**APPENDIX 3. METHODOLOGICAL ASPECTS OF EVALUATING EQUATIONS TO PREDICT GFR AND CALCULATIONS USING 24-HOUR URINE SAMPLES**

Many of the studies reviewed were small. Since estimates of accuracy from smaller studies can be unreliable, studies presented have at least 100 adults or 50 children. A smaller sample size was permitted for pediatric studies because large pediatric studies are rare. Several large validation studies evaluating the newly developed MDRD Study equation were conducted recently and were only available in abstract form.^{162}, 165 In order to capture these valuable data, the authors were contacted and asked to analyze their data and provide estimates of accuracy for this review.

Review of the literature showed great heterogeneity in how the performance of prediction equations was assessed. The mean difference between the actual measured GFR (gold standard) and the estimated GFR based on an equation provides a valid measure of bias. The median difference provides a measure that is valid and less susceptible to influence by outliers. The standard deviation of the difference between the measured and estimated GFR should be reported as a measure of precision. The difference from the gold standard can also be expressed as a relative difference, eg, percent difference from the measured GFR. This has the advantage of allowing for the decreased absolute precision in estimating higher values of GFR. Clinically this is relevant, as there is less concern about the difference between 100 and 130 mL/min/1.73 m^{2} than between 30 and 60 mL/min/1.73 m^{2}.

Most studies had a plot of the predicted versus measured GFR, which provided for a common basis for comparison. A magnified copy of the graph was used to estimate the proportion of GFR estimates within 30% and 50% of the measured GFR by counting the number of points outside of these limits. The average percent bias for the study was estimated as well. In most studies this had to be done by comparing the percent difference between the average estimated and measured GFR since average percent bias at the individual level was rarely available.

Correlation coefficients are frequently cited in the literature on prediction equations. However, they are inadequate for measuring the validity of a method in estimating GFR for two reasons. Although correlation coefficients (r) measure the association between prediction equation and measured GFR, the correlation coefficient is highly dependent on the distribution of GFRs in the study population selected. Even poor estimates can discriminate between a GFR of 20 and 120 very reliably. Second, correlation measures ignore bias and measure relative rather than absolute agreement. For example, in the MDRD Study the Cockroft-Gault equation had a similar correlation to GFR as the MDRD Study equation but overestimated GFR by 19%.^{17} Analogous studies in children show similar limitations in assessing the utility of a prediction equation by virtue of its correlation coefficient.^{124} The correlation between inulin clearance and estimated GFR by the Schwartz formula was 0.905, while in the same study, the standard deviation of the difference between the reference value (C_{in}) on the predicted value was 28.6%, indicating limited precision.

Regression equations are another commonly used measure of prediction equations. Regression equations relating an estimate of GFR and the measured GFR provide an estimate of systematic bias, in the relationship between the two variables, as well as the correlation and residual root mean error, measures of precision. However, such regression analyses have two drawbacks. First, ordinary least square regression does not allow for measurement error in the X-variable. As a result, the regression equation provides a prediction equation conditional of the X-value rather than an unbiased estimate of the relationship. For example, a regression of one GFR measure on a second GFR measure, using the same technique on another day, would have a slope that is substantially lower than 1.0 and an intercept greater than zero. The importance of measurement error in the X-values depends on the correlation, which in turn depends on the study population. Second, regression equations cannot be pooled across different studies. Finally, evaluation of the accuracy of any equation for estimating GFR must be made in an independent group from the group in which the equation itself was derived.

No peer-reviewed publications validating the MDRD Study equation were available. An analysis of 1,775 GFR measurements in participants of the African-American Study of Kidney Disease and Hypertension (AASK) indicates that the equation performs similarly in this study population.^{162} Accuracy was also similar among 321 kidney transplant recipients.^{165} Thus, the abbreviated MDRD Study equation provides a rigorously developed equation for estimating GFR, which may allow for improved prediction of GFR.

A direct comparison of the abbreviated MDRD Study equation with other equations developed in the same study that include other variables (serum urea nitrogen, serum albumin, and 24-hour creatinine clearance) shows only a marginal improvement in the prediction. The median percent difference from GFR was 12.1% versus 11.3% for a 6 variable equation, which includes serum urea nitrogen and albumin. Exclusion of these analytes decreases the cost of testing, the susceptibility to bias in calibration of these other analytes, and bias due to alteration of these analyses by diseases other than kidney disease. This abbreviated equation also predicted GFR better than 24-hour creatinine clearance, even after bias correction of the creatinine clearance. While the equation performed well in the AASK study where a substantial number of GFR values in the normal range were included, the equation was developed in a sample with few individuals with a GFR greater than 90 mL/min/1.73 m^{2}.

The daily urea clearance (U_{urea} × V)/P_{urea} and creatinine clearance (U_{Cr} × V)/S_{Cr} can be calculated from the concentrations of urea and creatinine and the volume (converted to mL/min) of the 24-hour urine collection. The weekly Kt/V_{urea} is equal to the daily urea clearance multiplied by seven (Kt) divided by the estimated total body water (V). Total body water can be estimated in adults by the Watson formula^{665} or the Mellits-Cheek method for children using measured weight and height.^{16} If daily protein intake is relatively constant and the patient is in a steady state, then urinary nitrogen excretion is roughly equal to nitrogen intake. Therefore, using the urea nitrogen concentration in the 24-hour urine, protein intake can be estimated from:^{666}

Urinary nitrogen excretion = Urine urea nitrogen + nonurea nitrogen

Nonurea nitrogen excretion is relatively constant at 30 mg/kg per day. Each gram of nitrogen is derived from 6.25 grams of protein. Therefore:

Estimated protein intake (

g/d) = 6.25 × (Urine urea nitrogen (g/d) + 30mg/kg/d× Weight (kg)

For example, a 50-kg woman with a 24-hour urine urea nitrogen excretion of 7 g has an estimated protein intake = 6.25 (7 + 1.5) = 53.1 g.

These parameters are useful in evaluating the patient’s nutritional status, need for dialysis, and prescription of dialysis dose and modality.^{320}, ^{667}