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Evolving Transductive Medical Decision Support Systems

Evolving Transductive Medical Decision Support Systems


The accurate evaluation of renal function is very important in the area of renal research and clinical practice. Glomerular filtration rate (GFR) is considered the best overall index to determine renal function in health and disease. Unfortunately, direct measurement of GFR is both too cumbersome and expensive for routine clinical care, so most clinicians rely upon the clearance of creatinine (CrCl) as a convenient surrogate for GFR, but the accuracy of CrCl is limited by methodological imprecision. Recently, the Modification of Diet in Renal Disease (MDRD) study developed a new formula more accurate to evaluate GFR, but it still may be insufficiently accurate outside of the trial setting to support good decision-making in routine clinical practice, so a novel transductive neuro-fuzzy inference system with weighted data normalization (TWNFI) was used for building personalized models for renal function evaluation.

MDRD Formula

The formula uses the following variables: age, race, gender, serum creatinine (Cr in mg/dl), serum albumin (Alb in g/dl) and blood urea nitrogen concentrations (Bun in mg/dl) and is defined as follows:

GFR = 170×Cr^(-0.999) × Age^(-0.176) × 0.762(if sex is female) ×1.18 (if race is black) × Bun^(-0.17) × Alb^(0.318)

The MDRD formulae to estimate renal function from serum creatinine may not be accurate in patient populations other than those in which they have been derived and validated. The performance of this formula within the general population can only be extrapolated from testing in a truly heterogeneous patient sample, in which the measurement of analytes such as serum creatinine is undertaken on a wide range of laboratories to reflect the reality of routine clinical practice.

Personalized Modeling for Medical Science

While inductive approaches are concerned with the development of a model to approximate data in the whole problem space (induction), and consecutively – using this model to calculate the output values for a new input vector (deduction) , in transductive systems a local model is developed for every new input vector, based on number of closest to this vector data from the training data set.

  • TWNFI is transductive - estimate the value of a potential model (function) only in a single point of the space (the new data vector) utilizing additional information related to this point. This approach seems to be more appropriate for clinical and medical applications of learning systems, where the focus is not on the model, but on the individual patient.
  • TWNFI is a better local generalisation over new data as it develops an individual model for each data vector that takes into account the new input vector location in the space.
  • TWNFI utilizes medical knowledge effectively as setting initial values for parameters of weighted data normalization.
  • TWNFI is an adaptive model, in the sense that input-output pairs of data can be added to the data set continuously and immediately made available for transductive inference of local models.

This type of modelling can be called “personalised”, and it is promising for medical decision support systems.


The data used in this research originate from the EPO AUS-14 study. GFR was measured as the renal clearance of chromium-51 ethylenediamine tetraacetic acid (51Cr-EDTA) corrected for body surface area (GFR-EDTA). The data set consists of 447 GFR-EDTA data in 178 patients.

Interface of GFR-TWNFI

Interface of GFR-TWNFI.

A GFR exemplar personalised model of a patient obtained with the use of the TWNFI

Rule 7:

Age is around 60.5
Gender is Male
Screat is around 0.31
Surea is around 20.7
Race is White
Salb is around 35.0

then GFR = 12.14 * Age^0.280 * Screat^-0.858 * Surea^0.029 * Salb^0.001

Rule 8:

Age is around 54.7
Gender is Male
Screat is around 0.45
Surea is around 24.9
Race is White
Salb is around 35.9

then GFR = 12.45 * Age^0.270 * Screat^-0.858 * Surea^0.038 * Salb^-0.003

Variable importances:

Age(0.80); Gender(0.60); Screat(1.00); Surea(0.60); Race(0.30); Salb(0.31)

Result and Conclusions

Comparative analysis of Global, Local and Personalised modelling on GFR

Weights of input variables

Model Neurons or rules Testing RMSE Testing MAE Age Sex Scr Surea Race


MDRD - 7.74 5.88 1 1 1 1 1 1
MLP 12 8.44 5.75 1 1 1 1 1 1
ANFIS 36 7.49 5.48 1 1 1 1 1 1
DENFIS 27 7.29 5.29 1 1 1 1 1 1
TNFI 6.8 (average) 7.31 5.30 1 1 1 1 1 1
TWNFI 6.8 (average) 7.11 5.16 0.89 0.71 1.00 0.92 0.31 0.56

The TWNFI method not only results in a “personalized” model with a better accuracy of prediction for every single person, but also depicts the most significant input variables (features) for the model that may be used for a personalized medicine and improved treatment.


[1] 2003 - Kasabov, N. and Song.Q., Neuro-fuzzy inference method and uses thereof, Patent Appl.529570, New Zealand, 17 November (2003)

[2] 2002 - Kasabov, N., and Song, Q., DENFIS: Dynamic Evolving Neural-Fuzzy Inference System and its Application for Time Series Prediction, IEEE Transactions on Fuzzy Systems, vol. 10, no.2, April, (2002) 144-154.

[3] 2002 - Kasabov, N. Evolving connectionist systems:Methods and applications in bioinformatics, brain study and intelligent machines, Springer,London (2002)

[4] 2000 - Song, Q., and Kasabov, N., Dynamic Evolving Neuro-Fuzzy Inference System (DENFIS): On-Line Learning and Application for Time-Series Prediction, Proceedings of the 6th International Conference on Soft Computing, October 1-4, 2000, Iizuka, Japan, 696-702

[5] 2004 - Song Qun and Kasabov Nikola, TWRBF - Transductive RBF Neural Network with Weighted Data Normalization, Lecture Notes in Computer Science, Vol.3316, ICONIP’2004, Springer Verlag, 2004

[6] 1999 - A. S. Levey, J. P. Bosch, J. B. Lewis, T. Greene, N. Rogers, and D. Roth, "A more Accurate Method To Estimate Glomerular Filtration Rate from Serum Creatinine: A new Prediction Equation," Annals of Internal Medicine, vol. 130, pp. 461-470, 1999.

[7] 2004 - Roger, S.D., McMahon, L.P., & Voss, D., et, al. Effects of early and late intervention with Epoetin a on Left Ventricular Mass among patients with Chronic Kidney Disease (Stage 3 or 4) : results of a randomised clinical trial. Journal of the American Society of Nephrology. 15(1), 2004, 148-156.


[1] 2006 - Qun Song, Nikola Kasabov, Tianmin Ma and Mark Roger Marshall, Integrating regression formulas and kernel functions into locally adaptive knowledge-based neural networks: A case study on renal function evaluation, Artificial Intelligence in Medicine, Volume 36, Issue 3, , March 2006, Pages 235-244.

[2] 2005 - Qun Song, Tianmin Ma, Nikola Kasabov, Transductive Knowledge Based Fuzzy Inference System for Personalized Modeling, Lecture Notes in Computer Science, Volume 3614, Dec 2005, Pages 528 - 535

[3] 2005 - M.R. Marshall, Q. Song, T.M. Ma, S. MacDonell, N.Kasabov, Evolving Connectionist System versus Algebraic Formulas for Prediction of Renal Function from Serum Creatinine, Kidney International, 2005, Vol. 67, Issue 5, pp.1944-1954

[4] 2005 - Q. Song and N. Kasabov, NFI: A Neuro-Fuzzy Inference Method for Transductive Reasoning, IEEE Transactions on Fuzzy Systems, IEEE Transactions on Fuzzy Systems, Vol 13, Issue 6, ISSN: 1063-6706, Pages 799- 808.

[5] 2004 - Song Qun and Kasabov Nikola, TWRBF - Transductive RBF Neural Network with Weighted Data Normalization, Lecture Notes in Computer Science, Vol.3316, ICONIP’2004, Springer Verlag, 2004

[6] 2004 - Song, Q., Ma, T. and Kasabov, N., "LR-KFNN: Logistic Regression-Kernel Function Neural etworks and the GFR-NN Model for Renal Function Evaluation", Proc. Of International Conference on Computational Intelligence for modelling, Control and Automation 2004 (CIMCA2004), Gold Coast, Australia, 12 - 14, July, 2004, pp. 946 - 951.

[7] 2003 - Q. Song, T. Ma and N. Kasabov, A Novel Generic Higher-Order TSK Fuzzy Model for Prediction and Applications for Medical Decision Support in Proc. of the Eight Australian and New Zealand Intelligent Information Systems Conference, Sydney, Australia Dec. 2003 (241-245)

[8] 2003 - Q. Song, N. Kasabov, Weighted Data Normalization and Feature Selection for Evolving Connectionist Systems Proceedings in Proc. of the Eight Australian and New Zealand Intelligent Information Systems Conference, Sydney, Australia Dec. 2003 (285-290)


The research presented in the paper is funded by the New Zealand Foundation for Research, Science and Technology under grant NERF/AUTX02-01, the New Zealand National Kidney Foundation under grant GSN-12, and the Auckland Medical Research Foundation. The Top Achiever Doctoral Scholarship from the Tertiary Education Commission (TEC) of New Zealand also funds the research.

Useful Links

  1. The Kidney Disease Outcomes Quality Initiative (K-DOQI)

  2. Evolving Connectionist Systems

  3. National Referral Guidelines for Renal Medicine (New Zealand Ministry of Health)

  4. The Medical Algorithms Project

  5. The CARI Guidelines

Last updated: 02 Dec 2011 10:38am

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