Published in:
01-03-2013 | Original Article
Development and validation of a new statistical model for prognosis of long-term graft function after pediatric kidney transplantation
Published in: Pediatric Nephrology | Issue 3/2013
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Background
No adequate statistical model has been established to estimate future glomerular filtration rate (GFR) in children after kidney transplantation (KTX). Equations based on simple linear regression analysis as used in adults are not established in children.
Methods
An optimal prognostic model of GFR was generated for 63 children at 3–7 years after KTX. The main regression model for prediction of the log-transformed GFR (logGFR) included the mean monthly change of GFR in the period 3–24 months after KTX (∆GFR), the baseline GFR at 3 months (bGFR), and an intercept. Additionally, we investigated if the inclusion of cofactors leads to more precise predictions. The model was validated by leave-one-out cross-validation for years 3–7 after KTX. Prognostic quality was determined with the mean squared error (MSE) and mean absolute error (MAE). Results were compared with the simple linear regression model used in adults.
Results
The following statistical model was calculated for every prognosis year (i = 3, …, 7):
$$ {{\mathrm{Y}}_i}={\beta_{i0 }}+{\beta_{i1 }}\cdot {{\mathrm{X}}_{i1 }}+{\beta_{i2 }}\cdot {{\mathrm{X}}_{i2 }}+{\varepsilon_i} $$
$$ \log (\mathrm{GF}{{\mathrm{R}}_i})={\beta_{i0 }}+{B_{i1 }}\cdot \varDelta \mathrm{GFR}+{\beta_{i2 }}\cdot \mathrm{bGFR} $$
Comparison of the new statistical model and the simple linear model for adults led to relevantly lower MSEs and MAEs for the new model (year 7: New model: MSE 0.1, MAE 0.3/adult model: MSE 1069, MAE 18). The benefit of inclusion of cofactors was not relevant.
Conclusions
This statistical model is able to predict long-term graft function in children with very high precision.