

REVIEW ARTICLE 

Year : 2018  Volume
: 5
 Issue : 2  Page : 4953 

A comparative analysis of formulae used for the estimation of glomerular filtration rate to determine the kidney function test in patients with chronic kidney disease
Prabhat Agrawal, Ashish Gautam, Nikhil Pursnani, Maaz Farooqui, Jitendra Doneria
Department of Medicine, S. N. Medical College, Agra, Uttar Pradesh, India
Date of Web Publication  11Oct2018 
Correspondence Address: Dr. Prabhat Agrawal Department of Medicine, S. N. Medical College, D1, Sulahkul Nagar, Bodla Road, Agra, Uttar Pradesh India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/jina.jina_6_18
There are many equations available for estimation of creatinine clearance, but regrettably, most of the formulae have many limitations. Prabhat's formula is a novel equation which provides appropriate values of creatinine clearance with the lesser or no limitations. The calculation can be done using the formula as follows: (i) CrCl = 100/(1.3 × S. Creatinine) × (0.8 if female) when age is between 30 and 40 years; (ii) CrCl = 100/(1.5 × S. Creatinine) × (0.8 if female) when age is between 41 and 50 years; and (iii) CrCl = 100/(1.8 × S. Creatinine) × (0.8 if female) if age >51 years. On the other hand, it is evident that using Prabhat's formula the calculated creatinine clearance is quite similar to the one that we get using other formulae for the same. Unlike other methods, this equation has no such limitations. The formula is quite reliable for calculating the creatinine clearance and estimating the kidney function test. However still, future studies with this formula in this field are very important and should focus on issues such as the elderly patients with decreased GFR and modification of this formula to get more accurate results.
Keywords: Cockroft–Gault equation, creatinine clearance, glomerular filtration rate, modification of diet in renal disease, Prabhat's formula
How to cite this article: Agrawal P, Gautam A, Pursnani N, Farooqui M, Doneria J. A comparative analysis of formulae used for the estimation of glomerular filtration rate to determine the kidney function test in patients with chronic kidney disease. J Integr Nephrol Androl 2018;5:4953 
How to cite this URL: Agrawal P, Gautam A, Pursnani N, Farooqui M, Doneria J. A comparative analysis of formulae used for the estimation of glomerular filtration rate to determine the kidney function test in patients with chronic kidney disease. J Integr Nephrol Androl [serial online] 2018 [cited 2019 Apr 23];5:4953. Available from: http://www.journalina.com/text.asp?2018/5/2/49/243122 
Introduction   
Kidneys are the major excretory organs which remove metabolic wastes through urine. Exposure to the plethora of chemicals that harm the kidneys, medications, natural products, industrial chemicals, environmental pollutants, pesticides, and other chemicals cause damage to different organs of the body at various levels. In addition, certain disease conditions such as diabetes mellitus, systemic lupus erythematosus, and hypertension lead to nephropathy. These causative agents and disease conditions impairs the Glomerular Filteration Rate (GFR) and thus increase the creatinine level in urine.^{[1],[2]}
Creatinine is secreted by the proximal tubule as well as filtered by the glomerulus. As a result, it goes beyond GFR. Creatinine clearance can be measured from creatinine excretion and serum creatinine or by estimation of serum creatinine using proper equations. Measurement of creatinine clearance requires the collection of a timed urine sample. GFR in chronic renal disease remains <60 mL × min^{–1} per 1.73 m^{2} body surface area; for at least 3 months, regardless to the presence of cause of kidney damage.^{[3]} Patients with renal damage and albuminuria suffering from nephropathy reported having GFR >60. Patients without signs of kidney damage whose GFR is >60 are highly unlikely to be nephropathic.^{[4]} A thorough assessment of GFR requires the estimation of renal clearance of an exogenous chemical or marker which can filter freely through the kidney, and should not undergo metabolism, and tubular secretion or absorption. Inulin is the example of such chemical. As inulin clearance gives the most precise method of measuring GFR, which is unsuitable for routine clinical practice. Some radiolabeled compounds (125Iiothalamate and 99 mTcdiethylenetriaminepentaacetic acid) provide accurate and precise GFR measurements, but they are not suggested for human use. To protect patients from radiation exposure, researchers have projected clearance procedures using minute doses of nonradioactive contrast agents, including iothalamate (ionic) and iohexol (nonionic). This approach provides similar accuracy to that of inulin clearance.^{[5]}
Moreover, to avoid the disadvantage of radiolabeled compounds, the concept of creatinine clearance arisen. Serum creatinine and calculated creatinine clearance yield a reasonable estimation of renal function with minimal cost and inconvenience. Urinary creatinine clearance is more accurate if the urine collection is complete. The normal creatinine clearance test value is 110–150 mL/min in male and in the female, it is 100–130 mL/min.^{[6]} Creatinine clearance (CrCl) is calculated from the creatinine concentration in the collected urine sample (UCr), urine flow rate (V), and the plasma concentration (PCr). The product of, urine concentration of creatinine and flow rate of urine, expresses the creatinine excretion rate, the rate of removal of creatinine from the blood. The CrCl is calculated as the removal rate per min (UCr × V) divided by the plasma creatinine concentration.^{[7]}
 Creatinine clearance CrCl = (Ucr × V)/Pcr.
Over again, GFR calculation using empirical mathematical formulae has been confident as an easy, fast, and dependable means of measuring kidney function. Several GFR forecast equations that take into account the serum creatinine, albumin, and certain patient variables (age, gender, and body weight) have been shown to generate sufficiently precise, unbiased, and easily calculated estimates of GFR although.^{[8],[9]} There are no fewer than 46 different prediction equations currently available, although the two most commonly used are the “Cockcroft–Gault” (CG) and the “modification of diet in renal disease” (MDRD) formulae.
We have introduced a novel method called Prabhat's formula. Prabhat's formula provides fairly accurate values of creatinine clearance. The main advantage of this formula is that it that makes the CrCl easy to calculate and therefore can be done by oneself and used in the outpatient department basis independent of other parameters, a calculator or a computer. Hence, the aim of the review is to compare and consolidate the advantages of Prabhat's formula over other creatinine clearance formulae.
Conventional Formulas for Estimation of Creatinine Clearance and their Limitation   
Cockroft–Gault equation
The Cockroft–Gault (CG) formula was developed in the year 1973 using the obtained data from 249 men with creatinine clearance (CCr) from approximately 30–130 mL/m^{2}. It is not adjusted for body surface area. This formula is no longer recommended for use because it has not been expressed using standardized creatinine values.^{[10]}
The CG equation is as follows:
 CCr = ([l40–age] × weight]/[72 × SCr]) × 0.85 (if female)
 where CrCl is creatinine clearance and SCr is serum creatinine.
 CCr (creatinine clearance) = mL/min
 Age = years
 Weight = kg
 SCr (serum creatinine) = mg/dL.
For women, the above equation should be multiplied by 0.85. In cases of persons of extreme weights, some have used lean body mass, whereas others have used correction of the CrCl to average body surface area. Some other limitations^{[11]} of this method are given below:
 Renal or extrarenal conditions affecting the steady state of creatinine in plasma. For example, the serum creatinine is fluctuating or a recovering frail cachectic elderly person
 Interference with creatinine's assay. For example, ketones, glucose, and medications such as cephalosporins interfering with the assay
 Variations in muscle mass or diet. For example, extremes of body mass, pure vegetarian diet, or proteinrich diet or amputees
 Values not adjusted for body surface area. For example, loss of precision in obese individuals.
Modification of diet in renal disease
The original equation was derived from a study of 1628 middleaged, nondiabetic, chronic renal insufficiency patients that used a directly measured GFR by urinary clearance of 125 iothalamate.^{[12]} It has quite a few advantages over the CG equation including providing an estimate of GFR rather than creatinine clearance, and a greater percentage of these estimates are within the clinically useful range for decisionmaking: 90% of the MDRD based estimates were within 30% of the measured GFR compared with about 75% of CGbased estimates. However, the MDRD equation also has several limitations including that it is less accurate at levels above 60 mL/min per 1.73 m^{2}. As a result, it may lead to misdiagnosis and misclassification of CKD in patients suffering from mild renal insufficiency.^{[13]}
The MDRD equation is as follows:
GFR (mL/min/1.73 m^{2}) =175× (Scr) − 1.154× (Age) − 0.203× (0.742 if female) × (1.212 if AfricanAmerican)
This equation does not depend on body weight or height variables as the result derived from this are tared to conventional average adult surface area i.e. 1.73 m^{2} body surface area.
The equation has been validated extensively in Caucasian and AfricanAmerican populations between the ages of 18 and 70 with impaired kidney function (GFR < 60 mL/min/1.73 m2) and has shown good performance for patients with all common causes of kidney disease.^{[14]} Some other limitations^{[11]} of this method are given below;
 Reliability and accuracy decreased in extremes of GFR. For example, healthy adults and dialysis patients
 Lack of validation studies in some ethnic groups
 Drugs dosing for the patients suffering from renal diseases was widely published based on creatinine clearance even before the origin of MDRD and is not adapted to it yet.
Mayo clinic quadratic formula
Mayo clinic quadratic (MCQ) was developed by Rule et al.^{[15]} to better estimate GFR in patients with preserved kidney function because the MDRD formula tends to undervalue GFR in such patients.
The equation is as follows:
CrCl = exp (1.911+ [5.29/S. Cr] − [2.114/S. Cr2] − [0.00686 × age] − [0.205 if female])
If serum creatinine is < 0.8 mg/dL, the value 0.8 mg/dL should be used.
Limitations
This MCQ formula equation proved inaccurate (excessive underestimation) in type 2 diabetic patients with hyperfiltration or normal renal function. With regard to chronic kidney disease (CKD), the results obtained provided no evidence of the superiority of the MCQ over the MDRD or the CG formula.^{[16]}
Chronic kidney disease epidemiology collaboration equation
The CKD epidemiology collaboration (CKDEPI) equation uses a twoslope “spline” to model the relationship between GFR and serum creatinine, age, sex, and race. CKDEPI equation expressed as a single equation:
GFR = 141 × min (Scr/κ, 1)α × max (Scr/κ, 1) − 1.209 × 0.993 Age × 1.018 (if female) ×1.159 (if black) where
 Scr is serum creatinine in mg/dL
 κ is 0.7 for females and 0.9 for males
 α is −0.329 for females and −0.411 for males
 min indicates the minimum of Scr/κ or 1, and max indicates the maximum of Scr/κ or 1.
Limitations of the chronic kidney disease epidemiology collaboration equations
Limitations using creatinine as a filtration marker
 CKDEPI equations are based on serum creatinine. Despite a modest reduction in bias with the CKDEPI equation, estimates remain imprecise, with some people showing large differences between the measured and estimated GFR. As with other equations in this equitation, patients suffer from physiological limitations of creatinine as a filtration marker.^{[17],[18]} The terms for age, sex, and race in both equations only capture some of the nationGFR determinants of creatinine concentration in blood plasma, and the coefficients represent average effects observed in the population used to develop the equations
 All estimates of GFR based on serum creatinine will be less accurate for patients at the extremes of muscle mass (including frail elderly, critically ill, or cancer patients), those with unusual diets, and those with conditions associated with reduced secretion or extrarenal elimination of creatinine. Confirmatory tests with exogenous measured GFR or measured creatinine clearance should be performed for people in whom estimates based on serum/plasma/blood creatinine alone may be inaccurate
 Populations were not well represented in the validation cohort study. For example, older adults and other racial communities with higher levels of GFR, racial and ethnic minorities other than blacks
 The influence of creatinine measurement imprecision at low creatinine concentrations (high GFR) has not been carefully studied but has likely contributed to the variability at higher GFR values.
Schwartz formula
This formula is especially used in children.^{[19]} The equation expressed as a single equation: CrCl = (k × height in cm)/S. Cr where k is a constant that depends on muscle mass, which varies with a child's age: For the first year, for preterm babies, K = 0.33 and for fullterm infants, K = 0.45 For infants and children of age 1–12 years, K = 0.55.
Prabhat's formula
The equation Prabhat's formula is expressed as:
 CrCl = 100/(1.3 × S. Creatinine) × (0.8 if female) if age is between 30 and 40 years
 CrCl = 100/(1.5 × S. Creatinine) × (0.8 if female) if age is between 41and 50 years
 CrCl = 100/(1.8 × S. Creatinine) × (0.8 if female) if age >51 years.
This formula is not valid for the age below 30 years (CKD is rare below this age group) and is only applicable to the patients with chronic renal failure. Since the normal values of GFR are around 100 for women and 120 for men, the numerator as 100 is taken in the equation of Prabhat's formula. It is divided by a denominator according to the age bracket in which he/she falls.^{[20]}
The utility of the equation has been reported using the following examples,^{[20]} by comparing the results obtained with it to the standard formula used to calculate the creatinine clearance.
Example 1 – A 60yearold male with CRF weighing 50 kg with a serum creatinine of 4 mg/dL creatinine clearance of that male would come out to be: (i) CG 13.89 mL/min, (ii) MDRD 16.4 mL/min, and (iii) Prabhat's formula 13.88 mL/min.
Example 2 – A 45yearold female with CRF weighing 45 kg with a serum creatinine of 10 mg/dL. Creatinine clearance of that female would come out to be: (i) CG 5 mL/min (ii) MDRD 4.5 mL/min, and (iii) Prabhat's formula 5.33 mL/min.
Example 3 – A 33yearold male with CRF, weighing 52 kg with a serum creatinine of 9 mg/dL Creatinine clearance of that male would come out to be: (i) CG 8.6 mL/min, (ii) MDRD 7.2 mL/min, and (iii) Prabhat's formula 8.54 mL/min.
Thus, it is evident that using Prabhat's formula, the calculated creatinine clearance is quite similar to the one that we get using another formula for the same.
Moreover, this equation has certain other advantages such as:
 The specific formula for every age group
 No interference with creatinine's assay
 Variations in muscle mass or diet fluctuation of creatinine clearance are lesser
 Better reliability and accuracy
 Creatinine clearance by this formula can be calculated by oneself by the easy way even without using a calculator or a computer.
Conclusion   
GFR is the best directory available to measure kidney function, which is creatinine based. There are some limitations with conventional and conservative methods of creatinine clearance estimation, particularly in elderly patients because the variables affecting creatinine tend to be more marked because of comorbid circumstances. At present, MDRD is an extensively used method to estimate GFR in elderly persons, but this method has many drawbacks. It is evident that using our formula (Prabhat's formula), the calculated creatinine clearance is quite similar to the one that we get using another formula for the same. Unlike other methods, this equation has no such limitations. Creatinine clearance by this formula can be calculated by oneself by the easy way of using a calculator or a computer. However still, future studies with this formula in this field are very important and should focus on issues such as the elderly patients with decreased GFR and modification of this formula to get more accurate results.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
References   
1.  Van Vleet TR, Schnellmann RG. Toxic nephropathy: Environmental chemicals. Semin Nephrol 2003;23:5008. 
2.  Cooper ME. Pathogenesis, prevention, and treatment of diabetic nephropathy. Lancet 1998;352:2139. 
3.  National Kidney Foundation. K/DOQI clinical practice guidelines for chronic kidney disease: Evaluation, classification, and stratification. Am J Kidney Dis 2002;39:S1266. 
4.  Coresh J, Astor BC, Greene T, Eknoyan G, Levey AS. Prevalence of chronic kidney disease and decreased kidney function in the adult US population: Third national health and nutrition examination survey. Am J Kidney Dis 2003;41:12. 
5.  Gaspari F, Perico N, Remuzzi G. Measurement of glomerular filtration rate. Kidney Int Suppl 1997;63:S1514. 
6.  Corbett JV, editor. Chapter 4: Renal Function Tests Laboratory Tests and Diagnostic Procedures with Nursing Diagnoses. Upper Saddle River: University of San Francisco; 2008. p. 90107. 
7.  Kim KE, Onesti G, Ramirez O, Brest AN, Swartz C. Creatinine clearance in renal disease. A reappraisal. Br Med J 1969;4:114. 
8.  Jones G, EeMun L. The national kidney foundation guideline on estimation of the glomerular filtration rate. Clin Biochem Rev 2003;24:958. 
9.  Giles PD, Fitzmaurice DA. Formula estimation of glomerular filtration rate: Have we gone wrong? BMJ 2007;334:1198200. 
10.  Cockcroft DW, Gault MH. Prediction of creatinine clearance from serum creatinine. Nephron 1976;16:3141. 
11.  Pedone C, Corsonello A, Incalzi RA, GIFA Investigators. Estimating renal function in older people: A comparison of three formulas. Age Ageing 2006;35:1216. 
12.  Levey AS, Bosch JP, Lewis JB, Greene T, Rogers N, Roth D, et al. A more accurate method to estimate glomerular filtration rate from serum creatinine: A new prediction equation. Modification of diet in renal disease study group. Ann Intern Med 1999;130:46170. 
13.  Froissart M, Rossert J, Jacquot C, Paillard M, Houillier P. Predictive performance of the modification of diet in renal disease and Cockcroft–Gault equations for estimating renal function. J Am Soc Nephrol 2005;16:76373. 
14.  Levey AS, Stevens LA, Schmid CH, Zhang YL, Castro AF 3 ^{rd}, Feldman HI, et al. A new equation to estimate glomerular filtration rate. Ann Intern Med 2009;150:60412. 
15.  Rule AD, Larson TS, Bergstralh EJ, Slezak JM, Jacobsen SJ, Cosio FG, et al. Using serum creatinine to estimate glomerular filtration rate: Accuracy in good health and in chronic kidney disease. Ann Intern Med 2004;141:92937. 
16.  Fontseré N, Bonal J, Salinas I, de Arellano MR, Rios J, Torres F, et al. Is the new mayo clinic quadratic equation useful for the estimation of glomerular filtration rate in type 2 diabetic patients? Diabetes Care 2008;31:22657. 
17.  Shemesh O, Golbetz H, Kriss JP, Myers BD. Limitations of creatinine as a filtration marker in glomerulopathic patients. Kidney Int 1985;28:8308. 
18.  Rule AD, Bailey KR, Schwartz GL, Khosla S, Lieske JC, Melton LJ 3 ^{rd}, et al. For estimating creatinine clearance measuring muscle mass gives better results than those based on demographics. Kidney Int 2009;75:10718. 
19.  Schwartz GJ, Feld LG, Langford DJ. A simple estimate of glomerular filtration rate in fullterm infants during the first year of life. J Pediatr 1984;104:84954. 
20.  Agarwal A, Agrawal P, Bansal M, Singh O. An OPD basis formula for calculating creatinine clearance. Int J Med Appl Sci 2013;2:16974. 
