Kidney Failure Risk Equation (KFRE): how the Tangri four-variable formula works

The Kidney Failure Risk Equation (KFRE) combines age, sex, eGFR and urine albumin-to-creatinine ratio (ACR) into a 2-year and a 5-year risk of kidney failure. A 55-year-old man with an eGFR of 30 and an ACR of 300 mg/g gets 9.6% at 2 years and 27.0% at 5 years.

Not a medical device. Not a diagnosis or dosing recommendation.

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Kidney calculators
Tangri N et al. · 2011
The KFRE formula
Worked examples
Frequently asked questions

What is the Kidney Failure Risk Equation?

Navdeep Tangri and colleagues published the equation in JAMA in 2011. Their abstract describes prediction models built in Canadian patients with chronic kidney disease (CKD) stages 3 to 5 who had been referred to nephrologists. Kidney failure meant needing dialysis or a preemptive kidney transplant.

This page uses the four-variable Tangri 2011 equation (age, sex, eGFR and urine ACR). The eight-variable model and the 2016 regional recalibrations are not applied, and race is not an input.

Magent's calculator returns a linear predictor (LP) to 4 decimals and the two risks as percents to 1 decimal. It doesn't attach a named risk class to either number.

This page explains the arithmetic. It doesn't say what a value means for a particular person.

The KFRE formula

LP = −0.2201 × (age ÷ 10 − 7.036)
   + 0.2467 × (male − 0.5642)            male = 1, female = 0
   − 0.5567 × (eGFR ÷ 5 − 7.222)
   + 0.4510 × (ln ACR − 5.137)           ACR in mg/g, natural log

2-year risk = 1 − 0.9750 ^ exp(LP)
5-year risk = 1 − 0.9240 ^ exp(LP)
LP to 4 decimals · risks as percents to 1 decimal

Exact expression the calculator uses:

LP = -0.2201*(age_years/10 - 7.036) + 0.2467*(male - 0.5642) - 0.5567*(egfr_ml_min/5 - 7.222) + 0.4510*(ln(acr_mg_g) - 5.137); 2-year risk = 1 - 0.9750^exp(LP); 5-year risk = 1 - 0.9240^exp(LP); Tangri 2011 4-variable only; male is 1 if true else 0; ACR mg/g natural log; caller supplies eGFR; not 8-variable; not Tangri 2016 country S0; no race

In words: each input is centered on the value in the formula, multiplied by its coefficient, and the four terms are added to give LP. Each risk is 1 minus a baseline survival raised to the power e^LP.

Inputs

Input	Meaning	Accepted range
`age_years`	Age in years, a whole number	18 to 90
`male`	true for male, false for female	true or false
`egfr_ml_min`	eGFR you supply, mL/min/1.73 m2	1 to 150
`acr_mg_g`	Urine albumin-to-creatinine ratio, mg/g	0.1 to 10000

How the calculation works

Age term: divide age by 10, take away 7.036, multiply by −0.2201.
Sex term: use 1 for male or 0 for female, take away 0.5642, multiply by 0.2467.
eGFR term: divide eGFR by 5, take away 7.222, multiply by −0.5567.
ACR term: take the natural log of ACR, take away 5.137, multiply by 0.4510.
Add the four terms to get LP, reported to 4 decimals.
2-year risk: 1 − 0.9750 raised to e^LP, shown as a percent to 1 decimal.
5-year risk: 1 − 0.9240 raised to e^LP, shown as a percent to 1 decimal.

eGFR has a negative coefficient, so a lower eGFR raises LP. ACR has a positive coefficient on its log, so a higher ACR raises LP. Because the 5-year baseline survival (0.9240) is lower than the 2-year one (0.9750), the 5-year risk is never smaller than the 2-year risk.

Units

Age is in whole years. eGFR is in mL/min/1.73 m2 and comes from you; the calculator doesn't estimate it from creatinine. ACR is in mg/g; the calculator doesn't convert from mg/mmol. A missing value, an age that isn't a whole number, a sex flag that isn't true or false, or a value outside its range is rejected with an error. The calculator returns the inputs, LP, both risk percents and the two baseline survivals (0.975 and 0.924).

Worked examples

These use Magent's own expected values for the calculator. Each is a 55-year-old man.

Example 1: eGFR 30, ACR 300 mg/g

Work out the four terms as above and add them: LP rounds to 1.3815.
2-year risk: 1 − 0.9750^e^LP → 9.6%.
5-year risk: 1 − 0.9240^e^LP → 27.0%.

Example 2: eGFR 30, ACR 1000 mg/g

Same age, sex and eGFR as Example 1, with a higher ACR. LP rounds to 1.9245.
2-year risk 15.9%, 5-year risk 41.8%.

Example 3: eGFR 55, ACR 10 mg/g

Higher eGFR and low ACR give a negative LP: −2.9359.
2-year risk 0.1%, 5-year risk 0.4%.

Example 4: eGFR 18, ACR 800 mg/g

LP rounds to 3.1599.
2-year risk 44.9%, 5-year risk 84.5%. No risk class is returned.

Example 5: eGFR 10, ACR 2000 mg/g

LP rounds to 4.4639.
2-year risk 88.9%, 5-year risk 99.9%.

Examples 1 and 2 differ in ACR alone, and the 5-year risk moves from 27.0% to 41.8%.

History of the KFRE

The equation comes from Tangri N, Stevens LA, Griffith J and colleagues, A predictive model for progression of chronic kidney disease to kidney failure, JAMA, 2011 (volume 305, issue 15, pages 1553–1559). The abstract describes developing and testing models with Cox proportional hazards methods in two independent Canadian cohorts. Its most accurate model added serum calcium, phosphate, bicarbonate and albumin to age, sex, eGFR and albuminuria; a simpler model used age, sex, eGFR and albuminuria. Magent's calculator is that simpler, four-variable form.

When it's used

The 2011 models were built for people with CKD stages 3 to 5, which the record describes as an eGFR of about 10 to 59 mL/min/1.73 m2, who were already seeing a nephrologist.

Where it's used

The equation needs four routine values: age, sex, an eGFR and a urine ACR.

Who uses it

The person using the calculator enters age, sex, an eGFR they already have and a urine ACR in mg/g. The calculator works out LP and the two risk percents.

Limits of the calculation

It's the four-variable equation. Calcium, phosphate, bicarbonate and albumin aren't inputs.
No 2016 regional recalibration is applied, and there's no race input.
The calculator doesn't estimate eGFR or convert ACR units. You supply eGFR, and ACR goes in as mg/g.
The 2011 models came from referred patients with CKD stages 3 to 5. The age range of 18 to 90 is Magent's own limit for adults.
It returns percents, not a named risk class.
This page doesn't say what to do with a result.

Clinical decisions belong to a qualified clinician who knows the patient.

eGFR (CKD-EPI) estimates kidney function from creatinine with the race-free CKD-EPI equation. The KFRE takes an eGFR as an input instead of working one out.
Creatinine clearance (Cockcroft–Gault) estimates creatinine clearance in mL/min using total body weight.

Glossary

eGFR: estimated glomerular filtration rate, entered in mL/min/1.73 m2.
ACR: urine albumin-to-creatinine ratio, entered in mg/g.
Linear predictor (LP): the sum of the four centered, weighted terms.
Baseline survival: 0.9750 at 2 years and 0.9240 at 5 years, the two constants in the risk formulas.
Kidney failure: in the 2011 paper, needing dialysis or a preemptive kidney transplant.

Common mistakes

Entering ACR in mg/mmol. The calculator expects mg/g and doesn't convert.
Using the log base 10. ACR enters as its natural log.
Expecting the eight-variable result. This calculator has four inputs.
Swapping the two baselines. 0.9750 goes with the 2-year risk and 0.9240 with the 5-year risk.
Reading a percent as a class. The calculator returns numbers, not labels.

Source

Tangri N, Stevens LA, Griffith J, et al. A predictive model for progression of chronic kidney disease to kidney failure. JAMA. 2011;305(15):1553-1559. DOI: 10.1001/jama.2011.451. PMID: 21482743

Frequently asked questions

How do you calculate the KFRE?

Add four centered, weighted terms for age, sex, eGFR and the natural log of ACR to get LP. The 2-year risk is 1 − 0.9750^e^LP and the 5-year risk is 1 − 0.9240^e^LP.

Does the KFRE use race?

No. Race isn't an input to this four-variable equation.

Is this the four-variable or the eight-variable KFRE?

The four-variable one: age, sex, eGFR and urine ACR.

What units does the KFRE use?

Age in years, eGFR in mL/min/1.73 m2 and urine ACR in mg/g.

Does the calculator work out eGFR for me?

No. You enter an eGFR you already have.