Estimation of glomerular filtration rate by a radial basis function neural network in patients with type-2 diabetes mellitus

Diabetic nephropathy is the leading cause of end stage renal disease, a condition characterized by abnormal glomerular filtration rate (GFR) and serum creatinine (SCr) [1]. The National Kidney Foundation (NKF) considers GFR as the best overall measure of kidney function in healthy and diseased individuals [2]. However, measurement of GFR by use of radioisotopes is time-consuming and expensive, so this method is not used in routine clinical practice. Instead, numerous equations have been proposed to estimate the GFR without the need for radioisotopes [2]. These equations consider SCr and several additional variables, such as age, gender, race, and body size [2]. The American Diabetes Association [3] also recommends estimation of GFR from serum creatinine (SCr) -based formulae, such as a Modification of Diet in Renal Disease (MDRD) study equation [4].

However, these equations may yield inaccurate estimates in some populations, such as elderly Chinese patients with CKD [5]. Recent studies have criticized the equations currently used to estimate GFR in diabetic patients [6‐10]. In particular, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation [6], the Mayo Clinic Quadratic (MCQ) equation [7], and the four-variable MDRD equation [8] all underestimated GFR in patients with type-2 diabetes, and the Cockcroft-Gault equation overestimated GFR in patients with type-2 diabetes [10]. These equations may be inaccurate because they do not account for ethnicity [11]. For example, in a group of Chinese patients with CKD, the MDRD equation 7 and the abbreviated MDRD equations underestimated GFR in patients with near-normal renal function and overestimated GFR in patients with advanced renal failure [12]. These equations may also be inaccurate because they were developed by linear regression methods [11, 13, 14]. Linear regression models do not account for the non-linear physiological processes that underlie GFR. Thus, it is important to develop better methodologies for estimation of GFR.

Artificial neural networks (ANNs) have been successfully used to model non-linear phenomena in the field of engineering forecasting. Modern ANNs provide effective nonlinear mapping of data, good fault tolerance, and good self-organization [15, 16]. Previous research demonstrated that an ANN was more accurate than a logistic regression model in prediction of clinical outcome in patients with systemic inflammatory response syndrome and hemodynamic shock [17]. Other research groups have used ANNs to estimate GFR, including a knowledge-based neural network (KBNN) model [18], an evolving connectionist systems (ECOS) model [19], and a tree-based model with 6 terminal nodes [15]. In all of these cases, the ANNs provided better estimates of GFR than the traditional equations.

Radial basis function (RBF) networks are among the most widely used ANNs, but there have been limited clinical applications of these networks. Our previous study [20] described a simple RBF network for estimation of GFR (eGFR_RBF) in a group of 327 Chinese patients with chronic kidney disease (CKD). The results indicated that the eGFR_RBF had less bias and greater precision than the traditional MDRD equations. The accuracy (deviation less than 30% from the sGFR) of the eGFR_RBF was significantly better than those from traditional eGFR equations, such as the Jelliffe-1973-equation and the Ruijin-equation [20].

In the present study, we tested the precision and accuracy of an RBF network model for estimation of GFR in an independent group of 207 Chinese patients who had type-2 diabetes and CKD and compared the results of the RBF network method with the results from two traditional MDRD formulae [13].

A total of 207 patients (119 males, 88 females) with a mean age of 61.43 years (SD = 12.03) were enrolled. Table 1 shows the baseline demographic and clinical characteristics of the 207 patients and of sub-groups with different stages of CKD. There were 64 patients (30.9%) with stage I/II disease, 81 patients (39.1%) with stage III disease, and 62 patients (30%) with stage IV/V disease. As expected, patients with more severe disease had lower serum Alb and sGFR, and higher SCr and BUN (Table 1).

Table 2 shows the sGFR values and the three different estimates of GFR (eGFR₄, eGFR₆, and eGFR_RBF) for all 207 patients and for sub-groups with different stages of CKD. As expected, GFR values were lower in patients with more advanced disease. The eGFR_RBF of all 207 CKD patients and of patients with different stages of CKD were significantly higher than the sGFR values (p < 0.01 for all). In addition, for patients with stage III or stage IV/V CKD, the eGFR_RBF values were significantly higher than those from eGFR₄ and eGFR₆ (p < 0.01 for both).

The validity of an estimate is a function of its accuracy and precision, and a valid estimate should be close to the true value (low bias) and be reproducible [26]. Table 3 presents the overall performances of the 3 different estimates of GFR in all 207 patients and in patients with different stages of CKD. Each row in the table shows the median difference of eGFR and sGFR and the inter-quartile range (IQR), the median absolute difference of eGFR and sGFR and the IQR, and the percent of GFR estimates within 15% (P₁₅), 30% (P₃₀), and 50% (P₅₀) of sGFR [26]. The results indicate that for all 207 patients, the IQR of the eGFR_RBF was smaller than those from eGFR₄ and eGFR₆, indicating better precision for the RBF network; however, the median difference of the eGFR_RBF from sGFR was significantly higher than those from eGFR₄ and eGFR₆ (p < 0.0167 for both). The same trends occurred in patients with stage III CKD and stage IV/V CKD. The eGFR_RBF had a lower median absolute difference from sGFR and a higher percent of estimates within 15% (P₁₅) and 30% (P₃₀) of sGFR, suggesting that eGFR_RBF had better accuracy. However, the differences between eGFR_RBF and eGFR₄ and eGFR₆ were not statistically different. The results also indicate that for the patients with stage I/II CKD, the median absolute difference of eGFR_RBF and sGFR (19.73) was significantly less than that of eGFR₄ and sGFR (27.28) (p < 0.0167), although the P₅₀ for eGFR_RBF (n = 56, 87.5%) was significantly higher than that for eGFR₄ (n = 49, 76.6%) (p < 0.0167).

Figure 1 shows Bland-Altman plots for comparisons of sGFR with GFR estimated by eGFR₄ (A), eGFR₆ (B), and eGFR_RBF (C). The precision is indicated by the distance between the dashed lines (95% limits of agreement) [27]. The results indicate that the distance between lines of 95% limits of agreement was 71.4 for eGFR_RBF, significantly lower than that for eGFR₄ (91.5) and eGFR₆ (85.2). Thus, this analysis also indicates that the eGFR_RBF had better precision than the two other estimates from the MDRD equations. However, Figure 1 also shows that the mean differences of sGFR and eGFR₄ was 3.1, sGFR and eGFR₆ was 1.0, and sGFR and eGFR_RBF was 11.1. This indicates that eGFR_RBF had greater bias than the estimates from the MDRD equations and over-estimate the GFR.

We compared the performance of an RBF neural network in the estimation of GFR with the performance of two traditional GFR estimates based on the MDRD equations (MDRD-4 and MDRD-6) in patients with type-2 diabetes and different stages of CKD. Our results indicate that the RBF network provided more precise estimates of GFR than the MDRD equations, and also provided significantly more accurate estimates of GFR for patients with stage I/II CKD. However, the RBF network also had higher bias than the traditional MDRD equations. In particular, the eGFR_RBF tended to over-estimate GFR more than eGFR₄ and eGFR₆, especially for patients with CKD stage IV/V (Table 2).

These advantages of ANNs have led to their use in several previous studies for estimation of GFR. Song et al. [18] used a knowledge-based neural network model (KBNN) for evaluation of renal function based on 441 GFR data vectors from 141 patients. Their proposed GFR prediction model had at least 10% better accuracy than any of the individual regression formulae or a standard neural network model. Marshall et al. [19] used evolving connectionist systems (ECOS), in which computing structures are trained to generate output from a given set of input variables. They concluded that their ECOS model provided better prediction of GFR in routine clinical practice. No ANNs have been used to estimate GFR of patients with type-2 diabetes mellitus.

It is noteworthy that the RBF network used in this study was only based on SCr measurements, in contrast to the re-expressed MDRD equations, which require measurement of 4 or 6 variables. The NKF does not recommend use of SCr alone for assessment of kidney function [2]. However, previous research indicated that use of fewer variables can yield acceptable estimates of GFR. For example, Bevc et al. [28] reported that a cystatin C-based estimate, which only requires measurement of serum cystatin C, is a reliable marker of GFR in elderly patients and is comparable to the creatinine-based formulae, including the CKD-EPI formulae. Our results suggest that an RBF model based on a single measurement (SCr) can provide precise and accurate estimates of GFR.

There are several limitations to our study. First, SCr was measured by the enzymatic method. Peake et al. [29] indicated that the enzymatic creatinine assay, although theoretically more specific, can have interference problems. However, this method produces results for patient samples that agree closely with the results from isotope dilution mass spectrometry (ID-MS). This motivated our use of the re-expressed MDRD equations (MDRD-4 and MDRD-6) instead of the original equation [4], because the original MDRD equation was developed for use with ID-MS traceable serum creatinine [30]. Second, ANN models can be difficult to display as equations and cannot be readily used without special software, so physicians may be reluctant to accept the results of ANN models. There is need for a platform that can display ANN models and that allows other researchers to readily perform external validation. Third, a previous study-indicated that GFR estimated by 99mTc-DTPA dynamic renal imaging might not better than the modified abbreviated MDRD equation [31], and the renal dynamic imaging method was less accurate than CKD-EPI equation as well [32]. However, the same study found that the two methods performed similar capability in determining GFR among higher-GFR patients [32], and ^99mTc-DTPA dynamic renal dynamic imaging yields accurate results that are nearly the same as those from measurements of inulin clearance [33]. Rehling et al. showed that a regression line between the values measured by these different methods did not differ from the line of identity [33]. Ma et al. (2007) suggested that, using proper reference GFR, more adequate background subtraction, and soft-tissue attenuation correction may improve the accuracy of ^99mTc-DTPA dynamic renal imaging [31]. Finally, our RBF network predicted a higher GFR than that from ^99mTc- DTPA renal dynamic imaging. This might be due to differences of participants in the training group (CKD patients with and without diabetes [20]) and the study group (diabetes patients with and without normal kidney function). Use of more similar training and study groups would provide better external validation and may provide improved results.

A recent survey in China [34] showed that the prevalence of diabetes was 9.7%, corresponding to 92.4 million people. Although some of the established methods used to estimate GFR are suitable for Chinese patients with CKD [22], it is important to have more accurate and precise estimations of GFR. In some measures of accuracy and precision, our RBF neural network performed significantly better than the re-expressed MDRD equations in the estimation of GFR. In particular, the IQRs (Table 3) and 95% limits of agreement (Figure 1) for the eGFR_RBF were smaller than those from eGFR₄ and eGFR₆, indicating better precision for the RBF network. However, our data indicated that eGFR estimated by the RBF neural network tended to be higher than the sGFR, and this would result in under-estimation of CKD stage. We suggest that use of an RBF network model with more variables and testing of the model with additional data sets may ultimately provide more accurate and precise estimates of GFR.

In patients with type-2 diabetes, GFR estimated by our RBF network provided better precision and accuracy for some groups of patients than GFR estimated by the traditional MDRD equations. However, the RBF network estimates of GFR tended to have greater bias and higher than those indicated by sGFR determined by ^99mTc-DTPA renal dynamic imaging.