NDT Advance Access originally published online on February 19, 2004
Nephrol Dial Transplant (2004) 19: 1204-1211
Nephrol Dial Transplant Vol. 19 No. 5 © ERA-EDTA 2004; all rights reserved
Original Article
Artificial neural networks improve the prediction of Kt/V, follow-up dietary protein intake and hypotension risk in haemodialysis patients
Luca Gabutti1,
Dario Vadilonga1,
Giorgio Mombelli2,
Michel Burnier3 and
Claudio Marone4
1Division of Nephrology and 2Department of Internal Medicine, Ospedale la Carità, Locarno, 3Division of Nephrology, University Hospital of Lausanne and 4Department of Internal Medicine, Ospedale San Giovanni, Bellinzona, Switzerland
Correspondence and offprint requests to: Luca Gabutti, Division of Nephrology, Department of Internal Medicine, Ospedale la Carità, Via Ospedale, 6600 Locarno, Switzerland. Email: lugabutti{at}swissonline.ch
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Abstract
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Background. Artificial neural networks (ANN) represent a promising
alternative to classical statistical and mathematical methods
to solve multidimensional non-linear problems. The aim of the
study was to compare the performance of ANN in predicting the
dialysis quality (Kt/V), the follow-up dietary protein intake
and the risk of intradialytic hypotension in haemodialysis patients
with that predicted by experienced nephrologists.
Methods. A combined retrospective and prospective observational study was performed in two Swiss dialysis units (80 chronic haemodialysis patients, 480 monthly clinical observations and biochemical test results). Using mathematical models based on linear and logistic regressions as background, ANN were built and then prospectively compared with the ability of six experienced nephrologists to predict the Kt/V and the follow-up protein catabolic rate (PCR) and to detect a Kt/V < 1.30, a follow-up PCR < 1.00 g/kg/day and the occurrence of hypotension.
Results. ANN compared with nephrologists gave a more accurate correlation between estimated and calculated Kt/V and follow-up PCR (P<0.001). The same superiority of ANN was also seen in the ability to detect a Kt/V < 1.30, a follow-up PCR < 1.00 g/kg/day and the occurrence of hypotension expressed as a percentage of correct answers, sensitivity, specificity and predictivity.
Conclusions. The use of ANN significantly improves the ability of experienced nephrologists to estimate the Kt/V and the follow-up PCR and to detect a Kt/V < 1.30, a follow-up PCR < 1.00 g/kg/day and the occurrence of intradialytic hypotension.
Keywords: artificial neural networks; haemodialysis; hypotension risk; Kt/V; prediction; protein catabolic rate
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Introduction
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Nephrologists treating haemodialysis patients are faced with
a large amount of clinical and biochemical historical data that
have to be used to make clinical decisions. In this task, the
physicians’ experience assigning different weights to
the known parameters continuously improves, allowing the elaboration
of diagnostic and therapeutic strategies. Statistical models
as multivariate linear or logistic regressions might ameliorate
the outcome of the prediction based on intuition, but even these
statistical procedures present limits due to the non-linearity
of the multidimensional functions studied. In many fields of
clinical medicine, artificial neural networks (ANN) have been
used successfully to solve complex and chaotic problems without
the need of mathematical models and a precise understanding
of the mechanisms involved [
1–
3]. Pharmacodynamic analysis
[
4–
6] (cyclosporin dosage adjustment [
7], heparin pharmacokinetics
during haemodialysis [
8]), time-course and diagnosis of chronic
nephropathies (IgA nephropathy [
9], glomerular
vs tubular renal
disease [
10]), allograft tolerance and function (chronic and
acute allograft rejection [
11–
14]), diagnosis of renal
transplant rejection [
15], prediction of cytomegalovirus disease
after renal transplantation [
16], stratification of cardiac
risk in renal transplantation [
17] and haemodialysis efficiency
evaluation (urea kinetic modelling [
18,
19]) are only a few examples
of the artificial intelligence opportunities.
We decided to investigate the ability of an artificial intelligence software based on ANN to predict the Kt/V, the follow-up protein catabolic rate (PCR) and the risk of hypotension during a dialysis session in a group of chronic haemodialysis patients. The predictions obtained with ANN, built keeping in mind the results of mathematical models based on linear or logistic regressions, were then compared with those obtained after submission of the same data to experienced nephrologists in charge of these patients.
The aim of the study was to verify whether ANN are useful tools in daily clinical practice to predict the dialysis quality, the follow-up dietary protein intake and the risk of hypotension.
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Subjects and methods
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A first random sample of chronic haemodialysis patients was
selected from two independent dialysis units in south Switzerland
in order to collect, retrospectively, the monthly clinical,
biochemical and anthropometric parameters necessary to calculate
the Kt/V, the theoretical Kt/V, the normalized PCR and to identify
the haemodialysis sessions with symptomatic hypotension episodes.
In order to estimate the changes of the protein intake, a supplementary
column listing the PCR value of 1 month after the basis PCR
(follow-up PCR) was added to the data table. With the intention
to identify, on the basis of a classical statistical method,
the data influencing the chosen dependent variables (Kt/V, follow-up
PCR and hypotension episodes) and to build a mathematical estimation
model, a linear regression for continuous data (Kt/V and follow-up
PCR) and a logistic regression for dichotomous data (hypotension
episodes) was performed. Furthermore, with the aim of building
non-linear continuous functions exploring and expressing the
interdependency between the collected data and the cited dependent
variables, a series of ANN were trained until they were successfully
tested. Finally, we selected, in a prospective way, a second
chronic haemodialysis patient group from the same two independent
dialysis centres in order to test the selected ANN and to compare
their performance with the prediction of six experienced nephrologists
of the same geographical region.
Patients and laboratory tests
We studied two random samples of 60 (control group; 420 biochemical and clinical monthly data) and 20 (experimental group; 60 biochemical and clinical monthly data) chronic haemodialysis patients (older than 17 years) treated for >6 months and without intercurrent illnesses at the moment of the enrolment.
The haemodialysis sessions were performed using a 4008 H bicarbonate-bag machine and a high-flux polysulfone membrane, both from Fresenius Medical Care (Stams, Switzerland).
Calculation of Kt/V, theoretical Kt/V and PCR
The Kt/V was calculated with a second generation single-pool Daugirdas formula [20]:
where R = post-dialysis blood urea nitrogen (BUN)/pre-dialysis BUN, UF = net ultrafiltration and W = weight. The theoretical Kt/V was calculated with the following formula [21]:
where Qb = blood flow, KoA = urea mass
transfer area coefficient, Qd = dialysate flow, dT = dialysis
duration and W = weight. The normalized PCR was calculated with
the Jindal and Goldstein formula [
22]:
where follow-up BUN = BUN at the beginning of the second dialysis session of the week, post-dialysis BUN = BUN at the end of the first dialysis session of the week and ID interval = time interval between the two dialyses.
The results of the calculated monthly dialysis quality and nutritional parameters were for the control and experimental groups, respectively: Kt/V 1.39±0.31 vs 1.38±0.25, theoretical Kt/V 1.41±0.39 vs 1.23±0.26 and PCR 1.16±0.26 vs 1.07±0.22 g/kg/day.
Definition of symptomatic hypotension during the dialysis treatment
Hypotension episodes were defined as symptomatic falls of the systolic blood pressure below 90 mmHg or sudden and symptomatic falls of the systolic blood pressure of > 30% of the previous measured values requiring isotonic saline infusion.
Artificial neural networks
ANN are accepted mathematical methods to translate complex multivariate non-linear relationships into continuous functions. According to Kolmogorov's theorem, paying attention to network structure, any arbitrary continuous function expressing the dependent variable on the basis of the input data may be built. ANN were created, trained (back-propagation algorithm) and tested using the BrainMaker Professional software (California Scientific Software 3.75). On the basis of a constant learning rate, the training tolerance and the percentage of good facts to stop training for each model were at first set at 15% and 95%, respectively. According to the recommendations of the software producer to optimize the performance of the network, the number of hidden layers was limited to one. This was built with the number of neurons equal to the number of input nodes if 
10 or with 10 neurons for a number of input nodes < 10 (default settings). Furthermore, to estimate the suitable minimum and maximum numbers of hidden neurons, the following two formulae were used:
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(guideline
2 of the BrainMaker Professional reference manual). The number
of connections was then calculated as follows (
Figure 1):
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Fig. 1. Schematic representation of the ANN used to predict the occurrence of hypotension episodes: 16 + 1a input variables, 16 + 1a hidden neurons and 289 connections (athreshold node and neuron added to avoid a zero output in the following layer).
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The ‘1’ added optionally to both the input and the
hidden layers represents a threshold neuron; an extra neuron
that always fires at full strength allows the neurons in the
next layer to have a non-zero output even if all inputs are
zeros. A sigmoid transfer function was chosen for each neuron.
An ANN was then designed and trained with the training tolerance
and the percentage of good facts to stop training set, respectively,
at 15% and 95% for the first attempt to obtain a successfully
testable ANN, modifying then the tolerance stepwise from alternately
plus or minus 0.5% until five ANN for each of the three dependent
variables (Kt/V, follow-up PCR and hypotension episodes) were
successfully tested (>85% of correct answers with a tolerance
of 20%). As input nodes, the variables known or supposed to
influence the value of the desired prediction (according to
literature data, intuition and results of the linear and logistic
regressions) have been used: nutritional (pre-dialysis serum
phosphate, serum albumin, pre-dialysis creatinine, pre-dialysis
BUN, pre-dialysis potassium and pre-dialysis ionized calcium),
anthropometric (sex, age and body mass index), biological (haematocrit)
and dialysis quality (post-dialysis weight, net ultrafiltration,
Qb
x dialysis duration and dialyser surface area) parameters
to predict Kt/V (15 input variables, 15 hidden neurons and 255
connections), nutritional (pre-dialysis serum phosphate, serum
albumin, net ultrafiltration, pre-dialysis BUN and PCR) and
dialysis quality (Kt/V) parameters to predict follow-up PCR
(six input variables, 10 hidden neurons and 81 connections)
and nutritional (serum albumin, body mass index, pre-dialysis
creatinine, pre-dialysis BUN, pre-dialysis ionized calcium and
pre-dialysis pH), anthropometric (sex, age and post-dialysis
weight), biological (haematocrit) and dialysis (dialysis duration,
Qb, net ultrafiltration, dialysate sodium and calcium concentrations
and dialyser surface area) parameters to predict the occurrence
of hypotension (16 input variables, 16 hidden neurons and 289
connections). The study was designed according to the prescriptions
of Cross
et al. [
3].
Statistical and data analysis
Statistical and data analysis was performed using two different statistical software packages (Systat 7.0 and SPSS 11.0; SPSS Inc.). Systat was used to perform the multivariate logistic regression involving the hypotension substudy, whereas SPSS was used to elaborate the multivariate linear regression of the Kt/V and follow-up PCR substudies. Non-parametric kernel density estimators were used to show the distribution of the relative error generated from the estimation of the Kt/V and follow-up PCR. The differences between kernel curves were judged with a repeated-measure analysis of variance (ANOVA) and a post-hoc Bonferroni test. In all cases a P-value of 
0.05 was considered statistically significant. Accuracy is expressed by the combined root mean square error calculated as the square root of [(mean difference in estimate – observed)2 + (SD of the difference)2]. Agreement between the predictions and the basis data is expressed by ‘limits of agreement’, ‘95% confidence interval for the bias’ and ‘95% confidence interval for the lower and upper limits of agreement’, according to Bland and Altman [23]. For Kt/V and follow-up PCR, results were expressed using a cut-off of, respectively, 1.30 and 1.00 g/kg/day to define correct answers and consequently sensitivity, specificity and predictivity (= positive predictive value) of the ANN or nephrologists estimations. The differences between these data were judged with a two samples Student's t-test. Values are presented as means±SD.
Comparison with experienced nephrologists
Six nephrologists from three different Swiss dialysis centres were shown the monthly clinical, biochemical and anthropometric data of the experimental group and they were asked to predict the Kt/V, the follow-up PCR and the occurrence of hypotension. The distribution of the error in the prediction (for Kt/V and follow-up PCR), the amount of correct answers, the sensitivity, the specificity and the predictivity were than compared with the results obtained with the selected ANN.
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Results
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The characteristics of the studied populations, the haemodialysis
prescriptions and the results of the monthly biochemical parameters
in the experimental and control groups are listed in
Table 1.
Table 2 shows the results of the logistic regression for the
estimation of occurrence of hypotension during dialysis (
P<0.001)
and of the linear regressions for the estimation of the Kt/V
(
P<0.001) and the follow-up PCR (
P<0.001). The model for
the estimation of occurrence of hypotension gives a significant
correlation only for age, net ultrafiltration, serum phosphate
and dialysate sodium; that for the estimation of Kt/V demonstrates
a significant correlation only for body mass index, net ultrafiltration
and serum pH, BUN and creatinine and, finally, only serum phosphate
and BUN, basis PCR and dialysate calcium show a significant
correlation for follow-up PCR.
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Table 1. Characteristics of the studied populations, haemodialysis prescriptions and results of the monthly biochemical parameters in the experimental and control groups
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Table 2. Results of the logistic regression for the estimation of occurrence of hypotension during dialysis and of the linear regressions for the estimation of Kt/V and follow-up PCR
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Figure 2 depicts graphically the distribution of the absolute
error for the estimation of Kt/V predicted from ANN, nephrologists
and obtained with the Brenner and Drukker formula. The ANOVA
of the absolute value of the error for the three predictions
reaches a significant level, which is compatible with the curves
behaviour. The differences between the ANN curve and the other
two is significant according to a post-hoc Bonferroni test.
Similarly,
Figure 3 shows the same curves for the estimation
of follow-up PCR predicted from ANN and nephrologists. The ANOVA
of the absolute value of the error for the two predictions also
reaches a significant level for these distributions.
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Fig. 2. Non-parametric kernel density estimator (analogous to a continuous histogram that shows where the data are most concentrated in the sample) showing the distribution of the absolute error for the estimation of Kt/V. Dashed line, ANN; solid line, nephrologists; dashed and dotted line, theoretical Kt/V obtained with the Brenner and Drukker formula. P-values for the differences between the curves have been superimposed on the graph.
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Fig. 3. Non-parametric kernel density estimator (analogous to a continuous histogram that shows where the data are most concentrated in the sample) showing the distribution of the absolute error for the estimation of follow-up PCR. Dashed line, ANN; solid line, nephrologists. P-values for the differences between the curves have been superimposed on the graph.
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According to Bland and Altman, agreements between the predictions
and the basis data expressed by ‘limits of agreement’,
‘95% confidence interval for the bias’ and ‘95%
confidence interval for the lower and upper limits of agreement’
are given in
Table 3. These results are concordant with the
previous statistical analysis and confirm the overall reduction
in the magnitude of the error by the use of ANN.
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Table 3. Accuracy expressed by the combined root mean square error, agreement expressed by the ‘limits of agreement’, the ‘95% confidence interval for the bias’ (95% bias) and the ‘95% confidence interval for the lower (95% lower) and upper (95% upper) limits of agreement’ in the estimation of Kt/V and follow-up PCR. P-values are specified only if differences are signifcant
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Histograms showing the percentage of correct answers, sensitivity,
specificity and predictivity in the estimation of the occurrence
of hypotension, of the Kt/V (lower or higher than 1.30) and
of follow-up PCR (lower or higher than 1.00 g/kg/day) for the
ANN and the nephrologists are presented in
Figure 4, whereas
the absolute numbers of correct answers, true and false positive
and false negative in the same estimations are listed in
Table 4.
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Fig. 4. Histograms showing the percentage of correct answers, the sensitivity, the specificity and the predictivity in the estimation of (A) the Kt/V (lower or higher than 1.30), (B) the follow-up PCR (lower or higher than 1.00 g/kg/day) and (C) the occurrence of hypotension episodes for, respectively, the ANN and the nephrologists (NEPH). Significant differences are highlighted (P-values are specified).
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Table 4. Ability to detect a Kt/V <1.30, a PCR <1.00 g/kg/day and hypotension episodes expressed as correct answers, true and false positive and false negative (n = 60). P-values are specified only if differences are significant
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Discussion
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In the evaluation of chronic haemodialysis patients, biochemical
data determined at monthly intervals, as well as clinical parameters
registered at each dialysis session, hide important information
that could be very useful for the management of the patients
and for the continuing education of the nephrologist himself.
Our data show that the use of ANN enables to achieve a better
prediction of Kt/V, follow-up PCR and occurrence of intradialytic
hypotension than the intuitive prediction of experienced nephrologists.
Mathematical models based on usual statistics are often disappointing when used to analyse multidimensional non-linear data. In fact, logistic regression applied to the risk of hypotension (dichotomous data) and linear regressions used to estimate Kt/V and follow-up PCR (continuous variables), on the one hand, did not permit building a model that could be used in the daily clinical practice and, on the other, sometimes gave disconcerting results. For instance, in the linear regression using Kt/V as the dependent variable, body mass index, dry weight, ultrafiltration and pre-dialysis BUN, creatinine, pH and haematocrit contrary to blood flow, dialyser area and dialysis duration surprisingly gave no significant correlations. Keeping in mind that for the calculation of Kt/V we used a single-pool model that gave an estimation of the true value based only on BUN, dry weight and ultrafiltration and that the variability in the distribution of the data for blood flow, dialyser area and dialysis duration in the studied population was low, the beta-coefficients and the P-values of the linear regression are not as strange as they appear at first sight. Furthermore, linear regressions, as expressed by their name, are not able to show positive correlations based on non-linear functions, such as logarithmic, exponential or polynomial.
Data multidimensionality and non-linearity are the typical application fields for artificial intelligence and, in particular, for ANN. These programs have been successfully utilized in various medical specialties and the number of published studies demonstrates that the subject is in continuous rapid expansion [4–19].
Our data, in the absence of previous comparable studies, show that:
- The information contained in the historical biochemical results and clinical parameters of the patients might significantly improve the ability of nephrologists to predict the occurrence of intradialytic hypotension episodes. This means that our intuition, even if supported by long experience and the classical statistical methods, misses out on an important part of the usually available information.
- The useful experience of the nephrologists enables a more accurate prediction of Kt/V than the algorithm proposed by Brenner and Drukker [22].
- Nevertheless, in the estimation of Kt/V, artificial intelligence can further improve the prediction.
- Even in the prediction of follow-up PCR, which in day to day experience might resemble an unsolvable task, ANN demonstrate their positive performance and potential usefulness.
In conclusion, our data show that ANN can give a significant contribution and be helpful tools in clinical practice for the nephrologist treating chronic haemodialysis patients. The correct appreciation of the intradialytic hypotension risk and of the trend in the evolution of the nutritional state are two capital challenges that could be solved by an ANN approach, thus permitting the application of prophylactic measures.
Future studies will show in which way the ANN performance could be further improved by increasing the extension of the retrospective data-pool and/or by the application of the method to the clinical course of a single patient.
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Acknowledgments
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This work was funded by a grant from the Fondazione Ettore Balli,
Locarno, Switzerland. We are indebted to Lisa Pellegrini, who
contributed to the conduct of the study and was involved in
data collection.
Conflict of interest statement. None declared.
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Received for publication: 27. 8.03
Accepted in revised form: 3.12.03
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Abstract
Introduction
