Equations for Estimating Creatinine Clearance or GFR
Considerations and Variations of Creatinine Clearance
Cockcroft-Gault 1976^{1}
The Cockcroft-Gault equation has been the standard method of estimating renal function (via creatinine clearance) for drug dosing for decades. Although some newer medications are now using eGFR (via the CKD-EPI equation) for renal dose adjustment, the vast majority of medications on the market still use Cockcroft-Gault.
The original study was based on data from 249 male patients with stable renal function. The study used actual body weight, but mentioned that a correction factor of some kind should be used in patients with marked obesity or ascites:
$$
\\ CrCl\;(mL/min) =\frac{(140-Age)*(WeightInKg)}{72*SCr} *0.85\;(if\;female)
$$
The following body weight measures are used for the Cockcroft-Gault equation to provide the most accurate estimate of renal function:^{2}
Actual Body Weight / Ideal Body Weight |
Weight for Cockcroft-Gault |
< 1 |
Actual body weight |
1 to 1.25 |
Ideal body weight |
> 1.25 (or BMI > 30 kg/m^{2}) |
Adjusted body weight |
CKD-EPI 2021^{3}
The 2009 CKD-EPI equation included race (Black vs. non-Black) as a variable in the eGFR equation because previous studies indicated that Black patients had a higher average serum creatinine level for the same measured GFR. Because race is a social and not a biological construct (and may contribute to systemic racism in medicine), this 2021 update to the CKD-EPI equation was developed specifically to NOT include race as part of the eGFR estimate. Prior to this publication, some institutions were assigning "non-Black" to all patients regardless of race, which may have reduced eGFR accuracy.
The 2021 updated equation was developed using previous CKD-EPI data sets and validated against 12 studies of 4,050 participants, of which included about 14% Black patients. Within the validation data set, the older 2009 CKD-EPI equation overestimated eGFR by 3.7 mL/min/1.73 m^{2} (95% CI 5.4 to 1.8) among Black patients, meaning the equation resulted in a number that as a median was 3.7 points higher than the true eGFR. In contrast, the older 2009 CKD-EPI equation had nearly no bias (overestimate of 0.5 mL/min/1.73 m^{2}, 95% CI 0 to 0.9) among non-Black patients. When the older 2009 CKD-EPI equation was used with a "non-Black" value assigned to Black patients, it resulted in more error (an underestimate of 7.1 mL/min/1.73 m^{2}, 95% CI 5.9 to 8.8). The 2021 CKD-EPI equation (which was designed to not incorporate race at all) on average underestimated eGFR in Black patients by 3.6 mL/min/1.73 m^{2} (95% CI 1.8 to 5.5) and overestimate eGFR in non-Black patients by 3.9 mL/min/1.73 m^{2} (95% CI 3.4 to 4.4). The authors did develop cystatin C-based equations, which resulted in better eGFR estimates; however, cystatin C is not a commonly available lab in many areas of clinical practice.
$$
\\ GFR\;(mL/min/1.73\;m^2) = \\ \hspace{5pt} Females\;with\;SCr\;≤\;0.7\;mg/dL: 142 * (SCr/0.7)^{-0.241} * 0.9938^{Age} * 1.012\\ \hspace{5pt} Females\;with\;SCr\;>\;0.7\;mg/dL: 142 * (SCr/0.7)^{-1.2} * 0.9938^{Age} * 1.012\\ \hspace{5pt} Males\;with\;SCr\;≤\;0.9\;mg/dL: 142 * (SCr/0.9)^{-0.302} * 0.9938^{Age}\\ \hspace{5pt} Males\;with\;SCr\;>\;0.9\;mg/dL: 142 * (SCr/0.9)^{-1.2} * 0.9938^{Age}
$$
DEPRECATED
CKD-EPI 2009^{4}
The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was developed as a follow-up to the MDRD equation to improve accuracy among patients with a higher GFR (> 60 mL/min/1.73 m^{2}). The CKD-EPI equation was developed and validated retrospectively in 8,254 patients from 10 studies. The study included all patients age > 20 years old who were not pregnant and did not have renal failure (eGFR < 15 mL/min/1.73 m^{2}). The data set included 45% women and 87% non-Black patients. This equation is no longer recommended and has been replaced by CKD-EPI 2021.
$$
\\ GFR\;(mL/min/1.73\;m^2) =\\ \hspace{5pt} Black\;females,\;SCr\;\le\;0.7\;mg/dL: 166 * (SCr/0.7)^{-0.329} * (0.993)^{Age}\\ \hspace{5pt} Black\;females,\;SCr\;>\;0.7\;mg/dL: 166 * (SCr/0.7)^{-1.209} * (0.993)^{Age}\\ \hspace{5pt} Black\;males,\;SCr\;\le\;0.9\;mg/dL: 163 * (SCr/0.9)^{-0.411} * (0.993)^{Age}\\ \hspace{5pt} Black\;males,\;SCr\;>\;0.9\;mg/dL: 163 * (SCr/0.9)^{-1.209} * (0.993)^{Age}\\ \hspace{5pt} Non-Black\;females,\;SCr\;\le\;0.7\;mg/dL: 144 * (SCr/0.7)^{-0.329} * (0.993)^{Age}\\ \hspace{5pt} Non-Black\;females,\;SCr\;>\;0.7\;mg/dL: 144 * (SCr/0.7)^{-1.209} * (0.993)^{Age}\\ \hspace{5pt} Non-Black\;males,\;SCr\;\le\;0.9\;mg/dL: 141 * (SCr/0.9)^{-0.411} * (0.993)^{Age}\\ \hspace{5pt} Non-Black\;males,\;SCr\;>\;0.9\;mg/dL: 141 * (SCr/0.9)^{-1.209} * (0.993)^{Age}
$$
DEPRECATED
Jelliffe 1973 (stable renal function)^{5}
Published as a "Letter to the Editor", the Jelliffe equation does not require a patient's height or weight because it describes renal function normalized to a body surface area of 1.73 m^{2}. While this was a landmark equation for its era, its use has become deprecated in favor of other equations, such as Cockcroft-Gault.
$$
\\ CrCl\;(mL/min/1.73\;m^2) = \frac{98 - 16*(\frac{Age-20}{20})}{SCr} * 0.9\;(if\;female)
$$
DEPRECATED
Salazar-Corcoran 1988^{6}
This equation was specifically designed to measure creatinine clearance in obese patients (defined as a BMI ≥ 30 m^{2}). The equation is derived from a "fat free mass" equation and was shown to be superior to the Cockcroft-Gault and Jelliffe methods when using actual body weight. Although interesting for historical reasons, the Salazar-Corcoran method has largely become deprecated in favor of the Cockcroft-Gault method with a body weight adjustment, such as the 40% adjustment factor equation.
$$
\\ CrCl\;(for\;men\;,\;mL/min)\;=\\ \hspace{5pt} \frac{(137-Age)*((0.285*WeightInKg) + (12.1*HeightInMeters^2) )}{51*SCr}\\ CrCl\;(for\;women,\;mL/min)\;=\\ \hspace{5pt} \frac{(146-Age)*((0.287*WeightInKg) + (9.74*HeightInMeters^2) )}{60*SCr}
$$
DEPRECATED
MDRD (four-variable)^{7}^{,}^{8}
The MDRD equation was originally developed in 1999^{9} as a six-variable equation, but was later updated to a simpler, four-variable equation in two variations (to reflect the conventional and IDMS laboratory methods). The MDRD equation was one of the first equations that was developed using a large patient data set that was more accurate than the Cockcroft-Gault method; however, MDRD was only studied in patients with renal impairment (GFR < 60 mL/min/1.73 m^{2}), and therefore it should not be used in patients with normal renal function. For this reason, the MDRD equation has become deprecated in favor of the CKD-EPI equations, which were developed similarly to the MDRD equation, but are able to accurately describe GFR in patients without renal dysfunction.
$$
\\ For\;IDMS-calibrated\;assays:\\ GFR\;(mL/min/1.73\;m^2) = 175 * (SCr)^{-1.154} * (Age)^{-0.203} \\ \hspace{5pt} * (0.742\;if\;female) \\ \hspace{5pt} * (1.210\;if\;Black)\\ \\ For\;non-IDMS\;assays:\\ GFR\;(mL/min/1.73\;m^2) = 186 * (SCr)^{-1.154} * (Age)^{-0.203} \\ \hspace{5pt} * (0.742\;if\;female) \\ \hspace{5pt} * (1.210\;if\;Black)
$$
Equations for Estimating Unstable Renal Function
Most conventional, commonly used equations to estimate renal function require that patients have a stable renal function. Usually, this is defined as having two consecutive serum creatinine values, drawn at least 24 hours apart, with values within 20% of each other. Because many hospitalized patients do not have stable renal function, other equations have been developed to aid clinicians in estimating renal function for the purposes of drug dosing.
Equations have been proposed for estimating creatinine clearance in patients with acutely changing renal function (Jelliffe 1972^{10}^{,}^{11}, Chiou 1975^{12}, and Chen 2013^{13}). Because these equations are based on one-compartment pharmacokinetic equations, the renal function estimate is often abbreviated as KeGFR (kinetic estimate of glomerular filtration rate), although KeCrCl (kinetic estimate of creatinine clearance) is a more accurate term. These equations have been studied and validated in much smaller patient populations compared to steady state estimates of renal function (e.g. Cockcroft-Gault and CKD-EPI 2021).
Two older equations (Jelliffe 1972^{10}^{,}^{11} and Chiou 1975^{12}) have been compared to each other and have similar performance.^{14} Both equations are less accurate when renal function is improving (rather than worsening). This calculator uses a variant of the Jelliffe 1972 equation that assumes a slightly different volume of distribution (0.6 L/kg instead of 0.4 L/kg) and ideal body weight (instead of actual body weight).^{15}
The newest equation (Chen 2013^{13}) is by far the most studied in the literature.^{15} The original equation relied on historical data (baseline GFR and maximum production of SCr), which is often unavailable in critically ill patients. For that reason, a variation of the equation that does not rely on these historical data points has been used and has similar performance to the Jelliffe 1972 and Chiou 1975 equations.^{15}
$$
\\ CrCl\;(mL/min)=\frac{(Pr-V*10*\frac{(SCr_2-SCr_1)}{\Delta Time})*100}{(SCr_x)*1440}\\ Pr = SCr\;production\;rate\;(mg/day)\\ \hspace{10pt} Pr\;(men) = BodyWeight*(29.3-(0.203*Age))\\ \hspace{10pt} Pr\;(women) = BodyWeight*(25.3-(0.175*Age))\\ SCr_1 = Less\;recent\;SCr\;(mg/dL)\\ SCr_2 = More\;recent\;SCr\;(mg/dL)\\ SCr_x = SCr_2\;(if\;SCr\;is\;increasing)\;or\;\frac{SCr_1+SCr_2}{2}\;(if\;SCr\;is\;decreasing)\\ \Delta Time\;(days) = Time\;between\;SCr_1\;and\;SCr_2\;(days)\\ V = SCr\;volume\;of\;distribution\;(mL) = 0.6\;L/kg * BodyWeight\\ BodyWeight = Ideal\;body\;weight\;or\;actual\;body\;weight\;(whichever\;is\;less)
$$
$$
\\ CrCl\;(mL/min)=\frac{2*Pr}{(SCr_1+SCr_2)*0.01} + \frac{2*V*(SCr_1-SCr_2)}{(SCr_1+SCr_2)*(\Delta Time)} - k_{NR}*V\\ Pr = SCr\;production\;rate\;(mg/min)\\ \hspace{10pt} Pr\;(men) = BodyWeight*(28-(0.2*Age))*\frac{1}{1440}\\ \hspace{10pt} Pr\;(women) = BodyWeight*(22.4-(0.16*Age))*\frac{1}{1440}\\ SCr_1 = Less\;recent\;SCr\;(mg/dL)\\ SCr_2 = More\;recent\;SCr\;(mg/dL)\\ \Delta Time\;(min) = Time\;between\;SCr_1\;and\;SCr_2\;(hours)*60\\ k_{NR} = Non-renal\;elimination\;constant\;of\;SCr\;(min^{-1}) = 8 * 10^{-5}\;min^{-1}\\ V = SCr\;volume\;of\;distribution\;(mL) = 0.6\;L/kg * BodyWeight * 1000\\ BodyWeight = Ideal\;body\;weight\;or\;actual\;body\;weight\;(whichever\;is\;less)
$$
$$
\\ CrCl\;(mL/min) = \frac{Pr/24}{SCr_{avg}} * (1-\frac{SCr_2-SCr_1}{(max \Delta SCr)}*\frac{24}{\Delta Time})\\ Pr = SCr\;production\;rate\;(mg/day)\\ \hspace{10pt} Pr\;(men) = BodyWeight*(28-(0.2*Age))\\ \hspace{10pt} Pr\;(women) = BodyWeight*(22.4-(0.16*Age))\\ SCr_1 = Less\;recent\;SCr\;(mg/dL)\\ SCr_2 = More\;recent\;SCr\;(mg/dL)\\ SCr_{avg} = \frac{SCr_1+SCr_2}{2}\\ max \Delta SCr = \frac{Pr}{0.6*BodyWeight}*0.1\;or\;(SCr_2-SCr_1)\;(whichever\;is\;greater)\\ BodyWeight = Ideal\;body\;weight\;or\;actual\;body\;weight\;(whichever\;is\;less)\\ \Delta Time\;(hours) = Time\;between\;SCr_1\;and\;SCr_2\;(hours)
$$
Creatinine Clearance (CrCl) vs. Glomerular Filtration Rate (GFR/eGFR) vs. Kinetic Estimate of GFR (KeGFR)
Creatinine clearance (CrCl) is an estimate of glomerular filtration rate (GFR); however, CrCl is slightly higher than true GFR because creatinine is secreted by the proximal tubule (in addition to being filtered by the glomerulus). The additional proximal tubule secretion falsely elevates the CrCl estimate of GFR.^{16}
In clinical practice, GFR (glomerular filtration rate) and eGFR (estimated glomerular filtration rate) are essentially synonymous; the latter emphasizes that the GFR was estimated using equations such as CKD-EPI. Equations that estimate GFR/eGFR express GFR in mL/min/1.73 m^{2}. For the purposes of drug dosing or estimating GFR in patients with body size that is very different than average, GFR can be non-normalized using the following equation:^{16}
$$
\\ BSA = \sqrt{\frac{(HeightInCm * WeightInKg)}{3600}}
\\ GFR\;(mL/min) = GFR\;(mL/min/\;1.73\;m^2) * BSA / 1.73
$$
The kinetic estimate of GFR (KeGFR) is a term used to describe renal function in patients with unstable (acutely changing) serum creatinine values. Because the equations used to estimate KeGFR are based on a one-compartment pharmacokinetic model, the term "kinetic estimate" (Ke) is used. Although a more precise term would be KeCrCl (kinetic estimate of creatinine clearance), KeGFR is more commonly used in the literature.^{15}
Adjustment Factors for Female Gender
Many equations have an adjustment factor to account for the fact that female patients have less muscle mass, and therefore produce less creatinine. Historically, the Cockcroft-Gault and Jelliffe equations used an arbitrary value of 0.85 or 0.9 as a correction factor, but this value was largely based on empiric estimates with limited data. Newer data have shown that this correction factor is actually relatively accurate, with an "optimal" correction factor between 0.84 and 0.88 being the most appropriate for female patients.^{17}
Adjustment for Obesity^{2}
Obesity has been a long-standing problem in the estimation of renal function. Serum creatinine production is approximated based on lean body weight because muscle tissue (not fat) is responsible for creatine production. Furthermore, a change in total body mass does not increase the size of the kidney (or GFR) proportionally. Equations that do not correct or adjust for obesity risk overestimation of true renal function.
Using the Cockcroft-Gault equation with a 40% adjustment is the most appropriate method for estimating creatinine clearance in obese patients. In one of the largest studies on the topic to date of nearly 3,000 overweight and obese patients, the following conclusions can be drawn:^{2}
- Actual body weight will significantly overestimate renal function
- Ideal body weight will significantly underestimate renal function
- The LBW2005 equation, while initially very promising,^{18}^{,}^{19} significantly underestimates renal function.
- For all classes of obesity (overweight, obese, and morbid obesity), the Cockcroft-Gault equation with a 40% adjustment provided the most accurate estimate of creatinine clearance (often within about 5 mL/min of accuracy)
There are equations that report GFR as a normalized value to body surface area (mL/min/1.73 m^{2}). While these may appear to circumvent the issue of obesity, in most cases, these values need to be converted to a non-normalized GFR (mL/min) for the purposes of drug dosing. In the process of conversion, however, the non-normalized value will also overestimate GFR in obese patients.
Cockcroft-Gault 40% Obesity Adjustment
The most accurate equation for creatinine clearance in obese patients is the Cockcroft-Gault equation with a 40% adjustment factor.^{2} This equation is most appropriate for patients who are greater than 20-30% of their ideal body weight.^{20} In essence, this correction accounts for 40% of body mass above a patient's "ideal" body weight:
$$
\\ Adjusted\;weight = IdealBW + 0.4*(ActualBW-IdealBW)
$$
Ideal and Lean Body Weight (Devine 1974 and LBW2005)
Historically, the Devine 1974 equation^{21} has been used to estimate fat-free, ideal, or lean body weight (all terms generally meaning the same thing). This equation was not scientifically derived or validated,^{18} but is extensively used in medicine. A newer equation, called LBW2005^{22} was developed as an alternative estimate of lean body weight and has been derived and validated with actual patient data.
$$
\\ Ideal\;body\;weight\;(men)\; = 50 + 2.3*(height\;over\;60\;inches)
\\ Ideal\;body\;weight\;(women)\; = 45.5 + 2.3*(height\;over\;60\;inches)
$$
$$
\\ Lean\;body\;weight\;2005\;(men) = \frac{9.27*10^3*ActualBW}{6.68*10^3+(216*BMI)}
\\ Lean\;body\;weight\;2005\;(women) = \frac{9.27*10^3*ActualBW}{8.78*10^3+(244*BMI)}
$$
Rounding Creatinine in the Elderly
Some practitioners routinely round the serum creatinine of elderly patients (e.g., > 60 years) to a value of 1 mg/dL in an effort to control for a reduced muscle mass. Intuitively, this practice does not make sense because rounding a serum creatinine of 0.3 mg/dL (230% increase) is much different than rounding a value of 0.8 mg/dL (25% increase). This practice becomes even more inconsistent when an elderly patient's serum creatinine is already above 1 mg/dL, in which rounding is not typically done. The literature does not support this practice as it often results in an underestimation of true renal function.^{23}^{,}^{24} If any correction factor is used, it is likely that a percent adjustment, similar to underweight patients, would be the most appropriate; however, such a correction factor has not been studied in elderly patients.
Rounding Creatinine in Underweight Patients
In underweight patients, a low serum creatinine may be more reflective of a decrease in production rather than an increased rate of renal elimination. Similarly to elderly patients, clinicians may be tempted to round creatinine in underweight patients to account for less muscle mass; however, this practice is not supported by the literature.^{25} The most accurate method to control for underweight patients is to multiply the patient's Cockcroft-Gault value by an adjustment factor of 0.69 (regardless of whether the patient's serum creatinine is above or below 1 mg/dL). This correction factor was shown to be more precise and less bias than rounding or making no adjustment.
Medications that Modify Serum Creatinine
Because serum creatinine undergoes tubular secretion, any medications that interfere with this process will falsely elevate the patient's serum creatinine; however, this will not impact the patient's true GFR. The following medications have been shown to falsely elevate serum creatinine:^{16}^{,}^{23}^{,}^{26}
- Cefoxitin
- Cimetidine
- Cisplatin
- Flucytosine
- Trimethoprim
Populations who are Difficult to Estimate
Certain patient groups have dramatically different serum creatinine production or elimination compared to the normal patient population. The following groups are difficult to estimate true renal function:
- Amputation - Falsely low serum creatinine due to less production from muscle mass. Estimated body weight lost (EBWL) based on the type of amputation can adjust for the muscle mass loss.
- Burn injury - Increased GFR
- Cirrhosis - Falsely low serum creatinine due to less muscle mass and reduced hepatic conversion of creatine to creatinine
- Cystic fibrosis - Increased GFR
- Muscle disorders - Muscular dystrophy and other muscle disorders that can cause cachexia, resulting in less creatinine production
- Pregnancy - Difficult to estimate lean body mass, increased GFR
- Unstable renal function - Equations used to estimate unstable renal function exist but are not well validated in large patient populations
Impact of IDMS
There are primarily two laboratory methods for measuring serum creatinine: a number of conventional (older) methods (e.g., alkaline picrate), and the newer IDMS method. The conventional methods have a positive bias (falsely elevated by up to 20%) because they detected non-creatinine chromagens.^{27} The conventional assay method is most susceptible to bias when serum creatinine is within the normal range. The NKDEP guidelines^{28} recommend that all laboratories convert their systems to use the newer, more accurate IDMS method. According to the NKDEP, almost all laboratories are expected to convert to the IDMS method by the end of 2010.
Note that this calculator automatically converts to and from IDMS as indicated based on the CrCl/GFR equation. All equations before the MDRD equation use non-IDMS creatinine values, the MDRD equation has two equations for either assay, and equations developed on or after 2010, such as the CKD-EPI 2009 equation are only standardized for IDMS. The following equations are used to convert between IDMS and non-IDMS:^{29}
$$
\\ Non-IDMS\;SCr\;(mg/dL) = (IDMS\;SCr)*1.065 + 0.067
\\ IDMS\;SCr\;(mg/dL) = ((Non-IDMS\;SCr)-0.067)/1.065
$$