mg/dl,albumin is in g/dl,and age is in years.

Modification of Original MDRD Equations

A total of720participants were included,and36outliers were deleted.The remaining684patients were used for further analysis. From these patients,454were randomly selected and used for the training model,and the remaining230patients were used to test the performance of the modified equations.

We assumed that the performances of MDRD equations could be improved in Chinese patients with CKD by adding a racial factor,so 7GFR and aGFR were calculated on the basis of data from the454 training samples;using7GFR and aGFR as dependent variables,re-spectively,two linear regression models were established to predict rGFR from7GFR or aGFR.It was decided that if the intercepts of the two models were not significantly different from zero,then the models should be simplified by forcing the intercepts to be zero.

In the former two models,the Pcr value that was calibrated to the MDRD laboratory was used to estimate7GFR and aGFR,so when the two modified equations are used,Pcr value that is calibrated to the MDRD laboratory should be used.This was inconvenient in clinical practice in China.In the above concern,we reconstructed another two regression models,using an approach similar to that used in the development of the original MDRD equations.In these two models,log transformation was applied before the linear regres-sion,and linearity and equal variance test were satisfactory.In the concern that retransforming back to the usual scale might induce bias,the predicted eGFR was adjusted using the smearing method (10).The smearing coefficients for these two models were calculated to be1.05.

eGFR was compared with rGFR using Bland-Altman analysis of the validation set.The difference between eGFR and rGFR was defined as eGFR minus rGFR;the absolute difference between eGFR and rGFR was defined as the absolute value of difference.The regression of the difference between eGFR and rGFR against the average of the two methods was measured.The bias for eGFR was expressed as the area between the regression line and a common distance along the zero difference line.Ninety-five percent limits of agreement then were con-structed around this linear regression line.The precision was expressed as the width between the95%limits of agreement.Accuracy was measured as the percentage of eGFR that did not deviate?15,30,and 50%from the rGFR.

2938Journal of the American Society of Nephrology J Am Soc Nephrol17:2937–2944,2006

Statistical Analyses

Quantitative variables of patient’s age,height,weight,BSA,body mass index,Pcr,plasma urea,plasma albumin,and rGFR were de-scribed as mean?SD or as median(Table1).The accuracy of the equations was compared in certain stages of CKD with?2test.Because of skewed distribution,Spearman correlation and linear regression were used to describe the relationship between eGFR and rGFR.The Wilcoxon signed ranks test was used to compare the difference and absolute difference in a certain stage of CKD.The results were consid-ered to be significant at P?0.05.Medcalc for Windows,version8.0 (Medcalc Software,Mariekerke,Belgium)was used for data analysis. Results

Patient Characteristics

A total of684patients with CKD were included in the final analysis,including352men and332women,and the average age was49.98?15.8yr.Causes and stages of CKD are listed in Table1.

Modification of MDRD Equations

In the first two linear regression,the intercepts of the modi-fied MDRD equation7(?0.383;95%confidence interval[CI]?3.104to2.337)and of the modified abbreviated MDRD equa-tion(0.311;95%CI?2.526to3.149)were not significantly different from0(P?0.78and P?0.83,respectively).By forcing the two intercepts to be zero,the form of two models was reduced and got the following equations(n?454,R2?0.95and0.94respectively):

c-7GFR1(ml/min per1.73m2)?170?Pcr?0.999

?age?0.176?BUN?0.170?albumin0.318?0.762

(if female)?1.202(if Chinese)(3) c-aGFR1(ml/min per1.73m2)?186?Pcr?1.154

?age?0.203?0.742(if female)?1.227(if Chinese)(4)

Development of New Equations

Calibrated CX3Pcr was needed in equations3and4,which were not convenient for clinical application in Chinese,so we tried to reconstruct another two regression models,using Pcr values measured with the Jaffe’s kinetic method on a Hitachi 7600analyzer.The first model used the same variables as MDRD equation7,and the second used the same variables as the abbreviated MDRD equation.The two resulted in equations

Table1.Basic characteristics of the patients a

Characteristic(n?684)Mean?SD(Median)

or n(%) Female(n?%?)332(48.53)

Age(yr)49.9?15.8(49.0) Height(cm)164.7?8.3(165.0) Weight(kg)64.5?12.4(63.0) BSA(m2) 1.7?0.18(1.7) BMI(kg/m2)23.6?3.6(23.4) Plasma creatinine(mg/dl) 2.0?1.8(1.3) Plasma urea nitrogen(mg/dl)28.4?19.9(21.5) Plasma albumin(g/dl) 3.99?0.6(4.1) rGFR(ml/min per1.73m2)55.1?35.1(49.9)

Causes of CKD

primary or secondary glomerular disease 264(38.6)

hypertension102(14.9)

obstructive kidney disease92(13.5)

renovascular disease89(13.0)

chronic tubulointerstitial disease44(6.4)

diabetic nephropathy37(5.4)

polycystic kidney disease18(2.6)

other causes or causes unknown38(5.6)

CKD stages

1125(18.3)

2161(23.6)

3197(28.8)

4101(14.7)

5100(14.6)

a BMI,body mass index;BSA,body surface area;CKD,

chronic kidney disease;rGFR,reference GFR.

Table2.Overall performance of eGFR equations compared with rGFR:Difference,absolute difference,bias, precision,and accuracy a

Parameter Equation1Equation2Equation3Equation4Equation5Equation6 Intercept(95%CI) 6.45(3.78to9.84) 6.58(3.75to9.39)7.76(4.54to10.98)8.06(4.61to11.53)8.55(5.45to11.64)9.54(6.26to12.81) Slope(95%CI)0.69(0.65to0.74)0.68(0.64to0.72)0.84b(0.78to0.88)0.83b(0.78to0.88)0.82b(0.77to0.87)0.81b(0.76to0.85) R0.910.900.910.900.920.91

R20.840.810.840.810.840.82

Median of difference

(ml/min per1.73m2;25%,75%

percentile)

?7.4(?19.5,?1.3)?7.8(?21.5,?1.8)?0.3b(?8.5,6.3)?0.9b(?9.6,7.4)?0.8b(?9.7,7.4)?0.8b(?9.7,7.4)

Median of absolute difference

(ml/min per1.73m2;

25%,75%percentile)

8.7(3.7,19.5)9.4(4.2,21.5)7.3b(2.7,15.1)8.8b(3.3,15.2)7.1b(2.7,15.6)7.9b(3.3,15.6)

Bias(arbitrary units)2133.92175.0605.8543.0685.6677.2

Precision(ml/min per1.73m2;%)57.660.75457.553.256.5

15%accuracy32.630.050.4b48.7b47.4b46.9b

30%accuracy70.466.176.177.8b79.6b79.6b

50%accuracy95.293.993.992.293.593.0

a The estimated GFR(eGFR)that resulted from these six equations all were significantly correlated with rGFR.Linear regressions were made using eGFR against rGFR.The six intercepts were much similar,but the slopes of equations3through 6were significantly closer to the identical line compared with the slopes of equations1and2.CI,confidence interval.

b P?0.05compared with equations1and2.

J Am Soc Nephrol17:2937–2944,2006Modified MDRD Equations for Chinese Patients2939

5and 6after adjustment using the smearing method,presented in the Appendix (n ?454;R 2?0.86for both).

Diagnostic Performance of the Equations

First,the overall diagnostic performance was compared among equations 1through 6.Linear regressions were made using eGFR against rGFR.The six intercepts were much similar,but the slopes of equations 3through 6were significantly closer to the identical line compared with the slopes of equations 1and 2).On the Bland-Altman plot,compared with equations 1and 2,the biases of equations 3through 6were much less,and precision of equations 3through 6were slightly higher (Table 2,Figure 1).The differences between eGFR resulted from equa-tions 3through 6,and rGFR were significantly less than the differences that resulted from the other two.Equations 3and 5showed fewer absolute differences than equation 1;so did equations 4and 6than equation 2.The 15%accuracy of equa-tions 3through 6was significantly higher compared with equa-tions 1and 2,30%accuracy of equations 4through 6was significantly higher than equations 1and 2;there also was some improvement in the 30%accuracy of equation 3but without statistically significant.The 50%accuracy was comparable for the six equations.There was no significant difference among equations 3through 6in 15to 50%accuracy (Table 2).

The performance of the six equations in various stages of CKD was analyzed.In CKD stages 1,2,3,4,and 5,the differ-ences between equations 3through 6and rGFR were signifi-cantly less than the differences that resulted from the other two equations (P ?0.05for all;Figure 2).Equations 3through 6also resulted in lower absolute differences compared with the other two equations in CKD stages 1and 2(P ?0.05for all).The absolute differences of equations 3through 6also were less than those of equations 1and 2in CKD stage 3but without statistical significance.The absolute differences of the six equa-tions were similar in stages 4and 5(Figure 3).

In CKD stages 1and 2,equations 3through 6showed sig-nificant improvements in 15and 30%accuracy compared with equations 1and 2(P ?0.05for all);in CKD stage 3,significant 15%accuracy was achieved comparing equations 3and 5with equations 1and 2(P ?0.05for both).Some improvement was achieved comparing equations 4and 6with equations 1and 2without statistical significance;in CKD stages 4and 5,15%accuracy improvements of equations 3through 6was gained without statistical significance.The 15and 30%accuracy among equations 3through 6was not significantly

different.

Figure 1.Bland-Altman plot showing the disagreement between estimated GFR (eGFR;including aGFR,c-aGFR1,and c-aGFR2)and reference GFR (rGFR).Solid line represents the regression line of difference between methods against average of methods,dashed lines represent 95%confidence intervals for the regres-sion line,and dotted lines represent 95%limits of agreement.aGFR,eGFR (ml/min per 1.73m 2)by original abbreviated

Modification of Diet in Renal Disease (MDRD)equation;c-aGFR1,eGFR (ml/min per 1.73m 2)by modified abbreviated MDRD equation by adding a racial factor for Chinese;c-aGFR2,eGFR (ml/min per 1.73m 2)by modified abbreviated MDRD equation based on the result of multiple linear regression from data of Chinese patients with chronic kidney disease (CKD).(A)Disagreement between aGFR and average of aGFR and rGFR.(B)Disagreement between c-aGFR1and average of c-aGFR1and rGFR.(C)Disagreement between c-aGFR2and av-erage of c-aGFR2and rGFR.

2940Journal of the American Society of Nephrology J Am Soc Nephrol 17:2937–2944,2006

The 50%accuracy of the six equations was not significantly different in each stage of CKD (Figure 4).

CKD Stage Misclassification by the Equations

We also evaluated CKD stage misclassification by the origi-nal MDRD equations and the modified MDRD equations.In CKD stage 1,71.4and 73.8%of patients were misclassified as in CKD stage 2by equations 1and 2;the percentages were 47.6,45.2,54.8,and 52.4%for equations 3through 6,respectively.In CKD stage 2,compared with the modified MDRD equations,more patients were misclassified as in CKD stage 3by equa-tions 1and 2;the percentages of incorrect stage were 60.0,68.3,30.0,31.7,31.7,and 31.7%for equations 1through 6,respec-tively (?2test,P ?0.05;Table 3).In CKD stages 3through 5,there was no significant difference in the percentages of mis-classification among the six equations (?2test,P ?0.05).

Final Equations

For more precise GFR prediction,we modified original MDRD equations on the basis of data from all 684patients with

CKD,using the similar methods in equations 3through 6.The final equations by adding racial coefficients were re-expressed as follows (n ?684for both,R 2?0.95):

c-7GFR 3(ml/min per 1.73m 2)?170?Pcr ?0.999?age ?0.176

?BUN ?0.170?albumin 0.318?0.762

(if female)?1.211(if Chinese)(7)c-aGFR 3(ml/min per 1.73m 2)?186?Pcr ?1.154?age ?0.203

?0.742(if female)?1.233(if Chinese)(8)The final equations 9and 10,based on the values of Pcr measured with a Hitachi 7600analyzer from our laboratory after smearing adjustment,also are described in the Appendix (n ?684for both;R 2?0.86).

Discussion

With the increasing emphasis on the earlier detection and management of CKD,estimation of urine albumin excretion and GFR has assumed greater importance.The MDRD equa-tions were developed on the basis of white and black

patients

Figure https://www.wendangku.net/doc/0118360793.html,parison of equations:Difference between eGFR and rGFR.The differences between equations 3through 6eGFR and rGFR were significantly less than those between equations 1and 2eGFR and rGFR in each CKD stage (P ?0.05for

all).

Figure https://www.wendangku.net/doc/0118360793.html,parison of equations:Absolute difference between eGFR and rGFR.The absolute differences between equations 3through 6eGFR and rGFR were significantly less than those between equations 1and 2eGFR and rGFR in CKD stages 1and 2(P ?0.05for all).The absolute differences of equations 3through 6were also less than those of equations 1and 2in CKD stage 3but without statistical significance.The absolute differences of the six equations were similar in stages 4and 5.J Am Soc Nephrol 17:2937–2944,2006Modified MDRD Equations for Chinese Patients 2941

and were not suitable for Asian individuals (6,11):Both original MDRD equation 7and the abbreviated MDRD equation under-estimated rGFR in patients with nearly normal kidney function (6,12,13).Underestimation of GFR in near-normal kidney func-tion causes misclassification and results in unnecessary inter-ventions,such as referral to nephrologists and/or excessive monitoring or other interventions (14,15).Therefore,we tried to fill a major void in the international classification of the stage of renal insufficiency by modifying the original MDRD equations for the estimation of GFR in Chinese patients.

In our study,all the modified MDRD equations showed lower bias and higher accuracy than the original MDRD equa-tions in each stage of CKD when applied to Chinese patients;particularly in patients with near-normal kidney function,cases of CKD stage 2that were misdiagnosed as CKD stage 3by modified equations were less by approximately 40%than those of original MDRD equations.This will help nephrologists to figure out a relatively correct prevalence of CKD and ensure that clinicians make a proper clinical action plan for patients with CKD and avoid unnecessary clinical intervention.

Because there were no significant performance difference among equations 3through 6and because the final equations 7through 10were based on all patients,which were assumed to be more accurate than equations 3through 6,we recommend that equations 7through 10be used.Because equations 8and 10require only one laboratory variable,Pcr,and the GFR estimat-ing process is simplified without decreasing accuracy,for easier application,especially in population screening,equations 8and 10are recommended.

There are several methods to measure Pcr in clinical labora-tories.Jaffe’s kinetic method on a Hitachi analyzer is the most widely used method in Chinese clinical laboratories.For better practicability,the Jaffe’s kinetic method on a Hitachi analyzer was used our study.For patients with Pcr value as measured on a Hitachi analyzer using the Jaffe’s kinetic method,equation 10could be used;for patients with Pcr as measured on Beckman analyzers using the Jaffe’s kinetic method,equation 8could be used.

Recently,some studies (16,17)emphasized the importance of calibration of https://www.wendangku.net/doc/0118360793.html,e of Pcr in MDRD equations requires

that

Figure https://www.wendangku.net/doc/0118360793.html,parison of equations:15,30,and 50%accuracy of equations in various stages of CKD.In CKD stages 1and 2,equations 3through 6showed significant improvements in 15and 30%accuracy compared with equations 1and 2(P ?0.05for all);significant 15%accuracy were achieved comparing equations 3and 5with equations 1and 2in CKD stage 3(P ?0.05for both);some improvement was achieved comparing equations 4and 6with equations 1and 2in CKD stage 3without statistical significance.In CKD stages 4and 5,15%accuracy improvements of equations 3through 6was gained without statistical significance.The 15and 30%accuracy among equations 3through 6were not significantly different.The 50%accuracy of the six equations was not significantly different in each stage of CKD.2942Journal of the American Society of Nephrology J Am Soc Nephrol 17:2937–2944,2006

the Pcr value be calibrated to the Cleveland Clinic Laboratory value.Failure to do so can introduce a systemic bias in the eGFR,so we think that it is important to calibrate Pcr to the Cleveland Clinic Laboratory value in equation8;for equation 10,Pcr calibration could be performed in the laboratory at the First Hospital,Beijing University.

There are several reasons for why the modified equations outperformed the original equations.First,there were racial differences,and addition of the Chinese racial factor certainly allowed performance improvement.Furthermore,the rGFR method that was used in our study—plasma clearance of99m Tc-DTPA—was different from that used in the MDRD study—renal clearance of125I-iothalamate.These two methods may differ from each other compared with inulin clearance(18–20). Therefore,GFR estimation equations that are derived from different rGFR might differ from each other,even in the same group of patients.

Several limitations in our study should be noted.First,ac-cording to Levey et al.(16),the Pcr-based equations were de-rived from the results of multiple regression analysis,their performance best fitted around the observed mean.The origi-nal MDRD equations were developed in patients with average GFR of39.8ml/min per1.73m2;the eGFR would underesti-mate rGFR in individuals with a higher range of GFR and overestimate rGFR in a group with advanced kidney failure. Although great improvement was achieved,equations3 through6still underestimate GFR when GFR is nearly normal. We modified MDRD equations on the basis of the original MDRD equations and used the same variables and a similar method so that it would not inevitably inherit the same short-comings of the original equations.

Second,in the modified MDRD equations,Pcr still was the important GFR-predicting variable,so the main,unavoidable pitfall of Pcr-based GFR estimation equations will contribute to the inaccuracy of each equation.It is a fundamentally different relationship between Pcr and GFR in populations with different levels of GFR(16);therefore,different levels of Pcr were not necessarily reflecting the true variation of GFR(21).In near-normal GFR levels,there was no significant decrease of Pcr with the increment of true GFR.However,in advanced kidney failure,with the prominent increment of Pcr,only a slight GFR decrease was detected.Some other potential GFR-predicting variables,such as plasma cystatin C,might be included to improve the performance of GFR-estimating equations,espe-cially in early stages of CKD(22).

Third,because the percentage of patients with CKD that was caused by hypertension and/or diabetes was relatively small in our studied population,the modified equations’performance in patients with hypertension and/or diabetes needs to be examined further.

Conclusion

The importance of being able to assess GFR accurately without complex procedures is especially important in China,a vast,de-veloping country with a population of1.3billion—almost one fifth of the world’s population—and the prevalence of CKD in this country seems to be increasing.From our study,we concluded that the accuracy of these modified MDRD equations on the basis of data that were obtained from Chinese patients with CKD was better than that of the original MDRD equations in Chinese pa-tients with CKD and provide clinicians with the opportunity to estimate GFR more accurately using simple Pcr and demographic variables.It will be interesting to know whether these modified MDRD equations will have the same performance in patients with CKD in other Asian individuals.

Appendix

The equations that are based on the result of multiple linear regression from data of454Chinese patients with CKD,as well as the final equations that were derived from data of684Chinese patients with CKD,after smearing adjustment,are as follows(R2?0.86for all):

c-7GFR2(ml/min per1.73m2)?184?Pcr?1.091?age?0.203

?BUN?0.161?albumin0.33?0.816(if female)(5) c-aGFR2(ml/min per1.73m2)?206

?Pcr?1.234?age?0.227?0.803(if female)(6)

Table3.Percentages of CKD stage misclassification by original and modified equations in CKD stages1and2a

Classification Based on:CKD Stage Based on rGFR 12

Equation1

CKD stage128.60

CKD stage271.440

CKD stage3060

Equation2

CKD stage126.2 1.7

CKD stage273.831.7

CKD stage3066.6

Equation3

CKD stage152.48.3

CKD stage247.670

CKD stage3021.7

Equation4

CKD stage154.813.3

CKD stage245.268.3

CKD stage3018.4

Equation5

CKD stage145.210

CKD stage254.868.3

CKD stage3021.7

Equation6

CKD stage147.611.7

CKD stage252.468.3

CKD stage3020

a In CKD stage1,equations3through6showed lower

percentages of misclassification than equations1and2(P?

0.05for equations3and4;NS for equations5and6).In CKD

stage2,equations3through6achieved lower percentages of

misclassification than equations1and2(P?0.05for all).

J Am Soc Nephrol17:2937–2944,2006Modified MDRD Equations for Chinese Patients2943

c-7GFR4(ml/min per1.73m2)?193?Pcr?1.064?age?0.161

?BUN?0.197?albumin0.274?0.80(if female)(9) c-aGFR4(ml/min per1.73m2)?175?Pcr?1.234?age?0.179

?0.79(if female)(10) Acknowledgments

This work was funded by National“211Project”Peking University Evidence Based Medicine Group(91000-246156061).

We are grateful to the Cleveland Clinic Laboratory for calibration of Pcr;without their kind help,this work could not have been accom-plished.We express our thanks to the Department of Mathematics, Peking University,for helpful statistical advice.We acknowledge Fre-senius Medical Care of China and PUMC Pharmaceutical Co.Ltd.for generous sponsorship.

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行业内计算公式大全

一、平整场地：建筑物场地厚度在±30cm以内挖、填、运、找平。 1. 平整场地计算规则 (1) 清单规则：按设计图示尺寸以建筑物首层面积计算。 (2) 定额规则：按设计图示尺寸以建筑物外墙外边线每边各加2米以平方米面积计算。 2. 平整场地计算公式 S=（A+4）×（B+4）=S底+2L外+16 式中：S——平整场地工程量； A——建筑物长度方向外墙外边线长度； B——建筑物宽度方向外墙外边线长度； S底——建筑物底层建筑面积； L外——建筑物外墙外边线周长。 该公式适用于任何由矩形组成的建筑物或构筑物的场地平整工程量计算。 二、基础土方开挖计算 1. 开挖土方计算规则 (1) 清单规则：挖基础土方按设计图示尺寸以基础垫层底面积乘挖土深度计算。 (2) 定额规则：人工或机械挖土方的体积应按槽底面积乘以挖土深度计算。槽底面积应以槽底的长乘以槽底的宽，槽底长和宽是指基础底宽外加工作面，当需要放坡时，应将放坡的土方量合并于总土方量中。 2. 开挖土方计算公式： (1) 清单计算挖土方的体积： 土方体积＝挖土方的底面积×挖土深度。

(2) 定额规则： 基槽开挖：V=（A+2C+K×H）H×L。 式中： V——基槽土方量； A——槽底宽度； C——工作面宽度； H——基槽深度； L——基槽长度。 其中外墙基槽长度以外墙中心线计算，内墙基槽长度以内墙净长计算，交接重合出不予扣除。基坑开挖： V=1/6H[A×B+a×b+(A+a)×(B+b)+a×b]。 式中： V——基坑体积； A——基坑上口长度； B——基坑上口宽度； a——基坑底面长度； b——基坑底面宽度。 三、回填土工程量计算规则及公式 1. 基槽、基坑回填土体积=基槽（坑）挖土体积-设计室外地坪以下建（构）筑物被埋置部分的体积。 式中室外地坪以下建（构）筑物被埋置部分的体积一般包括垫层、墙基础、柱基础、以及地下建

圆柱体的计算公式如下

圆柱体的计算公式如下: 圆柱体侧面积公式：侧面积=底面周长×高 S侧＝C底×h 圆柱体的表面积公式：表面积=2πr2+底面周长×高 S表＝S底+C底×h 圆柱体的体积公式：体积=底面积×高 V圆柱＝S底×h 长方体的体积公式： 长方体的体积=长X宽X高 如果用a、b、h分别表示长方体的长、宽、高则公式为：V长=abh 正方体的表面积公式： 表面积＝棱长×棱长×6 S正＝a＾2×6 正方体的体积公式： 正方体的体积＝棱长×棱长×棱长． 如果用a表示正方体的棱长，则正方体的体积公式为v正＝a·a·a ＝a＾3 圆锥体的体积=1/3×底面面积×高 V圆锥＝1/3×S底×h边坡坡度1：0.5 应是垂距（1）比水平距（0.5）。深是多少？什么结构的？地下室？还是普通的基础挖土？算不了 可以告诉你个公式

S1是基础底面积S1=（基础底边长+工作面）*（基础底边宽+工作面） S2是基础顶面积S2=（基础底边长+工作面+高*0.5*2）*（基础底边宽+工作面+高*0.5*2） V=（S1+S2+S1 *S2的开平方）*H/3 H是深也就是高相当于直角三角形较短的一条直角边是3，较长的一条直角边是4，那么角度（较大的那个角）是arctan(4/3),用计算器算出为53.13010235度！坡度的表示方法有百分比法、度数法、密位法和分数法四种，其中以百分比法和度数法较为常用。 (1) 百分比法 表示坡度最为常用的方法，即两点的高程差与其水平距离的百分比，其计算公式如下：坡度＝ (高程差/水平距离)ｘ100% 使用百分比表示时， 即：i=h/l×100％ 例如：坡度3% 是指水平距离每100米,垂直方向上升(下降) 3米；1%是指水平距离每100米,垂直方向上升(下降)1米。以次类推！ (2) 度数法 用度数来表示坡度，利用反三角函数计算而得，其公式如下： tanα(坡度)＝高程差/水平距离 所以α(坡度)＝ tan-1 (高程差/水平距离)

效率计算公式

其物理含义如下：IL：光生电流； Id：饱和暗电流； Rsh：并联电阻（电池边缘漏电和结区漏电会降低并联电阻值）； Rs：串联电阻（金属浆料电阻、烧结后的接触电阻、半导体材料电阻和横向电阻）；PN结：单二极管（理想因子n=1）或双二极管（另一个并联的二极管n=2）。 由此，我们可以得出电流的输出为：或 注：在表达式q/(nkT)中理想因子为n，可取1或者2。n=1反映体内或表面通过陷阱能级的复合；n=2描述载流子在电荷耗尽区（也就是结区）复合。 3 太阳电池的电特性测量： 测出的太阳电池的电特性为一曲线，相当于外接一个0~∞变化的电阻时太阳电池的电流电压输出曲线。具体如下图所示： 同时可根据该曲线计算出开路电压Voc、短路电流Isc、最佳工作点电压Vmp、最佳工作点电流Imp、最大功率点Pmax、填充因子FF和光电转换效率Eff及串联电阻Rs、并联电阻Rsh。 其中，Rs和Rsh采用近似计算。 计算Rsh时，忽略ID,并取Rs<

期权价格计算公式

期权价格计算公式 股票的价格变化遵循一维维纳过程，其微分方程如下 dz t s b dt t s a ds ),(),(+= 式中：dz 的差分?Z 满足如下条件的正态分布 t z ?=∈? 在一般情况下，ds 可用下式表示： sdz sdt ds σμ+=----------- （1） 或表示为： dz dt s ds σμ+= 式中：s μ股票价格的期望漂移率，μ 为一个恒定参数；2)(s σ为股票价格波动的方差， σ 为股票价格的波动率，可以通过观察股票价格的动态系列数据获得。 如果存在一个变量 G ，它是股票S 的一种衍生证卷，它的价格是S 和 t 的函数，G(s,t)，那么，S 和G 都受到同一个基本的不确定性因素的影响。根据ITO 定理，函数G 的行为遵循如下微分方程描述的过程： Sdz S G dt S S G t G S S G dG σσμ??+??+??+??=)21(2222 -------------（2） 函数G 的漂移率为 222221S S G t G S S G σμ??+??+?? 方差为 222)(S S G σ??

如果G 代表股票S 的一种期权，我们想用S 和G 构造一组风险中性的证卷组合。为此，首先将公式（1）、（2）改写成对应的差分形式： z S t S S ?+?=?σμ ---------------（3） z S S G t S G t G S S G G ???+???+??+??=?σμ)21(22 ----------（4） 由于公式（3）、（4）中的z ?t ?=∈(）是相同的维纳过程，只要证卷数量的搭配合理，整卷组合就可以消除z ?。 恰当的证卷组合是： -1； 卖空一个期权 S G ??+；买入期权价值变化对股票价格的敏感度，也就是他的偏微分那样多的股票。定义这个证卷组合的价值为∏，表达式为 S S G G ∏??+-= ---------（5） t ?时间后，这个证卷组合的价值变化为： S S G G ???+?-=?∏ -----------（6） 将（3）、（4）带入（6），消去z ?，得： t S S G t G ???-??-=?∏)21(2222σ ---------（7） 由于这个证卷组合是风险中性的，所以，它的收益一定与任何一个无风险证卷的收益相同，就是 ∏∏?=?t r ---------（8） 将（5）、（7）带入（8），得：

计算公式如下

计算公式如下： 1.计算角度闭合差及期限差 闭合导线角度闭合差 βf =∑=n i 1β-(n-2)×0180 测左角附合导线角度闭合差 终左始αβαβ-?-+=∑=n i n f 10180 测右角附合导线角度闭合差 终右始αβαβ-?+-=∑=01180n f n i 图根导线角度闭合差的限差 n f 04''±=容β 2.计算角度改正数 闭合导线及测左角附合导线的角度改正数 n f i β υ-= 测右角附合导线的角度改正数 n f i β υ= 3.计算改正后的角度 改正后角度 i i i υβ+= 4.推算方位角 左角推算关系 i i i i i βαα+±=-+0,11,180 右角推算关系 i i i i i βαα-±=-+0,11,180 5.计算坐标增量 纵向坐标增量 1,1,1,cos +++?=?i i i i i i D x α 横向坐标增量 1,1,1,sin +++?=?i i i i i i D y α

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利润表计算公式(必备)

利润表计算公式（必备） 利润表的格式主要有多步式和单步式两种，以会计等式“收入-费用=利润”为编制依据。我国《企业会计准则》规定，利润表采用多步式。其步骤和内容如下： 第一步，以主营业务收入为基础，计算主营业务利润。其计算公式为：主营业务利润=主营业务收入-主营业务成本-主营业务税金及附加。 第二步，以主营业务利润为基础，计算营业利润。其计算公式为：营业利润=主营业务利润+其他业务利润-营业费用-管理费用-财务费用。 第三步，以营业利润为基础，计算出利润总额。其计算公式为：利润总额=营业利润+投资收益+补贴收入+营业外收入-营业外支出。 第四步，以利润总额为基础，计算净利润。其计算公式为：净利润=利润总额-所得税。 利润表的编制 我国企业的利润表采用多步式格式，分以下三个步骤编制： 第一步，以营业收入为基础，减去营业成本、营业税金及附加、销售费用、管理费用、财务费用、资产减值损失，加上公允价值变动收益(减去公允价值变动损失)和投资收益(减去投资损失)，计算出营业利润； 第二步，以营业利润为基础，加上营业外收入，减去营业外支出，计算出利润总额； 第三步，以利润总额为基础，减去所得税费用，计算出净利润(或净亏损)。 例题： 截止到2008年12月31日，某企业“主营业务收入”科目发生额为1 990 000元，“主营业务成本”科目发生额为630 000元，“其他业务收入”科目发生额为500 000元，“其他业务成本”科目发生额为150 000元，“营业税金及附加”科目发生额为780 000元，“销售费用”科目发生额60 000元，“管理费用”科目发生额为50 000元，“财务费用”科目发生额为170 000元，“资产减值损失”科目借方发生额为50 000元（无贷方发生额），“公允价值变动损益”科目为借方发生额450 000元（无贷方发生额），“投资收益”科目贷方发生额为850 000元（无借方发生额），“营业外收入”科目发生额为100 000元，“营业外支出”科目发生额为40 000元，“所得税费用”科目发生额为171 600元。 该企业2008年度利润表中营业利润、利润总额和净利润的计算过程如下： 营业利润=1 990 000+500 000-630 000-150 000-780 000-60 000-50 000-170 000-50 000-450 000+850 000=1 000 000（元） 利润总额=1 000 000+100 000-40 000=1 060 000（元） 净利润=1 060 000-171 600=888 400（元） 本例中，企业应当根据编制利润表的多步式步骤，确定利润表各主要项目的金额，相关计算公式如下：

工程经济计算公式汇总78679

工程经济计算公式汇总 1.利息I=F-P 在借贷过程中, 债务人支付给债权人超过原借贷金额的部分就是利息。 从本质上看利息是由贷款发生利润的一种再分配。 在工程经济研究中，利息常常被看成是资金的一种机会成本。 I—利息 F—目前债务人应付（或债权人应收）总金额，即还本付息总额 P—原借贷金额，常称本金 2.利率i=I t/P×100‰ 利率就是在单位时间内所得利息额与原借贷金额之比, 通常用百分数表示。 用于表示计算利息的时间单位称为计息周期 i—利率 I t—单位时间内所得的利息额 P—原借贷金额，常称本金 3.单利I t＝P×i单 所谓单利是指在计算利息时, 仅用最初本金来计算, 而不计人先前计息周期中所累积增加的利息, 即通常所说的" 利不生利" 的计息方法。 I t—代表第t 计息周期的利息额 P—代表本金 i单—计息周期单利利率 而n期末单利本利和F等于本金加上总利息,即: 4. F=P＋I ＝P(1＋n×i单) n I n代表n 个计息周期所付或所收的单利总利息, 即:

5. I n＝P×i单×n 在以单利计息的情况下,总利息与本金、利率以及计息周期数成正比的关系. 6.复利I t＝i×F t-1 所谓复利是指在计算某一计息周期的利息时，其先前周期上所累积的利息要计算利息，即“利生利”、“利滚利”的计息方式。 I t—代表第t 计息周期的利息额 i—计息周期复利利率 F t-1—表示第（t-1）期末复利利率本利和 一次支付又称整存整付，是指所分析系统的现金流量，论是流人或是流出，分别在各时点上只发生一次。 n计息的期数 P现值( 即现在的资金价值或本金)，资金发生在(或折算为) 某一特定时间序列起点时的价值 F终值(即n 期末的资金值或本利和)，资金发生在(或折算为) 某一特定时间序列终点的价值 7.终值计算( 已知P 求F) 一次支付n年末终值( 即本利和)F 的计算公式为： 式中（1＋i)n 称之为一次支付终值系数, 用（F/P, i, n）表示，又可写成: F＝P（F/P, i, n）。 8.现值计算(已知F 求P) 式中（1＋i)-n称为一次支付现值系数, 用符号(P/F, i, n)表示。式又可写成: F＝P（F/P, i, n）。

圆柱体的计算公式如下之欧阳学文创作

圆柱体的计算公式如下: 欧阳学文 圆柱体侧面积公式：侧面积=底面周长×高S侧＝C底×h 圆柱体的表面积公式：表面积=2πr2+底面周长×高S表＝S 底+C底×h 圆柱体的体积公式：体积=底面积×高V圆柱＝S底×h 长方体的体积公式： 长方体的体积=长X宽X高 如果用a、b、h分别表示长方体的长、宽、高则公式为：V 长=abh 正方体的表面积公式： 表面积＝棱长×棱长×6 S正＝a＾2×6 正方体的体积公式： 正方体的体积＝棱长×棱长×棱长． 如果用a表示正方体的棱长，则正方体的体积公式为v正＝a·a·a＝a＾3

圆锥体的体积=1/3×底面面积×高V圆锥＝1/3×S底×h 边坡坡度1：0.5 应是垂距（1）比水平距（0.5）。深是多少？什么结构的？地下室？还是普通的基础挖土？算不了可以告诉你个公式 S1是基础底面积S1=（基础底边长+工作面）*（基础底边宽+工作面） S2是基础顶面积S2=（基础底边长+工作面+高*0.5*2）*（基础底边宽+工作面+高*0.5*2） V=（S1+S2+S1 *S2的开平方）*H/3 H是深也就是高相当于直角三角形较短的一条直角边是3，较长的一条直角边是4，那么角度（较大的那个角）是arctan(4/3),用计算器算出为53.13010235度！坡度的表示方法有百分比法、度数法、密位法和分数法四种，其中以百分比法和度数法较为常用。 (1) 百分比法 表示坡度最为常用的方法，即两点的高程差与其水平距离的百分比，其计算公式如下：坡度＝(高程差/水平距离)ｘ100%

使用百分比表示时， 即：i=h/l×100％ 例如：坡度3% 是指水平距离每100米,垂直方向上升(下降)3米；1%是指水平距离每100米,垂直方向上升(下降)1米。以次类推！ (2) 度数法 用度数来表示坡度，利用反三角函数计算而得，其公式如下： tanα(坡度)＝高程差/水平距离 所以α(坡度)＝tan-1 (高程差/水平距离) 不同角度的正切及正弦坡度 角度正切正弦 0° 0% 0% 5° 9% 9% 10° 18% 17% 30° 58% 50% 45° 100% 71% 60° 173% 87%

工程经济计算公式汇总

工程经济计算公式汇总 1.利息 I=F-P 在借贷过程中 , 债务人支付给债权人超过原借贷金额的部分就是利息。 从本质上看利息是由贷款发生利润的一种再分配。 在工程经济研究中，利息常常被看成是资金的一种机会成本。 I —利息 F —目前债务人应付（或债权人应收）总金额，即还本付息总额 P —原借贷金额，常称本金 2.利率 i=I t /P ×100‰ 利率就是在单位时间内所得利息额与原借贷金额之比 , 通常用百分数表示。 用于表示计算利息的时间单位称为计息周期 i —利率 I t —单位时间内所得的利息额 P —原借贷金额，常称本金 3.单利 I t ＝P ×i 单 所谓单利是指在计算利息时 , 仅用最初本金来计算 , 而不计人先前计息周期中所累积增加的利息 , 即通常所说的 " 利不生利 " 的计息方法。 I t —代表第 t 计息周期的利息额 P —代表本金 i 单—计息周期单利利率 而n 期末单利本利和F 等于本金加上总利息,即 : 4. F=P ＋I n ＝P(1＋n ×i 单 ) I n 代表 n 个计息周期所付或所收的单利总利息 , 即 :

5. I n ＝P ×i 单 ×n 在以单利计息的情况下,总利息与本金、利率以及计息周期数成正比的关系. 6.复利 I t ＝i ×F t-1 所谓复利是指在计算某一计息周期的利息时，其先前周期上所累积的利息要计算利息，即“利生利 ”、“利滚利”的计息方式。 I t —代表第 t 计息周期的利息额 i —计息周期复利利率 F t-1—表示第（t-1）期末复利利率本利和 一次支付又称整存整付，是指所分析系统的现金流量，论是流人或是流出，分别在各时点上只发生一次。 n 计息的期数 P 现值 ( 即现在的资金价值或本金)，资金发生在(或折算为) 某一特定时间序列起点时的价值 F 终值 (即n 期末的资金值或本利和)，资金发生在(或折算为) 某一特定时间序列终点的价值 7.终值计算 ( 已知 P 求 F) 一次支付n 年末终值 ( 即本利和 )F 的计算公式为： 式中（1＋i)n 称之为一次支付终值系数 , 用（F/P, i, n ）表示，又可写成 : F ＝P （F/P, i, n ）。 8.现值计算 ( 已知 F 求 P)

圆柱体的计算公式如下之欧阳家百创编

圆柱体的计算公式如下: 欧阳家百（2021.03.07） 圆柱体侧面积公式：侧面积=底面周长×高S侧＝C底×h 圆柱体的表面积公式：表面积=2πr2+底面周长×高S表＝S底+C底×h 圆柱体的体积公式：体积=底面积×高V圆柱＝S底×h 长方体的体积公式： 长方体的体积=长X宽X高 如果用a、b、h分别表示长方体的长、宽、高则公式为：V长=abh 正方体的表面积公式： 表面积＝棱长×棱长×6 S正＝a＾2×6 正方体的体积公式： 正方体的体积＝棱长×棱长×棱长． 如果用a表示正方体的棱长，则正方体的体积公式为v正＝a·a·a＝a ＾3 圆锥体的体积=1/3×底面面积×高V圆锥＝1/3×S底×h边坡坡度1：0.5 应是垂距（1）比水平距（0.5）。深是多少？什么结构的？地下室？还是普通的基础挖土？算不了 可以告诉你个公式 S1是基础底面积S1=（基础底边长+工作面）*（基础底边宽+工作面）

S2是基础顶面积S2=（基础底边长+工作面+高*0.5*2）*（基础底边宽+工作面+高*0.5*2） V=（S1+S2+S1 *S2的开平方）*H/3 H是深也就是高相当于直角三角形较短的一条直角边是3，较长的一条直角边是4，那么角度（较大的那个角）是arctan(4/3),用计算器算出为53.13010235度！ 坡度的表示方法有百分比法、度数法、密位法和分数法四种，其中以百分比法和度数法较为常用。 (1) 百分比法 表示坡度最为常用的方法，即两点的高程差与其水平距离的百分比，其计算公式如下：坡度＝(高程差/水平距离)ｘ100% 使用百分比表示时， 即：i=h/l×100％ 例如：坡度3% 是指水平距离每100米,垂直方向上升(下降)3米；1%是指水平距离每100米,垂直方向上升(下降)1米。以次类推！ (2) 度数法 用度数来表示坡度，利用反三角函数计算而得，其公式如下： tanα(坡度)＝高程差/水平距离 所以α(坡度)＝tan-1 (高程差/水平距离) 不同角度的正切及正弦坡度 角度正切正弦 0°0% 0%

计算公式

所得税后的财务净现值=预计所得税后利润/(1+预计投资回报率)投资期的乘方 财务净现值 定义：按电力行业基准收益率将该项目各年的净现金流量折现到建设起点的现值之和。当财务净现值大于或等于零时，项目是可行的。财务净现值越大，项目的获利水平越高。 财务净现值(NPV),是指项目按行业的基准收益率或设定的目标收益率,将项目计算期内各年的净现金流量折算到开发活动起始点的现值之和,它是房地产开发项目财务评价中的一个重要经济指标.其计算公式为: NPV=∑〔CI-CO〕ˇt〔1+ i 〕ˉt(∑的上面是n 下面是t=0 , 表示第0期到第n期的累计 ) NPV = 项目在起始时间点上的财务净现值 i = 项目的基准收益率或目标收益率 〔CI-CO〕ˇt〔1+ i 〕ˉt 表示第t期净现金流量折到项目起始点上的现值 财务净现值率即为单位投资现值能够得到的财务净现值。 其计算公式为： FNPVR＝FNPV／PVI （16—40) 式中FNPVR——财务净现值率； FNPV——项目财务净现值； PVI——总投资现值。 内部收益率 定义：投资项目各年现金流量的折现值之和为项目的净现值，净现值为零时的折现率就是项目的内部收益率。 （1）计算年金现值系数(p／A，FIRR，n)=K／R； （2）查年金现值系数表，找到与上述年金现值系数相邻的两个系数(p／A，i1，n)和(p／A，i2，n)以及对应的i1、i2，满足(p／A，il，n) >K／R>(p／A，i2，n)； （3）用插值法计算FIRR： （FIRR-I）/（i1—i2）=[K／R-(p/A，i1，n) ]/[(p／A，i2，n)—(p／A，il，n)] 若建设项目现金流量为一般常规现金流量，则财务内部收益率的计算过程为： 1、首先根据经验确定一个初始折现率ic。 2、根据投资方案的现金流量计算财务净现值FNpV(i0)。 3、若FNpV(io)=0，则FIRR=io； 若FNpV(io)>0，则继续增大io； 若FNpV(io)<0，则继续减小io。

道路照度计算公式_如下

道路照度计算公式如下： Ｅ＝φ（光通量）Ｎ（路灯单双侧）Ｕ（利用系数）／Ｋ（路面材料砼1.3、沥青2）Ｂ（路宽）Ｄ（电杆间距） 具体解释/定义 Ｅ：道路照度 φ：灯具光通量 Ｎ：路灯为对称布置时取２，单侧和交错布置时取１ Ｕ：利用系数 K：混泥土路面取1.3，沥青路面取2 B：路面宽度 D：电杆间距 关于平均照度的计算公式 偶然间得到一个求平均照度的公式 E=F.U.K.N/S.W 并有几组计算数据 E= 2x9000x0.65x0.36/18/30＝7.8Lx （110w高压钠灯，杆高10米，间距30米，道路有效宽度：20－1－1，双侧对称布置） E＝2x16000x0.65x0.36/18/30=13.8Lx （150W高压钠灯，杆高10米，间距30米，道路有效宽度：20－1－1，双侧对称布置） E＝2x9000x0.65x0.36/18/28=8.35Lx （110W高压钠灯，杆高10米，间距28米，道路有效宽度：20－1－1，双排对称布置） 我查了资料了解到 U为利用系数 k为维护系数（混泥土路面取1.3，沥青路面取2 ） S为路灯安装间距（28，30为安装间距） W为道路宽度（18为道路有效宽度） N为路灯排列方式（(N路灯为对称布置时取2，单侧和交错布置时取1） 我想问的是： 1、上边举例的数据中，2是代表对称布置取2，还是沥青路面取2（我得到资料中为提及路面） 2、U利用系数和K维护系数，分别代表数据中哪个数值？ 3、公式中的F是什么数据？它对应数据中哪个数值？

4、除道路宽度W，路灯排列方式N，安装间距S以外，F、U、K的数据在新的计算中如何得到 1、上边举例的数据中，2是代表对称布置取2 2、U利用系数=0.65,K维护系数=0.36 3、公式中的F是光通量，它对应数据是9000和16000 4、除道路宽度W，路灯排列方式N，安装间距S以外，F、U、K的数据都是根据所选择的灯具和光源的类型得到的。 五，路灯灯具布置设计 以30米宽的混凝土路面道路为例，假设该道路为次干路，车流较多，车速较快，则可选择双侧对称布置。 灯具高度H=8.5米，间距S=25米，灯具悬挑长2米，则有效路宽为26米，根据国家照明标准要求，其照明平均照度Eav不低于5.6Lx，照度均匀度Emin/ Eav不小于0.35。 灯具采用超级LED路灯，功率为70W，其光通量为8000Lm，灯高8.5米道路平面等照度曲线为: 选用灯具道路平面照度曲线图 根据城市路面比较清洁的情况，选用路灯利用系数U=0.32（国际照明委员会推荐0.3），维护系数K=0.8；则路面平均照度为： Eav =U xфx N x K/W x S =0.32 x8000 x1 x0.8/13 x25 =6.3Lx 根据灯具的等照度曲线图可以得出其最小照度值Emin不小于3Lx则其平均均匀度为： Emin/ Eav=3/6.3=0.47 所以该安装方案路面平均照度Eav=6.3Lx 平均均匀度Emin/ Eav=0.47符合国家标准要求

道路照度计算公式 如下

道路照度计算公式如下：Ｅ＝φＮＵ／ＫＢＤ 具体解释/定义 Ｅ：道路照度 φ：灯具光通量 Ｎ：路灯为对称布置时取２，单侧和交错布置时取１ Ｕ：利用系数 K：混泥土路面取1.3，沥青路面取2 B：路面宽度 D：电杆间距 关于平均照度的计算公式 偶然间得到一个求平均照度的公式 E=F.U.K.N/S.W 并有几组计算数据 E= 2x9000x0.65x0.36/18/30＝7.8Lx （110w高压钠灯，杆高10米，间距30米，道路有 效宽度：20－1－1，双侧对称布置） E＝2x16000x0.65x0.36/18/30=13.8Lx （150W高压钠灯，杆高10米，间距30米，道路有 效宽度：20－1－1，双侧对称布置） E＝2x9000x0.65x0.36/18/28=8.35Lx （110W高压钠灯，杆高10米，间距28米，道路有 效宽度：20－1－1，双排对称布置） 我查了资料了解到 U为利用系数 k为维护系数（混泥土路面取1.3，沥青路面取2 ） S为路灯安装间距（28，30为安装间距） W为道路宽度（18为道路有效宽度） N为路灯排列方式（(N路灯为对称布置时取2，单侧和交错布置时取1） 我想问的是： 1、上边举例的数据中，2是代表对称布置取2，还是沥青路面取2（我得到资料中为提及路 面）

2、U利用系数和K维护系数，分别代表数据中哪个数值？ 3、公式中的F是什么数据？它对应数据中哪个数值？ 4、除道路宽度W，路灯排列方式N，安装间距S以外，F、U、K的数据在新的计算中如何得 到 1、上边举例的数据中，2是代表对称布置取2 2、U利用系数=0.65,K维护系数=0.36 3、公式中的F是光通量，它对应数据是9000和16000 4、除道路宽度W，路灯排列方式N，安装间距S以外，F、U、K的数据都是根据所选择的灯 具和光源的类型得到的。 五，路灯灯具布置设计 以30米宽的混凝土路面道路为例，假设该道路为次干路，车流较多，车速较快，则可选择 双侧对称布置。 灯具高度H=8.5米，间距S=25米，灯具悬挑长2米，则有效路宽为26米，根据国家照明标准要求，其照明平均照度Eav不低于5.6Lx，照度均匀度Emin/ Eav不小于0.35。 灯具采用超级LED路灯，功率为70W，其光通量为8000Lm，灯高8.5米道路平面等照度曲线 为: 选用灯具道路平面照度曲线图 根据城市路面比较清洁的情况，选用路灯利用系数U=0.32（国际照明委员会推荐0.3），维 护系数K=0.8；则路面平均照度为： Eav =U xфx N x K/W x S =0.32 x8000 x1 x0.8/13 x25 =6.3Lx 根据灯具的等照度曲线图可以得出其最小照度值Emin不小于3Lx则其平均均匀度为：

频段与频率计算公式关于频段与频率计算公式如下

频段与频率计算公式关于频段与频率计算公式如下：(1) GSM 900频段GSM使用900MHz频段如下：890~915MHz (移动台发，基站收)；935~960MHz (移动台发，基站收) 其频段与频率计算公式关于频段与频率计算公式如下： (1) GSM 900频段 GSM使用900MHz频段如下：890~915MHz (移动台发，基站收)；935~960MHz (移动台发，基站收) 其中，可用收发工作频带为25MHz，相邻频道间隔为200KHz，GSM采用等频道间隔配置方式，频道序号为0~124，共125个频道，频道序号和频道标称中心频率的关系为： F1(N)=890.200MHz+(N-1)×0.2.MHz (移动台发，基站收) Fu(N)=F1(N)+45MHz （基站发，移动台收） N=0~124 移动890－909 频点1－94 联通909－915 频点96－124 (2) DCS 1800频段 GSM使用的1800MHz频段如下：1710~1785MHz (移动台发，基站收)；1805~1880MHz (基站发，移动台收) 其收发工作频带为75 MHz，相邻频道间隔为200 KHz，频道序号和频道标称中心频率的关系为： F1(N)=1710.2+(N-512)×0.2( MHz) Fu(N)=F1+95(MHz) N=512~885 (3) EGSM 900频段 EGSM使用的900MHz频段如下：885.2~889.8MHz (移动台发，基站收)；930.2~934.8MHz (基站发，移动台收) 其收发工作频带为5 MHz，相邻频道间隔为200 KHz，频道序号和频道标称中心频率的关系为： F1(N)=880+(N-974)×0.2( MHz) Fu(N)=F1+45(MHz) N=1000~1023

会计基础,会计学的计算公式

会计基础，会计学的计算公式 1、税 税负率=当期应纳增值税/当期应税销售收入 当期应纳增值税=当期销项税额-实际抵扣进项税额 实际抵扣进项税额=期初留抵进项税额+本期进项税额-进项转出-出口退税-期末留抵进项税额 消费税=应税消费品的销售额*消费税税率 城建税额=（当期的营业税+消费税+增值税的应交额）*城市维护建设税税率 教育费附加=（当期的营业税+消费税+增值税的应交额）*教育费附加税率 进口增值税=（完税价格+关税）/（1-增值税率）×增值税率 2、计提折旧有很多种方法，采用不同的方法算出计提折旧的金额也会有所不同 下面是有关于计提固定资产折旧的一些实例，希望能够对你有帮助！！ (一)平均年限法 平均年限法又称直线法，是指按固定资产使用年限平均计算折旧的一种方法。按照这种方法计算提取的折旧额，在各个使用年份或月份都是相等的，折旧的积累额呈直线上升趋势。计算公式如下： 固定资产年折旧额＝[固定资产原价-（预计残值收入-预计清理费用）] ÷固定资产预计使用年限 固定资产月折旧额＝固定资产年折旧额/12 [例10]甲企业某项固定资产原价为50000元，预计使用年限为10年，预计残值收入为3000元，预计清理费用为1000元，则： 固定资产年折旧额＝[50000-（3000-1000）]/10＝4800元/年 固定资产月折旧额＝(4800÷12)＝400元／月 在实际工作中，为了反映固定资产在一定时间内的损耗程度和便于计算折旧，企业每月应计提的折旧额一般是根据固定资产的原价乘以月折旧率计算确定的。固定资产折旧率是指

一定时期内固定资产折旧额与固定资产原价之比。其计算公式表述如下： 固定资产年折旧率＝[（固定资产原价-预计净残值）÷固定资产原价] ÷固定资产预计使用年限 ＝（1-预计净残值率）÷固定资产预计使用年限 固定资产月折旧率＝固定资产年折旧率÷12 固定资产月折旧额＝固定资产原价×固定资产月折旧率 依例10，固定资产月折旧额的计算如下： 固定资产年折旧率＝[50000-（3000-1000）]÷（10×50000）＝9.6％ 固定资产月折旧率＝9.6％÷12＝0.8％ 固定资产月折旧额＝50000元×0.8％＝400元 上述计算的折旧率是按个别固定资产单独计算的，称为个别折旧率，即某项固定资产在一定期间的折旧额与该项固定资产原价的比率。此外，还有固定资产分类折旧率和综合折旧率。 固定资产的分类折旧率是指固定资产分类折旧额与该类固定资产原价的比例。采用这种方法，应先把性质、结构和使用年限接近的固定资产归纳为一类，再按类别计算平均折旧率。固定资产分类折旧率的计算公式如下： 某类固定资产年折旧率=该类固定资产年折旧额÷该类固定资产原价 固定资产的综合折旧率是指某一期间企业全部固定资产折旧额与全部固定资产原价的比例。固定资产综合折旧率的计算公式如下： 固定资产年综合折旧率=∑（各项固定资产年折旧额）÷∑各项固定资产原价 (二)工作量法 工作量法是根据实际工作量计提折旧额的一种方法。其基本计算公式为： 每一工作量折旧额=[固定资产原价×（1-净残值率）]÷预计总工作量 某项固定资产月折旧额=该项固定资产当月的工作量×每一工作量折旧额 [例11]某公司有货运卡车一辆，原价为150000元，预计净残值率为5％，预计总行驶

比较好的计算公式如下

比较好的计算公式如下 =DATEDIF(B2,TODAY(),"y")&"年"&DATEDIF(B2,TODAY(),"ym")&"月"&DATEDIF(B2,TODAY(),"md")&"天" 前提:保证B2是日期型的. 公式中的引用要改为B2 例如： 实际工龄的计算公式为 =DATEDIF(A2,B2-DATEDIF(C2,D2,"d"),"y")&"年"&ROUNDUP(DATEDIF(A2,B2-DATEDIF(C2,D2,"d"),"ym"),1)&"个月"&ROUNDUP(DATEDIF(A2,B2-DATEDIF(C2,D2,"d"),"md"),1)&"日" DATEDIF函数，计算两个日期之间的天数、月数或年数。 语法：DATEDIF(Start_Date,End_Date,Unit)。 Start_Date——为一个日期，它代表时间段内的第一个日期或起始日期； End_Date——为一个日期，它代表时间段内的最后一个日期或结束日期；Unit——为所需信息的返回类型。 参数可以是： "y":计算周年 "m":计算足月 "d":计算天数 "ym":计算除了周年之外剩余的足月 "yd":计算除了周年之外剩余的天数 "md":计算除了足月之外剩余的天数 如：DATEDIF(today()-5,today(),"D") 说明 日期是作为有序序列数进行存储的，因此可将其用于计算。默认情况下，1899 年12 月 31 日的序列数为 1，而 2008 年 1 月 1 日的序列数为 39448，因为它是 1900 年 1 月 1 日之后的第 39,448 天。

DATEDIF 函数在需要计算年龄的公式中很有用。 示例 Start_date End_date 公式说明（结果） 2001-1-1 2003-1-1 DATEDIF(Start_date,End_date,"Y") 这段时期经历了两个完整年 (2) 2001-6-1 2002-8-15 DATEDIF(Start_date,End_date,"D") 2001 年 6 月 1 日和 2002 年 8 月 15 日之间有 440 天 (440) 2001-6-1 2002-8-15 DATEDIF(Start_date,End_date,"YD") 6 月 1 日和 8 月15 日之间有 75 天，忽略日期的年数 (75) 2001-6-1 2002-8-15 DATEDIF(Start_date,End_date,"MD") 1 和15（start_date 的天数和 end_date 的天数）之间相差的天数，忽略日期的月数和年数 (14) 另外：可以如下计算 1.将格式-单元格-数字-分类-日期中选择----------------保证是日期型的 2.=TEXT(A2-A1,"Y年零M个月"),A2,A1是你的两个日期(这种计算方法缺点是：多一天也按照一个月计算）

单利终值的一般计算公式为

单利终值的一般计算公式为： ，单利现值的一般计算分式为： 其中是单利情况下的现值系数。 复利现值的一般计算公式为： 公式中（1+i）n和 年金终值的一般计算公式为： 偿债基金的计算也就是年金终值的逆算。其计算公式如下： 年金现值的一般的计算公式为： 年资本回收额（已知年金现值PVA0,求年金A） =PVA0×i/[1-（1+i）-n] 先付年金终值计算 （1）V n=A×FVIFA i，n×（1+i），（2）V n=A×FVIFA i，n+1-A=A×[（F/A，i，n+1）-1] 递延年金现值的计算 =A×PVIFA i，n×PVIF i，m=A×（P/A，i，n）×（P/A，i，m）2. V0=A×PVIFA i，m+n-A×PVAFA i，m 永续年金是指无期限支付的年金。V0=A×预期收益 1.标准离差应得风险收益率=风险价值系数b×标准离差率V 因素分析法的公式如下： 资本需要量＝（上年资本实际平均占用量－不合理平均占用额） ×（1±预测年度销售增减率） ×（1±预测期资本周转速度变动率） 预测外部筹资额的公式如下： 需要追加的外部筹资额＝＝ 新股发行价格的计算：股票发行价格=溢价倍数×每股面值。 （1）分析法 （2）综合法 （3）市盈率法 每股价格=市盈率×每股面值 市盈率=每股市价÷每股收益 银行借款的筹资成本应是企业实际支付的利息，其相对数则应是实际利率。 实际利率=借款人实际支付的利息/借款人所得的借款 ①按复利计算。如复利按年计算，借款年限为n，则实际单利率的换算公式为： 按复利计息 年限为n，名义利率为i，实际单利利率为k（贷款额为P） 则 2）一年内分次计算利息的复利。如年利率为k，一年分m次计息，则实际年利率为： 采用贴现利率计息情况下，实际利率k的计算：k=i/（1-i） ③采用补偿性余额贷款情况下，求R=?

财务管理计算公式

A时间价值的计算 B各系数之间的关系：

C风险衡量 D风险收益率 风险收益率是指投资者因冒风险进行投资而要求的、超过资金时间价值的那部分额外的收益率。风险收益率、风险价值系数和标准离差率之间的关系可用公式表示如下： RR＝b·V 式中：RR为风险收益率；b为风险价值系数；V为标准离差率。 在不考虑通货膨胀因素的情况下，投资的总收益率(R)为： R＝RF＋RR＝RF+b·V 上式中，R为投资收益率；RF为无风险收益率。其中无风险收益率RF可用加上通货膨胀溢价的时间价值来确定，在财务管理实务中，一般把短期政府债券(如短期国库券)的收益率作为无风险收益率。 E比率预测法（重点） 比率预测法是依据有关财务比率与资金需要量之间的关系预测资金需要量的方法。 1、常用的比率预测法是销售额比率法，这是假定企业的变动资产与变动负债与销售收入之间存在着稳定的百分比关系。 大部分流动资产是变动资产（如现金、应收账款、存货），固定资产等长期资产视不同情况而定，当生产能力有剩余时，销售收入增加不需要增加固定资产；当生产能力饱和时，销售收入增加需要增加固定资产，但不一定按比例增加。部分流动负债是变动负债（随销售收入变动而变动，如应付费用、应付账款）。 外部筹资额＝预计资产增加－预计负债自然增加－预测期留存收益 预计资产增加△变动资产＝△收入×变动资产占销售百分比＝△S×A/S1＝△S/S1×A △非变动资产（如固定资产） △变动负债＝△收入×变动负债占销售百分比 ＝△S×B/S1＝△S/S1×B 预测期留存收益＝预计的收入×预计销售净利率×留存收益率＝S2·P·E 外部筹资额＝△S×A/S1－△S×B/S1－S2·P·E＋△非变动资产 2、销售额比率法解题步骤 （1）分别确定随销售收入变动而变动的资产合计A和负债合计B（变动资产和变动负债）。 （2）用基期资料分别计算A和B占销售收入（S1）的百分比，并以此为依据计算在预测期销售收入（S2）水平下资产和负债的增加数（如有非变动资产增加也应考虑）。 （3）确定预测期收益留存数（预测期销售收入×销售净利率×收益留存比例，即S2·P·E）。（4）确定对外界资金需求量： 外界资金需求量＝A/S·△S－B/S1·△S－S2·P·E＋△非变动资产 F资金习性预测法（重点） 资金习性预测法是根据资金习性预测未来资金需要量的一种方法。所谓资金习性，是指资金变动与产销量之间的依存关系。按照资金习性可将资金分为不变资金、变动资金和半变动资金。

工程经济计算公式顺口溜

一级建造师《建设工程经济》计算公式汇总 1、单利计算 单i P I t ?= 式中 I t ——代表第t 计息周期的利息额；P ——代表本金；i 单——计息周期单利利率。 2、复利计算 1-?=t t F i I 式中 i ——计息周期复利利率；F t-1——表示第（t －1）期末复利本利和。 而第t 期末复利本利和的表达式如下： ) 1(1i F F t t +?=- 3、一次支付的终值和现值计算 ①终值计算（已知P 求F 即本利和） n i P F )1(+= ②现值计算（已知F 求P ） n n i F i F P -+=+= )1() 1( 4、等额支付系列的终值、现值、资金回收和偿债基金计算 等额支付系列现金流量序列是连续的，且数额相等，即： ） ，，，，常数（n t A A t 321=== ①终值计算（即已知A 求F ） i i A F n 11-+=）（ ②现值计算（即已知A 求P ） n n n i i i A i F P ）（）（）（+-+=+=-1111 ③资金回收计算（已知P 求A ） 111-++=n n i i i P A ）（）（ ④偿债基金计算（已知F 求A ） 1 1-+=n i i F A ）（ 5、名义利率r 是指计息周期利率：乘以一年内的计息周期数m 所得的年利率。即：m i r ?= 6、有效利率的计算 包括计息周期有效利率和年有效利率两种情况。 （1）计息周期有效利率，即计息周期利率i ，由式（1Z101021）可知： m r I = （1Z101022-1） （2）年有效利率，即年实际利率。 年初资金P ，名义利率为r ，一年内计息m 次，则计息周期利率为 m r i = 。