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Development and validation of a new statistical model for prognosis of long-term graft function after pediatric kidney transplantation

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Abstract

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.

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Abbreviations

GFR:

Glomerular filtration rate

KTX:

Kidney transplantation

MAE:

Mean absolute error

MDRD:

Modification of Diet in Renal Disease

MSE:

Mean squared error

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Authors and Affiliations

  1. Department of Pediatric Nephrology, Hannover Medical School, Carl-Neuberg-Straße 1, 30625, Hannover, Germany

    Lars Pape, Thurid Ahlenstiel & Christin D. Werner

  2. Institute of Biometry, Medical School of Hannover, Hannover, Germany

    Antonia Zapf

Authors
  1. Lars Pape
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  2. Thurid Ahlenstiel
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  3. Christin D. Werner
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  4. Antonia Zapf
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Corresponding author

Correspondence to Lars Pape.

Additional information

Lars Pape and Thurid Ahlenstiel contributed equally to this work.

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Pape, L., Ahlenstiel, T., Werner, C.D. et al. Development and validation of a new statistical model for prognosis of long-term graft function after pediatric kidney transplantation. Pediatr Nephrol 28, 499–505 (2013). https://doi.org/10.1007/s00467-012-2346-y

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  • DOI: https://doi.org/10.1007/s00467-012-2346-y

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