Bed Side Linear Regression Equations to estimate Equilibrated Urea

FERNÁNDEZ, ELMER ANDRÉS; VALTUILLE, RODOLFO; BALZARINI, MÓNICA

Hemodialysis / Book 2

InTechOpen

Lugar: Heidelberg; Año: 2011;

Three decades ago Sargent and Gotch established the clinical applicability of Kt/V, a dimensionless ratio which includes clearance of dialyzer(K),duration of treatment(t) and volume of total water of the patient (V), as an index of Hemodialysis (HD) adequacy (Gotch & Keen,2005). This parameter derived from single-pool(sp) urea(U) kinetic modeling has become the gold standard for HD dose monitoring and it is widespread used as a predictor of outcome in HD populations (Locatelli et al.,1999; Eknoyan et al.,2002; Locatelli,2003).However,this spKt/V overestimates the HD dose because it does not take into account the concept of U rebound (UR).UR begins immediately at the end of HD session and it is completed 30-60 minutes after. UR is related to disequilibriums in blood/cell compartments as well as the flow between organs desequilibriums, both produced during HD treatment. Therefore,equilibrated (Eq) Kt/V is the true HD dose and it requires the measurement of a true EqU when UR is completed. A blood sample to obtain an EqU concentration has several drawbacks that make this option impractical (Gotch and Keen,2005).For this reason in the last decade several formulas were developed to predict the EqU and also (Eq) Kt/V avoiding to retain the patient for the extraction of a new blood sample.The “rate formula” (Daurgidas et al., 1995) is the most popular and validated equation and it is based in the prediction of (Eq)Kt/V as a linear function of (sp)Kt/V and the rate of dialysis(K/V). Tattersall has also device a robust formula which is based in the double–pool analysis (Smye et al.1999). This EqU prediction approach is conceptually rigorous but it is not accurate (Gotch, 1990; Guh et al., 1999; Fernandez et al., 2001) because it needs an intradialytic blood sample at 2/3 of the session time. Consequently, the availability of a model to predict subject-specific equilibrated concentration will be very helpful. Although the behaviour of urea is non-linear since its extraction from blood follows some exponential family model as a function of time, we found that prediction of its equilibrated concentration after the end of the treatment session by means of linear models is accurate. In this study, we have show how to build linear models to predict equilibrated urea based on two statistical procedures and one machine learning methods that can be implemented in hemodialysis centre based on their own patients. The fitted model can be used for daily treatment monitoring and is easily implemented in common available spreadsheets. A linear model is based on linear combinations of unknown parameters which must be estimated from data. The first step in looking for an appropriate model relies on prior knowledge or basic assumptions about the problem at hand that should be expressed in a hypothesized mathematical structure. The model can be expressed as E(Y)=f (X,β) , where E(Y) is the expected value of the output vector, “f “ is a linear function, i.e. , X is a matrix of input variables and β is a vector of parameters that needs to be estimated. In this way a set of potential mappings has been defined. The second step implies the estimation of the components of the vector β. This step includes the selection of a specific mapping (a ‘proper’ β) from the set of possible ones, choosing the parameter vector β that performs best according to some optimization criteria. There are several techniques to find a proper when using a linear model, being an estimation of β vector. Each of them has its own assumptions and requirements. Here we explore three different approaches for the estimation of the parameters of the β vector. They are: the Ordinary Least Square (OLS) procedure, based on the minimization of the sum of squared residuals which assume independence on the X matrix columns. The Partial Least Square (PLS) method based on decomposition schema maximizing the estimated covariance between the input and its outputs, and which is able to handle co-linearity or lack of independence among the X matrix columns. Finally, we use the Support Vector Machine algorithm (SVM) which is based on the minimization of the empirical risk over ε-sensitive loss functions. In this study, the three regression procedures were used to estimate the β coefficients in order to predict the equilibrated urea concentration at the end of the dialysis session. The input variables were the intradialysis urea concentrations (U0, U120, U240), the predialysis body weight and ultrafiltration patient data. Data analysis and modeling requires performing several tasks. In this work we use the Knowledge Discovery in Data Base (KDD) strategy as an ordered analysis framework. In this sense several steps involving different KDD stages such as problem/data understanding, collection, cleaning, pre-processing, analysis-modeling and results interpretation were implemented.