

ORIGINAL ARTICLE 

Year : 2019  Volume
: 22
 Issue : 2  Page : 258264 

Significance of the difference in the estimates of glomerular filtration rate obtained using different models
J Onyekwelu^{1}, CH Nwankwo^{2}
^{1} Department of Research, Obinwanne Hospital and Maternity, Nkpor, Idemili North, Nigeria ^{2} Department of Statistics, NnamdiAzikiwe University, Awka, Anambra, Nigeria
Date of Acceptance  05Nov2018 
Date of Web Publication  7Feb2019 
Correspondence Address: Dr. J Onyekwelu Obinwanne Hospital and Maternity, 19 Uba Street, Nkpor, Idemili North, Anambra Nigeria
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/njcp.njcp_360_17
Abstract   
Objective: Chronic kidney disease (CKD) prevalence is rising in Nigeria. Most cases are diagnosed as end stage disease despite availability of formulae to estimate glomerular filtration rate (GFR). Existing formulae, none of which is modelled on Nigerian variables, give different estimates. This study tests the significance of the difference in the estimates obtained using Modified Diet in Renal Disease (MDRD) Study and Chronic Kidney DiseaseEpidemiology (CKDEpi) formulae. Methodology: This is a crosssectional study. Data on age, gender, and serum creatinine were used to estimate GFR. Paired sample t test was used to check for difference in means, Pearson correlation test for correlation and Bland and Altman plot for systematic bias. Simple linear regression was used to check for presence and significance of proportional bias. Results: Of the 166 patients studied, 62 were males and 104 were females. Mean age was 49.06 years ± 15.26. Youngest was 18 years and the oldest 81 years. Mean eGFR of 69.4 and 72.77 ml/min/1.73m^{2} for MDRD and CKDEpi models respectively differed significantly, P < 0.001. Bland and Altman plot showed lack of agreement of eGFR estimates from the two models with significant bias of 3.37ml/min/1.73m^{2} despite good correlation, r = 0.984. There was significant proportional bias, P < 0.001. Conclusion: MDRD significantly underestimated GFR compared to CKDEpi in a Nigerian population. This bias was proportional and increased as mean eGFR increased. MDRD and CKDEpi models do not agree in their measurements of eGFR and should not be used interchangeably. There is urgent need for further studies to develop GFR estimating model on Nigerian variables.
Keywords: CKDEpi, difference, GFR, MDRD, models, Nigeria
How to cite this article: Onyekwelu J, Nwankwo C H. Significance of the difference in the estimates of glomerular filtration rate obtained using different models. Niger J Clin Pract 2019;22:25864 
How to cite this URL: Onyekwelu J, Nwankwo C H. Significance of the difference in the estimates of glomerular filtration rate obtained using different models. Niger J Clin Pract [serial online] 2019 [cited 2019 Sep 15];22:25864. Available from: http://www.njcponline.com/text.asp?2019/22/2/258/251789 
Introduction   
The glomeruli act as sieve for blood passing through the kidneys. The rate at which filtered blood passes through the kidneys is glomerular filtration rate (GFR). The GFR is the best indicator of renal health.^{[1]} Creatinine, an endogenous end product of creatine phosphate metabolism, is solely excreted through the kidneys, and the volume of plasma that is cleared of this creatinine in a unit time, creatinine clearance (CL_{cr}), estimates the GFR. Creatinine, however, is secreted by the proximal tubules of the kidney, and this makes CL_{cr} to overestimate the GFR.^{[2]} Fortunately, this bias is known to be about 15% of the total estimate.^{[2]} Exogenous markers such as diethylenetriaminepentaacetic acid, ethylenediaminetetraacetic acid, and iothalamate are also used to estimate the GFR. Exogenous markers are expensive and technically difficult to use. These make them difficult to use in clinical settings in developing countries like Nigeria. Creatinine is an endogenous marker that is excreted solely by the kidney, and its clearance is a good estimator of renal health.^{[1]}
The GFR is used to stage chronic kidney disease (CKD) as shown in [Table 1].^{[1]}
Management of CKD depends on the stage of the disease. The stage influences the choice and dosage of drugs, restriction of certain food and salts, commencement of dialysis, and decision to do renal transplant.
Where, U_{c } is urine creatinine, Urine vol is 24h urine volume, S_{cr} is serum creatinine, and 1440 mins is minutes in 24 h.
This requires the collection of 24h urine. There are technical difficulties in timing, proper collection, and storage of 24h urine. One also has to wait for 24 h to make diagnosis and take decision. It therefore became necessary to develop models that can be used to estimate GFR without using 24h urine.
There are many models used to estimate GFR, but two are mainly used in Nigeria. The models depend on age, gender, race, and serum creatinine. They are the Modification of Diet in Renal Disease (MDRD) study equation and Chronic Kidney Disease Epidemiology Collaboration (CKDEPI) formula.
MDRD formula:^{[3]}
Where, Scr is serum creatinine
CKDEPI formula:^{[4]}
Where, Scr is serum creatinine (mg/dl).
k is 0.7 for females and 0.9 for males.
α is −0.329 for females and −0.411 for males.
min indicates minimum of Scr/k and 1.
max indicates maximum of Scr/k and 1.
Despite the availability of these equations that can be used to estimate the GFR and make diagnosis of CKD early, the prevalence of CKD is rising in Nigeria. In 2009, Afolabi et al. found a prevalence of 20.4%.^{[5]} In 2014, Odenigbo et al. got a prevalence of 43.5%.^{[6]} Most (80%) cases that reach nephrologists involve young and middle aged people and are diagnosed as end stage, when treatment becomes difficult.^{[7]}
The apparent rise in the prevalence of CKD in Nigeria may be because of the rising prevalence of the predisposing factors: hypertension,^{[8]} diabetes mellitus ^{[9]} cystic kidney disease, and glomerulonephritis.^{[10]} The patients present late to nephrologists.^{[7]} The late presentation may be because the primary care physicians fail to make appropriate diagnosis early enough. The tools to make this diagnosis are the estimated GFR (eGFR) estimating formulas: MDRD and CKDEPI formulas. If the estimates show significant differences, then there will be significant differences in staging the disease. The primary care physician, depending on the tool he uses, may miss early CKD, and hence, miss early referral.
The MDRD, as the name implies, was developed with renal disease patients in mind. It has been found to be imprecise and to underestimate GFR in high values.^{[11]} The developers thus developed a new equation that should be as accurate as MDRD in low GFRs and more precise and less underestimated at GFRs above 60 ml/min/1.7sm ^{2}. Hence, the development of CKDEPI model.^{[4]} These equations may expectedly disagree and it may be possible that this disagreement makes proper classification of CKD patients, and thus, proper diagnosis and early referral difficult.
There have been studies that compared the equations for estimating GFR in Nigeria that found different estimates from different equations ^{[12],[13],[14]} but few if any actually tested the significance of the differences in the estimates. These formulae were not modeled with Nigerian variables. The developers of MDRD developed CKDEPI formula because of inadequacies in the MDRD formula. The population is American, and they put in factors to capture black Americans showing that the accuracy of the model depends on race. If different models give different estimates of same variable and the models are not done with the index population in mind, then the difference in the estimates could be because of the peculiarity of the index population. The peculiarity of Chinese race informed the modification of MDRD study model to suit the Chinese population.^{[15]} Similar reasoning informed the development of a model in Bangladesh for the Bangladesh population.^{[16]} Greece also had to develop their own formula for their population.^{[17]} Eastwood et al. in 2010 stressed the urgent need for an equation tailored specifically to the needs of the lean populations of Africa.^{[18]}
The aim of this research is to investigate the significance of the difference in the estimates from the two models used in Nigeria to estimate GFR. The objective is to use the two models to estimate GFR from the same population of patients and test the difference in the estimates for significance for a set of data collected in a private general practice hospital in Nkpor, Anambra State of Nigeria.
The diagnosis and staging of CKD and cutting edge decisions on its management require eGFR estimates that will be very close to the real GFR. This research would have been the stimulus Nigerian researchers need to develop a model for Nigerian population with Nigerian variables.
Materials and Methods   
Study design
This is a crosssectional study of patients attending a general practice hospital.
Methods of data collection
Obinwanne hospital is a general practice hospital situated at Nkpor, an urban town close to Onitsha in Anambra State of Nigeria. The records of patients attending the hospital that had kidney function tests as part of the investigations in their management were extracted for study. Data on gender, age in years, weight in kg, and serum creatinine in mg/dl were extracted from the patients' folders. The serum creatinine tests were done by Jaffe kinetic method using Randox kit (USA). The kit is calibrated with isotope dilution mass spectrometrytraceable calibrator reportable in mg/dl. The data were analyzed with International Business Machines Corporation Statistical Package for the Social Science (SPSS) version 20, Armonk, NY, United States of America.^{[19]}
Sample size calculation
The formula ^{[20]} is (1)
Where, n = sample size.
α = significance level (fixed at 0.01).
z = critical value for 99% confidence level corresponding to 0.01 significance level = 2.58 for a 2tailed test.
p = prevalence of CKD is 0.435^{[6]} from previous study.
q = 1p
d = error level which the researchers are willing to tolerate (set at 0.1).
Renal failure is endstage kidney disease, and the researchers want to be 99% confident that the sample size will be large enough to pick any difference in the tests. The error level of 10% is used because the researchers want to be 90% confident that the calculated sample size will not be more than 5% away from the actual value.
Substituting the figures into equation (1) we have
Eventually, n = 166 was used because the number of case notes with relevant data from July 31, 2016 to June 30, 2017, a period of one calendar year, was 166.
Ethical issues
This study involved only records. Strict confidentiality was maintained not to disclose the identity of the patients that have the records. The content of the records includes: age, gender, and serum creatinine levels of the patients. The medical director of the hospital from where the data were obtained gave his consent for the study to be done in his facility.
Statistics
The eGFR is obtained using MDRD and CKDEPI models. The mean eGFR and standard deviation (sd) are obtained. Paired sample t test is used to test for significance of the difference in the means. The null hypothesis is that there is no difference in the means
where, , is the mean eGFR from MDRD.
is the mean eGFR from CKDEPI.
A scatter plot of the eGFRs from MDRD against CKDEPI is performed to show correlation visually. The Pearson's correlation coefficient is calculated.
The mean difference is calculated, and Bland and Altman plot is used to test for agreement of the two formulae and quantify bias by plotting the differences against the mean eGFR.^{[21]} The mean difference is the bias. There may be good correlation but still a consistent tendency for one method to exceed the other in the measurements. In the absence of a reference standard, the mean of the eGFR obtained from the same sample from same patient by the two methods is taken as the reference standard.
Mean eGFR = (MDRD + CKDEPI)/2.
Let x_{i} be eGFR from MDRD and x_{j } be eGFR from CKDEPI.
Let the mean of the difference , be the mean difference and is denoted as d¯ and the standard deviation as S_{d}, then the limit of agreement (LOA) is d¯±1.96S_{d}, where 1.96 is the standard normal variate for 95% confidence interval. Hence, 95% of the values should lie within the upper and lower LOA. The import of this LOA is subject to its clinical importance.^{[21]} For eGFR, two eGFRs are statistically different if they differ by more than 11 ml/min/1.73m ^{2}.^{[22]}
The standard error of the mean difference is estimated, and the 95% confidence interval around it is calculated. If it does not include zero, then the bias is significant.
A simple linear regression is used to test for the presence of proportional bias. Precision is assessed using the variability of the data. The assumption is that the differences in the eGFR from the models are normally distributed. This assumption is tested pictorially using histogram.
Results   
A total of 166 patients were studied, 62 males (37.3%) and 104 females (62.7%). The mean age was 49.06 years with sd 15.26. The youngest was 18 years and the oldest 82 years. The data on eGFR may not have a normal distribution, but the differences are approximately normally distributed (skewness is 0.579), see [Figure 1].  Figure 1: Histogram of differences in eGFR obtained using MDRD and CKDEPI models to test for normality of data. Skewness = 0.579
Click here to view 
The models show high correlation as shown by fitting a regression line on the scatter plot, see [Figure 2].  Figure 2: Scatter plot of eGFR of MDRD and CKDEPI models with fitted regression line to show correlation, r = 0.984. P < 0.001
Click here to view 
The mean and sd of the eGFRs from the two models are as in [Table 2]. The mean eGFR values from the two models significantly differ, P < 0.000. The mean difference, bias, is significant P < 0.000, showing that there is a consistent tendency for MDRD model to underestimate GFR compared with CKDEPI model using the mean of the two values as reference standard. The MDRD model is more precise because the sd of its mean is smaller.  Table 2: Mean and standard deviation of the eGFR from MDRD and CKDEPI formulae, the mean difference and limits of agreement
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Bland and Altman plot shows clearly a lack of agreement between the two models, with a bias of –3.37, and the confidence interval around the mean difference does not include zero. The upper and lower levels are shown by thick red parallel lines above and below the mean error, see [Figure 3]. Despite their high correlation, the two models consistently differ in their measurements.  Figure 3: Bland and Altman plot of difference of eGFRs obtained from MDRD and CKDinformation models against the mean values. As shown in Table 2, the bias is –3.37 and the models disagree
Click here to view 
[Table 3] shows the upper and lower confidence intervals around the mean difference using the standard error of mean. The upper level is −2.75, and the lower level is −3.99.  Table 3: Upper and lower confidence interval around the mean difference using the standard error of mean
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There is also evidence that there is proportional bias. The difference in the means of the eGFRs obtained from the models increase as the mean increases, see [Figure 4]. When the difference is plotted against the mean eGFR, the estimated coefficient is significant, t = −5.475, P < 0.000  Figure 4: Regression of difference in eGFR of MDRD and CKDEPI models against the mean eGFR. P – value is 0.000
Click here to view 
Discussion   
Our result shows a good correlation between MDRD and CKDEPI models in estimating GFR. This is expected because CKDEPI model was developed to be an improvement on the earlier MDRD model.^{[4]} Uche and Osegbo also noted this correlation even among sickle cell patients in South West Nigeria.^{[23]} However, correlation does not imply agreement. The mean eGFR obtained from the different models significantly differ on the paired t test. There is a mean difference whose confidence interval does not include zero. The 95% confidence interval of the mean difference illustrates the magnitude of a systematic difference in the measurements. If the line of equality, zero, is not in the interval, then the systematic difference is significant. This means that one method consistently under or overestimates compared with the other. It is known from previous research works that MDRD underestimates GFR more than CKDEPI. This bias has been quantified to be between 2 mls/min/1.73 m ^{2} and 5ml/min/1.73m ^{2}.^{[24],[25],[26]} Ours is 3.37.
Earlier work did not construct confidence interval around the mean difference to establish whether the bias is by chance or statistically significant. A confidence interval around the mean difference should be constructed and if the line of equality is not within the interval, then there is a significant systematic difference.
This research shows the interval as −2.75 to −3.99. It certainly does not include zero. This shows beyond reasonable doubt that MDRD systematically significantly underestimates GFR compared with CKDEPI model in this study on a Nigerian population.
The interval in the level of agreement from the Bland and Altman plot within which 95% of the measurement should fall is 15.88 (from upper Limit of Agreement (LOA) to lower LOA). This is the distance between mean difference ±2 sd (sd is standard deviation of the mean difference). Badrick and Turner had established that for clinical purposes, GFR fluctuation should not exceed 11 mls/min/1.73^{2}.^{[22]} The finding in this research is that the confidence interval is too wide and this even compounds the disagreement in the two models studied. Similar studies on Nigerian population could not be seen to compare this study with.
The regression of the difference against the mean eGFR also shows that this significant systematic bias is proportional. It increases as mean eGFR increases. The import of this proportional bias is that at higher levels of GFR, values obtained cannot be relied on and one can easily miss or wrongly diagnose early CKD. Good management outcome of CKD depends on its early detection. This tendency of MDRD to underestimate GFR compared with CKDEPI model suggests that MDRD model will be a good sensitive screening tool. CKD stage 1 is kidney damage with normal GFR (90 and above). This is the stage where management gives the best outcome. Intuitively, a screening tool that underestimates GFR will pick low normal GFR around 90 mls/min as below 90 mls/min. This high sensitivity inadvertently creates opportunity for picking up CKD early. Considering the high morbidity and mortality associated with CKD, it will be better to have a more sensitive screening test than a more specific one. There may be other factors that lead to increase in prevalence of CKD and late presentation to nephrologists but one cannot rule out the possibility that the screening test tool used may contribute if it is not sensitive enough. Fischer et al. noted that late referral of CKD patients to nephrologists may, in part, be because of the perceptions and knowledge limitations of the primary care providers.^{[27]}
Conclusion   
MDRD significantly underestimates GFR compared to CKDEPI in a Nigerian population. This bias is proportional and increases as mean eGFR increases.
The MDRD and CKDEPI models do not agree in their measurements of eGFR and should not be used interchangeably
Recommendation
There is urgent need for further studies to develop GFR estimating model on Nigerian variables.
MDRD can be used for screening purposes because it underestimates GFR compared to CKDEPI more at high values of GFR and as such is intuitively more sensitive.
Limitations
We could not establish the reference standard using CL_{cr} in 24h urine. Hence, the mean of the values from MDRD and CKDEPI models was used as the reference standard.
Financial support and sponsorship
There was no financial support or sponsorship to the researchers. The research was funded exclusively by the researchers.
Conflict of interest
There is no conflict of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4]
[Table 1], [Table 2], [Table 3]
