ORIGINAL RESEARCH
Estimation of 24-Hour Urine Phosphate Excretion From Spot Urine Collection: Development of a Predictive Equation Cassianne Robinson-Cohen, PhD,* Joachim H. Ix, MD, MAS,†,‡ Gerard Smits, PhD,§ Martha Persky, RN,§ Glenn M. Chertow, MD, MPH,{ Geoffrey A. Block, MD,§ and Bryan R. Kestenbaum, MD, MS*,** Background: The management of hyperphosphatemia in patients with moderate to severe chronic kidney disease (CKD) includes dietary phosphate restriction and/or prescription of phosphate binders. Measuring phosphate intake in CKD is important for monitoring dietary adherence and for the effectiveness of therapeutic interventions. The 24-hour urine collection is the gold standard method for determining phosphate intake; however, timed urine collections are cumbersome and prone to error. We investigated the precision and accuracy of spot urine phosphate measurements, compared to 24-hour urine phosphate (24hUrP) collection. Study Design, Setting, and Participants: We evaluated simultaneous spot and 24hUrP measurements, collected on multiple occasions, from 143 participants in the Phosphate Normalization Trial, a randomized trial of phosphate binders versus placebo among persons with an estimated glomerular filtration rate between 20-45 mL/minute per 1.73 m2. We used residual analyses and graphical methods to model the functional relationship of spot urine phosphate and creatinine measurements with 24hUrP. We used multiple linear regression to test whether additional covariates improved model prediction, including treatment assignment, age, sex, height, weight, urine collection time, and last meal time. We internally validated results using leave-one-out cross-validation, and externally validated in an independent replication cohort. Results: A log-log relation between the spot urine phosphate-to-creatinine ratio and 24hUrP excretion yielded the best model fit. In addition to spot urine phosphate and creatinine concentrations, inclusion of age, sex, and weight significantly improved prediction of 24hUrP. Compared with a spot urine phosphate-to-creatinine ratio alone (r2 5 0.12, P , .001), the new equation more accurately predicted 24hUrP (leave-one-out validation r2 5 0.43, P , .001, independent validation r2 5 0.39, P , .001). Conclusion: We describe a novel equation to predict 24hUrP excretion using spot urine phosphate and creatinine, age, sex, and weight. The equation is more accurate and precise than the urine phosphate-to-creatinine ratio alone, and it provides a simple method for estimating 24hUrP excretion in patients with nondialysis-requiring CKD. Ó 2014 by the National Kidney Foundation, Inc. All rights reserved.
Introduction
T
HE OPTIMAL MANAGEMENT of mineral metabolism disorders among patients with nondialysisrequiring chronic kidney disease (CKD) is unknown. National and international guidelines recommend *
Kidney Research Institute, University of Washington, Seattle, Washington. Division of Nephrology and Hypertension, Department of Medicine, University of California–San Diego, San Diego, California. ‡ San Diego Veterans’ Administration Healthcare System, San Diego, California. § Denver Nephrology, Denver, Colorado. { Stanford University School of Medicine, Palo Alto, California. ** Department of Medicine, Division of Nephrology, University of Washington, Seattle, Washington. Financial Disclosure: The authors declare that they have no relevant financial interests. Address correspondence to Cassianne Robinson-Cohen, PhD, Kidney Research Institute, University of Washington, 325 9th Avenue, Box 359606, Seattle, WA 98104. E-mail: [email protected] Ó 2014 by the National Kidney Foundation, Inc. All rights reserved. 1051-2276/$36.00 http://dx.doi.org/10.1053/j.jrn.2014.02.001 †
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maintaining serum phosphate concentrations close to the normal laboratory reference range using dietary phosphate restriction and/or phosphate binders. These guidelines are motivated by the sentinel role of phosphate retention in the pathogenesis of CKD-mineral bone disorder, by experimental evidence for a direct calcifying effect of phosphate on vascular smooth muscle tissue, and by clinical data demonstrating associations of higher serum phosphate concentrations with vascular calcification, cardiovascular events, and mortality. Determining phosphate intake is important for monitoring dietary adherence and for evaluating the effectiveness of phosphate binders or other therapies. Under steady-state conditions, 24-hour urinary phosphate (24hUrP) excretion equals gastrointestinal phosphate absorption; therefore, it provides a reasonable estimate of phosphate intake. However, collection of 24-hour urine specimens is time-consuming, cumbersome, and prone to collection errors. A spot urinary phosphate-to-creatinine ratio from a single voided sample accounts for differences in urine concentration and may correspond with 24-hour
Journal of Renal Nutrition, Vol 24, No 3 (May), 2014: pp 194-199
ESTIMATION OF URINE PHOSPHATE EXCRETION FROM SPOT COLLECTION
phosphate excretion. However, the urine creatinine concentration may reflect anthropomorphic and other individual patient characteristics other than urine volume. The ability of a single voided urine sample to accurately predict 24hUrP excretion has not been thoroughly investigated. Moreover, the potential influence of demographics, body size, kidney function, and collection times has not been systemically evaluated. In the study presented here, we develop and validate a novel equation to predict 24hUrP excretion from a spot urinary specimen using data from multiple simultaneous assessments that were performed in a clinical trial of CKD.
Materials and Methods Study Population: Derivation Cohort We derived equations for predicting 24hUrP excretion using data from the Phosphate Normalization Trial (PNT), a placebo-controlled randomized trial to determine the effectiveness of 3 commercially available phosphate binders on lowering serum phosphate concentrations in patients with moderate to severe (nondialysis-requiring) CKD over a 9-month period (ClinicalTrials.gov identifier: NCT00785629).1 In brief, the trial enrolled 148 patients with an estimated glomerular filtration rate (eGFR) between 20 and 45 mL/minute per 1.73 m2, a serum phosphate concentration greater than 3.5 and 6.0 mg/dL or less, and willingness to avoid any intentional change in diet. Exclusion criteria included the use of a phosphate binder other than sevelamer, calcium acetate, or lanthanum; use of activated vitamin D sterols or cinacalcet; an intact parathyroid hormone concentration of 500 pg/ mL or greater; or uncontrolled hyperlipidemia. The primary trial endpoint was the time-averaged change in serum phosphate concentration from baseline to month 9. In total, 144 PNT study subjects were asked to collect their urine over the 24-hour period before each scheduled study visit, which occurred at baseline and 3, 6, and 9 months after randomization. Subjects provided a spot urine specimen the day of their scheduled study visits. For the purpose of this analysis, we excluded study visits for which 24-hour urine collections were inadequate (24-hour urine creatinine ,600 mg for women or ,800 mg for men; n 5 21 visits, 11 subjects).2,3 The sample comprised 133 subjects. The study was approved by the local ethics committees, and all patients that enrolled in the study provided written informed consent. Study Population: Validation Cohort We validated our equations using a unique random sample of 70 patients with nondialysis-requiring CKD from an unrelated observational study of salivary phosphate levels within PNT study center clinics. Validation cohort members were asked to collect a 24-hour urine specimen on the day before their visit. On their visit day, they were seen in the morning to collect blood, saliva, and a spot urine
195
sample, and again in the afternoon to collect blood and saliva.
Study Measurements For all 24-hour urine collections, participants were instructed to immediately begin their 24-hour urine collection after discarding the first morning void and to collect all of their urine for 24 consecutive hours, including the final void at completion of the 24-hour period. Spot urine collections were obtained in a nonfasting state and generally at the same time of day. All of the urine phosphate and creatinine measurements in this study were performed by Litholink Corporation (Chicago, IL). Serum creatinine was measured by Quest Diagnostics (Denver, CO) using the modified rate Jaffe method and with an assay traceable to isotope dilution mass spectrometry. Coordinators measured weight using calibrated scales, and they measured height with a wall-mounted tape measure. The CKD-Epidemiology Collaboration formula was used to estimate glomerular filtration rate.4 Statistical Analysis We tabulated baseline characteristics on demographics, anthropometric measures, and kidney function among the discovery and validation cohorts. We report continuous variables as mean and standard deviation or median and interquartile range (IQR) if skewed. We constructed multivariable equations to predict 24hUrP excretion in 2 steps. First, we assessed appropriate functional relations between spot urine phosphate and urine creatinine concentrations and 24hUrP excretion by constructing linear, log, and fractional polynomial models with clustered variance to account for the multiple measurements per subject.5 For each model, we compared the transformed linear combination of spot urine phosphate and spot urine creatinine with the corresponding transformed spot urinary phosphate-to-creatinine ratio. We considered model performance to be improved if there were a 5% or more increase in the adjusted model R2 plus any reduction in the Akaike information criterion (AIC), an established measure of model fit, with smaller values indicating better fit. We generated fitted lines and scatterplots of model-predicted versus observed 24hUrP excretion. We formally evaluated bias by Pitman’s test of equality of variance and informally by visual inspection of Bland-Altman plots. Second, we assessed candidate patient characteristics that might improve model prediction using forward stepwise multiple linear regression with clustered variance. We specifically assessed the following study variables: age, gender, height, weight, eGFR, treatment arm (phosphate binder vs. placebo), time of urine collection (morning vs. afternoon), and time since last meal. We separately entered each variable in a model that included the best fitting spot urine phosphate and creatinine functional form and retained the variable that explained the largest percentage of
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residual variability in measured 24hUrP excretion. We then individually added the remaining variables and assessed whether the adjusted R2 increased by at least 5% and the AIC was reduced. We repeated this procedure until no further variables met these criteria. With each variable added to the model, we repeated an assessment of bias using Bland-Altman plots and Pitman’s test of difference in variance.6,7 In addition, we assessed the potential effect modifying behavior of these characteristics by including a multiplicative interaction term (e.g., time since last meal * spot phosphorus-to-creatinine ratio) and testing for improved model fit by R2 increase by at least 5% and reduction of AIC.
Validation of the Prediction Equation We validated the developed model internally using a leave-one-out cross-validation approach, and we externally validated the model using the independent validation cohort. The leave-one-out cross-validation procedure leaves out one observation from the training data set and iteratively estimates models on the basis of the remaining n 2 1 observations over n procedures. We tested the predictive accuracy of the model in internal and external validation by reporting the regression-based coefficient of determination (R2), derived from correlations between predicted and observed values, and the root mean squared error, taking into account absolute values in terms of mean
squared prediction error rather than merely correlation. All analyses were conducted using STATA version 11.2 (Stata, College Station, TX).
Results Baseline Characteristics Among subjects in the derivation cohort, the mean 24hUrP excretion was 736 mg/day (standard deviation 358 mg/day). Higher 24hUrP values were associated with younger mean age, male sex, higher mean BMI, and nonWhite race (Table 1). Subjects who had higher 24hUrP excretion also had modestly higher serum phosphate and creatinine concentrations. The median number of simultaneous 24-hour and spot urine measurements per PNT subject was 4 (interquartile range: 3, 4) and did not differ by tertile of 24hUrP excretion. The subjects in the validation cohort were of similar mean age and eGFR compared with subjects in the derivation cohort, were more likely to be White, were leaner, and had lower 24hUrP excretion and a shorter time from last meal to spot urine collection. Model Development For each of the 3 functional models tested (untransformed, log-transformed 24hUrP only, log-transformed 24hUrP and spot urine measurements), the spot urine phosphate-to-creatinine ratio outperformed the linear combination of both characteristics (Fig. 1). The best
Table 1. Baseline Demographic Characteristics of Derivation and Validation Cohorts Participant Characteristic Baseline 24-h urine phosphate excretion, mg/d Number of participants Estimated GFR (mL/min per 1.73 m2) Age (y) Male gender Body mass index (kg/m2) Race White Black Other Serum phosphate (mg/dL) Serum creatinine (mg/dL) Treatment group Lanthanum Sevelamer Calcium acetate Placebo Time from last meal to spot urine collection (h) Spot urine collection time Morning Afternoon Urine collections per participant 24-h urine phosphate, mg/d 24-hour urine creatinine, mg/d Spot urine phosphate, mg/dL Spot urine creatinine, mg/dL Spot phosphate/creatinine ratio
Derivation Cohort
Validation Cohort
185-616 44 32 6 9 66 6 13 12 (27%) 30 6 7
616-921 45 30 6 9 66 6 13 20 (45%) 32 6 7
921-2,400 44 31 6 8 64 6 10 35 (80%) 34 6 7
IQR (504-941) 70 32 6 13 69 6 11 35 (50%) 29 6 5
33 (73%) 11 (24%) 1 (2%) 4.1 6 0.4 1.9 6 0.6
34 (77%) 2 (5%) 8 (18%) 4.2 6 0.4 2.1 6 0.6
36 (84%) 3 (7%) 4 (9%) 4.3 6 0.4 2.2 6 0.6
61 (87.1%) 6 (8.6%) 3 (3.3%) 3.8 6 0.7 2.2 6 1.0 NA
10 (23%) 7 (16%) 11 (25%) 17 (39%) 6.2 6 5.9
10 (22%) 10 (22%) 7 (16%) 17 (38%) 4.7 6 4.9
5 (11%) 9 (20%) 9 (20%) 21 (47%) 5.1 6 5.1
25 (56%) 20 (44%) 3.3 6 0.9 468.5 6 102.4 962.7 6 266.4 43.9 6 19.4 101.6 6 55.5 0.46 6 0.15
26 (59%) 18 (41%) 3.2 6 1.1 778.0 6 91.9 1,228.9 6 291.4 42.1 6 19.9 93.4 6 61.7 0.51 6 0.17
19 (43%) 25 (57%) 3.7 6 0.7 1,172.3 6 278.6 1,713.5 6 454.8 46.7 6 24.6 91.2 6 47.7 0.57 6 0.23
GFR, glomerular filtration rate; IQR, interquartile range; NA, not applicable.
2.4 6 0.8 69 (99%) 1 (1.4%) 1.0 749.2 6 365.1 1,461.6 6 612.0 40.9 6 26.6 97.2 6 59.5 0.46 6 0.21
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Figure 1. Correlations of measured versus predicted 24-h urine phosphate.
fitting model was log-transformed 24hUrP with the log-transformed spot urine phosphate-to-creatinine ratio (model R2 5 0.27, AIC 5 536). This functional form was conserved and used in subsequent forward stepwise regression models. On the basis of the R2 and AIC criteria, age, sex, and weight were identified as independent predictors of 24hUrP in addition to the phosphate-to-creatinine ratio (Table 2). The time of urine collection, eGFR, treatment arm, and time since last meal were not independently related to the 24hUrP after accounting for spot urine phosphate and creatinine values and did not improve model prediction. Interaction terms between gender and the spot phosphate-to-creatinine ratio and between time of spot collection and spot phosphate also did not improve model fit. The final derived equation explained an estimated 48% of variation in 24hUrP (R2 5 0.48, root mean square error 5 0.36, AIC 5 367.0, Table 2). The Bland-Altman plot suggested no observable bias for predicted versus
measured 24hUrP measurements (Pitman’s test for proportional bias 5 0.067, P 5.16).
Model Validation In the derivation cohort, the leave-one-out cross-validation procedure yielded a coefficient of determination, R2, of 0.43. In the validation cohort, the derived equation explained 39% of the variability of 24hUrP excretion. The median predicted 24hUrP excretion among patients in the validation cohort was similar to the median measured value (662 mg/day; IQR 523-822 mg/day vs. 688 mg/day; IQR 504-940 mg/day). 24hUrP was predicted within 10% of the measured value in 91% of subjects and was underestimated in 49% of subjects.
Discussion Using contemporaneous 24-hour and spot urine measurements, we derived and validated a novel equation to predict 24hUrP excretion from spot urine phosphate
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Table 2. Independent Predictors of log 24-h Urine Phosphate Beyond the Spot Urine Phosphate-to-Creatinine Ratio Variable Intercept ln(UP/Cr) Age, y Male gender Body weight, kg
b
95% CI
P
Incremental R2
Incremental AIC
6.697 0.440 20.006 0.302 0.005
6.384, 7.010 0.332, 0.548 20.010, 20.002 0.202, 0.401 0.003, 0.007
,.001 ,.001 .001 ,.001 ,.001
– 0.27 0.29 0.43 0.48
– 535.8 508.6 411.0 368.2
AIC, Akaike information criterion; CI, confidence interval; UP/Cr, urinary phosphate-to-creatinine ratio. Final predictive equation ln(24-h P) 5 6.7 1 0.44*(lnUP/Cr) 2 0.006*(age) 1 0.005*(weight, kg) 1 0.30 if male 24-h P 5 e(6.7 0.006 (age) 1 0.005 (weight, kg) 1 0.30 if male) * * .
and creatinine measurements plus age, sex, and weight. In an independent validation cohort, predicted 24hUrP explained approximately 40% of the variance in measured values and typically fell within 10%. The equation substantially improves on the simple spot phosphate-tocreatinine ratio alone and provides a reasonable estimate of 24-hour phosphate excretion that can be used for clinical purposes and future research studies. We confirmed that 24-hour phosphate excretion is determined largely by the phosphate-to-creatinine ratio from a spot urine sample with routinely available clinical data (sex, body weight, and age) incrementally improving predictive capacity. Two small validation studies have previously investigated the agreement between spot urine phosphate concentrations and 24hUrP excretion. The relation was most recently investigated in a cohort of 30 urinary stoneformers recruited from a urology clinic in Kuala Lumpur. Investigators found a weak direct correlation between the spot phosphate-to-creatinine ratio and 24-hour phosphate excretion (R2 5 0.06); however, they did not investigate whether nonlinear transformation could improve prediction.8 In contrast, in an earlier study of 67 patients from a tertiary care hospital in Turkey, representing a wide range of kidney function and phosphate excretion, a nearly perfect correlation between 24hUrP and spot urine phosphate-to-creatinine ratios was noted (R2 5 0.93). This publication is often cited as justification for interchangeable use of spot phosphate-to-creatinine ratios, without conversion factors, in place of the 24-hour phosphate excretion. However, the regression models in this study were forced through the origin, greatly inflating model R2 values without regard to goodness of fit.9 As an illustration of this phenomenon, our predictive model would yield an R2 value of 0.995 if the intercept term were suppressed. A moderate and not perfectly precise relation between the spot urine sample and the 24-hour excretion is to be expected because phosphate intake and excretion are constantly changing throughout the course of a day; approximately half of the variation in 24hUrP excretion was not explained by our equation. Further studies are warranted to explore other characteristics that may account for the remaining between-subject variation and error in our
1 0.44 (ln(Up/cr)) 2
*
predictive equation. Some medications could alter urinary phosphate excretion. For example, thiazide or loop diuretics might directly (or indirectly, via parathyroid hormone) alter phosphate and creatinine excretion rates throughout the course of 1 day, resulting in different spot concentrations depending on the time of collection. We found that time of urine collection, treatment arm, and time since last meal were not independently associated with 24hUrP excretion after accounting for spot urine phosphate and creatinine values. It was interesting to note that there was no difference in the correlation of spot measurements with 24hUrP excretion between morning spot and afternoon spot collection times, nor did collection time independently predict 24-hour phosphate concentration. In our derivation cohort, most spot urine samples were collected between 9:00 a.m. and 1:00 p.m., and it is possible that the limited variation in collection times across participants may have hampered the uncovering of differential performance by time of day. The derivation cohort comprised a relatively homogeneous group of patients that was selected on the basis of clinical characteristics and willingness to adhere to treatment in the setting of a randomized controlled study. Although clinical trial settings have the limitation of being selective compared with general practice, they provide the advantage of systematic, complete, and high-quality data collection. Still, out of concern for the generalizability of our findings, we conducted external validation of our predictive equation in an independent sample. In conclusion, we developed a new equation to accurately predict 24-hour urinary phosphate excretion using spot phosphate and creatinine concentrations and readily available clinical data, including age, body mass, and gender.10
Practical Application We describe a novel equation to predict 24hUrP excretion using spot urine phosphate and creatinine, age, sex, and weight. Although the equation accounts for less than half of the variation in 24-hour urine phosphorus concentration, the equation is more accurate and precise than the urine phosphate-to-creatinine ratio alone and provides a valid and simple method for estimating 24hUrP excretion in patients with nondialysis-requiring CKD.
ESTIMATION OF URINE PHOSPHATE EXCRETION FROM SPOT COLLECTION
Acknowledgments An abstract describing these findings was presented at the meeting of the American Society of Nephrology 2012. They have not been published elsewhere.
References 1. Block GA, Wheeler DC, Persky MS, et al. Effects of phosphate binders in moderate CKD. J Am Soc Nephrol. 2012;23:1407-1415. 2. Taylor EN, Curhan GC. Differences in 24-hour urine composition between black and white women. J Am Soc Nephrol. 2007;18:654-659. 3. Connor SL, Connor WE, Henry H, Sexton G, Keenan EJ. The effects of familial relationships, age, body weight, and diet on blood pressure and the 24 hour urinary excretion of sodium, potassium, and creatinine in men, women, and children of randomly selected families. Circulation. 1984;70:76-85. 4. Levey AS, Stevens LA. Estimating GFR using the CKD Epidemiology Collaboration (CKD-EPI) creatinine equation: more accurate GFR
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estimates, lower CKD prevalence estimates, and better risk predictions. Am J Kidney Dis. 2010;55:622-627. 5. Royston P, Ambler G, Sauerbrei W. The use of fractional polynomials to model continuous risk variables in epidemiology. Int J Epidemiol. 1999;28:964-974. 6. Martin Bland J, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet. 1986;327:307-310. 7. Pitman EJG. Significance tests which may be applied to samples from any populations: III. The analysis of variance test. Biometrika. 1938;29:322-335. 8. Hong YH, Dublin N, Razack AH, Mohd MA, Husain R. Twenty-four hour and spot urine metabolic evaluations: correlations versus agreements. Urology. 2010;75:1294-1298. 9. Casella G. Leverage and regression through the origin. Am Stat. 1983;37:147-152. 10. Robinson-Cohen C, Ix JH, Smits G, et al. 24-hour urine phosphate excretion concentration calculator 2013. Available at: http://kri.washington. edu/urine-phosphate-calculator. Accessed March 14, 2014.
Estimation of 24-Hour Urine Phosphate Excretion From Spot Urine Collection: Development of a Predictive Equation Cassianne Robinson-Cohen, PhD,* Joachim H. Ix, MD, MAS,†,‡ Gerard Smits, PhD,§ Martha Persky, RN,§ Glenn M. Chertow, MD, MPH,{ Geoffrey A. Block, MD,§ and Bryan R. Kestenbaum, MD, MS*,** Background: The management of hyperphosphatemia in patients with moderate to severe chronic kidney disease (CKD) includes dietary phosphate restriction and/or prescription of phosphate binders. Measuring phosphate intake in CKD is important for monitoring dietary adherence and for the effectiveness of therapeutic interventions. The 24-hour urine collection is the gold standard method for determining phosphate intake; however, timed urine collections are cumbersome and prone to error. We investigated the precision and accuracy of spot urine phosphate measurements, compared to 24-hour urine phosphate (24hUrP) collection. Study Design, Setting, and Participants: We evaluated simultaneous spot and 24hUrP measurements, collected on multiple occasions, from 143 participants in the Phosphate Normalization Trial, a randomized trial of phosphate binders versus placebo among persons with an estimated glomerular filtration rate between 20-45 mL/minute per 1.73 m2. We used residual analyses and graphical methods to model the functional relationship of spot urine phosphate and creatinine measurements with 24hUrP. We used multiple linear regression to test whether additional covariates improved model prediction, including treatment assignment, age, sex, height, weight, urine collection time, and last meal time. We internally validated results using leave-one-out cross-validation, and externally validated in an independent replication cohort. Results: A log-log relation between the spot urine phosphate-to-creatinine ratio and 24hUrP excretion yielded the best model fit. In addition to spot urine phosphate and creatinine concentrations, inclusion of age, sex, and weight significantly improved prediction of 24hUrP. Compared with a spot urine phosphate-to-creatinine ratio alone (r2 5 0.12, P , .001), the new equation more accurately predicted 24hUrP (leave-one-out validation r2 5 0.43, P , .001, independent validation r2 5 0.39, P , .001). Conclusion: We describe a novel equation to predict 24hUrP excretion using spot urine phosphate and creatinine, age, sex, and weight. The equation is more accurate and precise than the urine phosphate-to-creatinine ratio alone, and it provides a simple method for estimating 24hUrP excretion in patients with nondialysis-requiring CKD. Ó 2014 by the National Kidney Foundation, Inc. All rights reserved.
Introduction
T
HE OPTIMAL MANAGEMENT of mineral metabolism disorders among patients with nondialysisrequiring chronic kidney disease (CKD) is unknown. National and international guidelines recommend *
Kidney Research Institute, University of Washington, Seattle, Washington. Division of Nephrology and Hypertension, Department of Medicine, University of California–San Diego, San Diego, California. ‡ San Diego Veterans’ Administration Healthcare System, San Diego, California. § Denver Nephrology, Denver, Colorado. { Stanford University School of Medicine, Palo Alto, California. ** Department of Medicine, Division of Nephrology, University of Washington, Seattle, Washington. Financial Disclosure: The authors declare that they have no relevant financial interests. Address correspondence to Cassianne Robinson-Cohen, PhD, Kidney Research Institute, University of Washington, 325 9th Avenue, Box 359606, Seattle, WA 98104. E-mail: [email protected] Ó 2014 by the National Kidney Foundation, Inc. All rights reserved. 1051-2276/$36.00 http://dx.doi.org/10.1053/j.jrn.2014.02.001 †
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maintaining serum phosphate concentrations close to the normal laboratory reference range using dietary phosphate restriction and/or phosphate binders. These guidelines are motivated by the sentinel role of phosphate retention in the pathogenesis of CKD-mineral bone disorder, by experimental evidence for a direct calcifying effect of phosphate on vascular smooth muscle tissue, and by clinical data demonstrating associations of higher serum phosphate concentrations with vascular calcification, cardiovascular events, and mortality. Determining phosphate intake is important for monitoring dietary adherence and for evaluating the effectiveness of phosphate binders or other therapies. Under steady-state conditions, 24-hour urinary phosphate (24hUrP) excretion equals gastrointestinal phosphate absorption; therefore, it provides a reasonable estimate of phosphate intake. However, collection of 24-hour urine specimens is time-consuming, cumbersome, and prone to collection errors. A spot urinary phosphate-to-creatinine ratio from a single voided sample accounts for differences in urine concentration and may correspond with 24-hour
Journal of Renal Nutrition, Vol 24, No 3 (May), 2014: pp 194-199
ESTIMATION OF URINE PHOSPHATE EXCRETION FROM SPOT COLLECTION
phosphate excretion. However, the urine creatinine concentration may reflect anthropomorphic and other individual patient characteristics other than urine volume. The ability of a single voided urine sample to accurately predict 24hUrP excretion has not been thoroughly investigated. Moreover, the potential influence of demographics, body size, kidney function, and collection times has not been systemically evaluated. In the study presented here, we develop and validate a novel equation to predict 24hUrP excretion from a spot urinary specimen using data from multiple simultaneous assessments that were performed in a clinical trial of CKD.
Materials and Methods Study Population: Derivation Cohort We derived equations for predicting 24hUrP excretion using data from the Phosphate Normalization Trial (PNT), a placebo-controlled randomized trial to determine the effectiveness of 3 commercially available phosphate binders on lowering serum phosphate concentrations in patients with moderate to severe (nondialysis-requiring) CKD over a 9-month period (ClinicalTrials.gov identifier: NCT00785629).1 In brief, the trial enrolled 148 patients with an estimated glomerular filtration rate (eGFR) between 20 and 45 mL/minute per 1.73 m2, a serum phosphate concentration greater than 3.5 and 6.0 mg/dL or less, and willingness to avoid any intentional change in diet. Exclusion criteria included the use of a phosphate binder other than sevelamer, calcium acetate, or lanthanum; use of activated vitamin D sterols or cinacalcet; an intact parathyroid hormone concentration of 500 pg/ mL or greater; or uncontrolled hyperlipidemia. The primary trial endpoint was the time-averaged change in serum phosphate concentration from baseline to month 9. In total, 144 PNT study subjects were asked to collect their urine over the 24-hour period before each scheduled study visit, which occurred at baseline and 3, 6, and 9 months after randomization. Subjects provided a spot urine specimen the day of their scheduled study visits. For the purpose of this analysis, we excluded study visits for which 24-hour urine collections were inadequate (24-hour urine creatinine ,600 mg for women or ,800 mg for men; n 5 21 visits, 11 subjects).2,3 The sample comprised 133 subjects. The study was approved by the local ethics committees, and all patients that enrolled in the study provided written informed consent. Study Population: Validation Cohort We validated our equations using a unique random sample of 70 patients with nondialysis-requiring CKD from an unrelated observational study of salivary phosphate levels within PNT study center clinics. Validation cohort members were asked to collect a 24-hour urine specimen on the day before their visit. On their visit day, they were seen in the morning to collect blood, saliva, and a spot urine
195
sample, and again in the afternoon to collect blood and saliva.
Study Measurements For all 24-hour urine collections, participants were instructed to immediately begin their 24-hour urine collection after discarding the first morning void and to collect all of their urine for 24 consecutive hours, including the final void at completion of the 24-hour period. Spot urine collections were obtained in a nonfasting state and generally at the same time of day. All of the urine phosphate and creatinine measurements in this study were performed by Litholink Corporation (Chicago, IL). Serum creatinine was measured by Quest Diagnostics (Denver, CO) using the modified rate Jaffe method and with an assay traceable to isotope dilution mass spectrometry. Coordinators measured weight using calibrated scales, and they measured height with a wall-mounted tape measure. The CKD-Epidemiology Collaboration formula was used to estimate glomerular filtration rate.4 Statistical Analysis We tabulated baseline characteristics on demographics, anthropometric measures, and kidney function among the discovery and validation cohorts. We report continuous variables as mean and standard deviation or median and interquartile range (IQR) if skewed. We constructed multivariable equations to predict 24hUrP excretion in 2 steps. First, we assessed appropriate functional relations between spot urine phosphate and urine creatinine concentrations and 24hUrP excretion by constructing linear, log, and fractional polynomial models with clustered variance to account for the multiple measurements per subject.5 For each model, we compared the transformed linear combination of spot urine phosphate and spot urine creatinine with the corresponding transformed spot urinary phosphate-to-creatinine ratio. We considered model performance to be improved if there were a 5% or more increase in the adjusted model R2 plus any reduction in the Akaike information criterion (AIC), an established measure of model fit, with smaller values indicating better fit. We generated fitted lines and scatterplots of model-predicted versus observed 24hUrP excretion. We formally evaluated bias by Pitman’s test of equality of variance and informally by visual inspection of Bland-Altman plots. Second, we assessed candidate patient characteristics that might improve model prediction using forward stepwise multiple linear regression with clustered variance. We specifically assessed the following study variables: age, gender, height, weight, eGFR, treatment arm (phosphate binder vs. placebo), time of urine collection (morning vs. afternoon), and time since last meal. We separately entered each variable in a model that included the best fitting spot urine phosphate and creatinine functional form and retained the variable that explained the largest percentage of
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residual variability in measured 24hUrP excretion. We then individually added the remaining variables and assessed whether the adjusted R2 increased by at least 5% and the AIC was reduced. We repeated this procedure until no further variables met these criteria. With each variable added to the model, we repeated an assessment of bias using Bland-Altman plots and Pitman’s test of difference in variance.6,7 In addition, we assessed the potential effect modifying behavior of these characteristics by including a multiplicative interaction term (e.g., time since last meal * spot phosphorus-to-creatinine ratio) and testing for improved model fit by R2 increase by at least 5% and reduction of AIC.
Validation of the Prediction Equation We validated the developed model internally using a leave-one-out cross-validation approach, and we externally validated the model using the independent validation cohort. The leave-one-out cross-validation procedure leaves out one observation from the training data set and iteratively estimates models on the basis of the remaining n 2 1 observations over n procedures. We tested the predictive accuracy of the model in internal and external validation by reporting the regression-based coefficient of determination (R2), derived from correlations between predicted and observed values, and the root mean squared error, taking into account absolute values in terms of mean
squared prediction error rather than merely correlation. All analyses were conducted using STATA version 11.2 (Stata, College Station, TX).
Results Baseline Characteristics Among subjects in the derivation cohort, the mean 24hUrP excretion was 736 mg/day (standard deviation 358 mg/day). Higher 24hUrP values were associated with younger mean age, male sex, higher mean BMI, and nonWhite race (Table 1). Subjects who had higher 24hUrP excretion also had modestly higher serum phosphate and creatinine concentrations. The median number of simultaneous 24-hour and spot urine measurements per PNT subject was 4 (interquartile range: 3, 4) and did not differ by tertile of 24hUrP excretion. The subjects in the validation cohort were of similar mean age and eGFR compared with subjects in the derivation cohort, were more likely to be White, were leaner, and had lower 24hUrP excretion and a shorter time from last meal to spot urine collection. Model Development For each of the 3 functional models tested (untransformed, log-transformed 24hUrP only, log-transformed 24hUrP and spot urine measurements), the spot urine phosphate-to-creatinine ratio outperformed the linear combination of both characteristics (Fig. 1). The best
Table 1. Baseline Demographic Characteristics of Derivation and Validation Cohorts Participant Characteristic Baseline 24-h urine phosphate excretion, mg/d Number of participants Estimated GFR (mL/min per 1.73 m2) Age (y) Male gender Body mass index (kg/m2) Race White Black Other Serum phosphate (mg/dL) Serum creatinine (mg/dL) Treatment group Lanthanum Sevelamer Calcium acetate Placebo Time from last meal to spot urine collection (h) Spot urine collection time Morning Afternoon Urine collections per participant 24-h urine phosphate, mg/d 24-hour urine creatinine, mg/d Spot urine phosphate, mg/dL Spot urine creatinine, mg/dL Spot phosphate/creatinine ratio
Derivation Cohort
Validation Cohort
185-616 44 32 6 9 66 6 13 12 (27%) 30 6 7
616-921 45 30 6 9 66 6 13 20 (45%) 32 6 7
921-2,400 44 31 6 8 64 6 10 35 (80%) 34 6 7
IQR (504-941) 70 32 6 13 69 6 11 35 (50%) 29 6 5
33 (73%) 11 (24%) 1 (2%) 4.1 6 0.4 1.9 6 0.6
34 (77%) 2 (5%) 8 (18%) 4.2 6 0.4 2.1 6 0.6
36 (84%) 3 (7%) 4 (9%) 4.3 6 0.4 2.2 6 0.6
61 (87.1%) 6 (8.6%) 3 (3.3%) 3.8 6 0.7 2.2 6 1.0 NA
10 (23%) 7 (16%) 11 (25%) 17 (39%) 6.2 6 5.9
10 (22%) 10 (22%) 7 (16%) 17 (38%) 4.7 6 4.9
5 (11%) 9 (20%) 9 (20%) 21 (47%) 5.1 6 5.1
25 (56%) 20 (44%) 3.3 6 0.9 468.5 6 102.4 962.7 6 266.4 43.9 6 19.4 101.6 6 55.5 0.46 6 0.15
26 (59%) 18 (41%) 3.2 6 1.1 778.0 6 91.9 1,228.9 6 291.4 42.1 6 19.9 93.4 6 61.7 0.51 6 0.17
19 (43%) 25 (57%) 3.7 6 0.7 1,172.3 6 278.6 1,713.5 6 454.8 46.7 6 24.6 91.2 6 47.7 0.57 6 0.23
GFR, glomerular filtration rate; IQR, interquartile range; NA, not applicable.
2.4 6 0.8 69 (99%) 1 (1.4%) 1.0 749.2 6 365.1 1,461.6 6 612.0 40.9 6 26.6 97.2 6 59.5 0.46 6 0.21
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Figure 1. Correlations of measured versus predicted 24-h urine phosphate.
fitting model was log-transformed 24hUrP with the log-transformed spot urine phosphate-to-creatinine ratio (model R2 5 0.27, AIC 5 536). This functional form was conserved and used in subsequent forward stepwise regression models. On the basis of the R2 and AIC criteria, age, sex, and weight were identified as independent predictors of 24hUrP in addition to the phosphate-to-creatinine ratio (Table 2). The time of urine collection, eGFR, treatment arm, and time since last meal were not independently related to the 24hUrP after accounting for spot urine phosphate and creatinine values and did not improve model prediction. Interaction terms between gender and the spot phosphate-to-creatinine ratio and between time of spot collection and spot phosphate also did not improve model fit. The final derived equation explained an estimated 48% of variation in 24hUrP (R2 5 0.48, root mean square error 5 0.36, AIC 5 367.0, Table 2). The Bland-Altman plot suggested no observable bias for predicted versus
measured 24hUrP measurements (Pitman’s test for proportional bias 5 0.067, P 5.16).
Model Validation In the derivation cohort, the leave-one-out cross-validation procedure yielded a coefficient of determination, R2, of 0.43. In the validation cohort, the derived equation explained 39% of the variability of 24hUrP excretion. The median predicted 24hUrP excretion among patients in the validation cohort was similar to the median measured value (662 mg/day; IQR 523-822 mg/day vs. 688 mg/day; IQR 504-940 mg/day). 24hUrP was predicted within 10% of the measured value in 91% of subjects and was underestimated in 49% of subjects.
Discussion Using contemporaneous 24-hour and spot urine measurements, we derived and validated a novel equation to predict 24hUrP excretion from spot urine phosphate
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Table 2. Independent Predictors of log 24-h Urine Phosphate Beyond the Spot Urine Phosphate-to-Creatinine Ratio Variable Intercept ln(UP/Cr) Age, y Male gender Body weight, kg
b
95% CI
P
Incremental R2
Incremental AIC
6.697 0.440 20.006 0.302 0.005
6.384, 7.010 0.332, 0.548 20.010, 20.002 0.202, 0.401 0.003, 0.007
,.001 ,.001 .001 ,.001 ,.001
– 0.27 0.29 0.43 0.48
– 535.8 508.6 411.0 368.2
AIC, Akaike information criterion; CI, confidence interval; UP/Cr, urinary phosphate-to-creatinine ratio. Final predictive equation ln(24-h P) 5 6.7 1 0.44*(lnUP/Cr) 2 0.006*(age) 1 0.005*(weight, kg) 1 0.30 if male 24-h P 5 e(6.7 0.006 (age) 1 0.005 (weight, kg) 1 0.30 if male) * * .
and creatinine measurements plus age, sex, and weight. In an independent validation cohort, predicted 24hUrP explained approximately 40% of the variance in measured values and typically fell within 10%. The equation substantially improves on the simple spot phosphate-tocreatinine ratio alone and provides a reasonable estimate of 24-hour phosphate excretion that can be used for clinical purposes and future research studies. We confirmed that 24-hour phosphate excretion is determined largely by the phosphate-to-creatinine ratio from a spot urine sample with routinely available clinical data (sex, body weight, and age) incrementally improving predictive capacity. Two small validation studies have previously investigated the agreement between spot urine phosphate concentrations and 24hUrP excretion. The relation was most recently investigated in a cohort of 30 urinary stoneformers recruited from a urology clinic in Kuala Lumpur. Investigators found a weak direct correlation between the spot phosphate-to-creatinine ratio and 24-hour phosphate excretion (R2 5 0.06); however, they did not investigate whether nonlinear transformation could improve prediction.8 In contrast, in an earlier study of 67 patients from a tertiary care hospital in Turkey, representing a wide range of kidney function and phosphate excretion, a nearly perfect correlation between 24hUrP and spot urine phosphate-to-creatinine ratios was noted (R2 5 0.93). This publication is often cited as justification for interchangeable use of spot phosphate-to-creatinine ratios, without conversion factors, in place of the 24-hour phosphate excretion. However, the regression models in this study were forced through the origin, greatly inflating model R2 values without regard to goodness of fit.9 As an illustration of this phenomenon, our predictive model would yield an R2 value of 0.995 if the intercept term were suppressed. A moderate and not perfectly precise relation between the spot urine sample and the 24-hour excretion is to be expected because phosphate intake and excretion are constantly changing throughout the course of a day; approximately half of the variation in 24hUrP excretion was not explained by our equation. Further studies are warranted to explore other characteristics that may account for the remaining between-subject variation and error in our
1 0.44 (ln(Up/cr)) 2
*
predictive equation. Some medications could alter urinary phosphate excretion. For example, thiazide or loop diuretics might directly (or indirectly, via parathyroid hormone) alter phosphate and creatinine excretion rates throughout the course of 1 day, resulting in different spot concentrations depending on the time of collection. We found that time of urine collection, treatment arm, and time since last meal were not independently associated with 24hUrP excretion after accounting for spot urine phosphate and creatinine values. It was interesting to note that there was no difference in the correlation of spot measurements with 24hUrP excretion between morning spot and afternoon spot collection times, nor did collection time independently predict 24-hour phosphate concentration. In our derivation cohort, most spot urine samples were collected between 9:00 a.m. and 1:00 p.m., and it is possible that the limited variation in collection times across participants may have hampered the uncovering of differential performance by time of day. The derivation cohort comprised a relatively homogeneous group of patients that was selected on the basis of clinical characteristics and willingness to adhere to treatment in the setting of a randomized controlled study. Although clinical trial settings have the limitation of being selective compared with general practice, they provide the advantage of systematic, complete, and high-quality data collection. Still, out of concern for the generalizability of our findings, we conducted external validation of our predictive equation in an independent sample. In conclusion, we developed a new equation to accurately predict 24-hour urinary phosphate excretion using spot phosphate and creatinine concentrations and readily available clinical data, including age, body mass, and gender.10
Practical Application We describe a novel equation to predict 24hUrP excretion using spot urine phosphate and creatinine, age, sex, and weight. Although the equation accounts for less than half of the variation in 24-hour urine phosphorus concentration, the equation is more accurate and precise than the urine phosphate-to-creatinine ratio alone and provides a valid and simple method for estimating 24hUrP excretion in patients with nondialysis-requiring CKD.
ESTIMATION OF URINE PHOSPHATE EXCRETION FROM SPOT COLLECTION
Acknowledgments An abstract describing these findings was presented at the meeting of the American Society of Nephrology 2012. They have not been published elsewhere.
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