Application of fuzzy logic to predicting erythropoietic response in hemodialysis patients

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The purpose of this study was to demonstrate how fuzzy sets can be used in a pharmacodynamic model to represent the uncertainty about the classification of an end-stage renal disease patient’s response to erythropoietin.


A pharmacodynamic model was developed to predict future hemoglobin response to administered erythropoietin for a population of 186 patients with end-stage renal failure and anemia. The prediction was performed by a weighted linear combination of past hemoglobin, transferrin saturation, and erythropoietin dose. Patients were classified based on their response to administered erythropoietin into (i) all patients into 1 group (population approach), (ii) all patients into either a poor or normal responder group (subpopulation approach - traditional classification), and (iii) all patients by partial membership into the poor and normal responder groups (subpopulation approach - fuzzy classification). One half of the data set was randomly selected to estimate the model parameters, and the second half was used to test the estimated model. This randomization was repeated 100 times for both males and females.


Mean square error decreased significantly through the incorporation of hemoglobin response categorization from the control group (1.32 ± 0.07), to crisp coding (1.23 ± 0.07), to fuzzy coding (1.20 ± 0.07) with an overall p value < 0.001.


Uncertainty in the categorization of subjects into 2 erythropoietin response groups of poor or normal response has been shown to benefit from the use of fuzzy categories, with a significant improvement in model performance. (Int J Artif Organs 2008; 31: 1035–42)

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