A novel approach for prediction of tacrolimus blood concentration in liver transplantation patients in the intensive care unit through support vector regression

Abstract

Introduction: Tacrolimus is an important immunosuppressive drug for organ transplantation patients. It has a narrow therapeutic range, toxic side effects, and a blood concentration with wide intra- and interindividual variability. Hence, it is of the utmost importance to monitor tacrolimus blood concentration, thereby ensuring clinical effect and avoiding toxic side effects. Prediction models for tacrolimus blood concentration can improve clinical care by optimizing monitoring of these concentrations, especially in the initial phase after transplantation during intensive care unit (ICU) stay. This is the first study in the ICU in which support vector machines, as a new data modeling technique, are investigated and tested in their prediction capabilities of tacrolimus blood concentration. Linear support vector regression (SVR) and nonlinear radial basis function (RBF) SVR are compared with multiple linear regression (MLR).

Methods: Tacrolimus blood concentrations, together with 35 other relevant variables from 50 liver transplantation patients, were extracted from our ICU database. This resulted in a dataset of 457 blood samples, on average between 9 and 10 samples per patient, finally resulting in a database of more than 16,000 data values. Nonlinear RBF SVR, linear SVR, and MLR were performed after selection of clinically relevant input variables and model parameters. Differences between observed and predicted tacrolimus blood concentrations were calculated. Prediction accuracy of the three methods was compared after fivefold cross-validation (Friedman test and Wilcoxon signed rank analysis).

Results: Linear SVR and nonlinear RBF SVR had mean absolute differences between observed and predicted tacrolimus blood concentrations of 2.31 ng/ml (standard deviation [SD] 2.47) and 2.38 ng/ml (SD 2.49), respectively. MLR had a mean absolute difference of 2.73 ng/ml (SD 3.79). The difference between linear SVR and MLR was statistically significant (p < 0.001). RBF SVR had the advantage of requiring only 2 input variables to perform this prediction in comparison to 15 and 16 variables needed by linear SVR and MLR, respectively. This is an indication of the superior prediction capability of nonlinear SVR.

Conclusion: Prediction of tacrolimus blood concentration with linear and nonlinear SVR was excellent, and accuracy was superior in comparison with an MLR model.

Figure 1

The support vector algorithm heuristic. In support vector machines, classification of datapoints or prediction of an outcome parameter is done by finding the 'hyperplane' that separates the datapoints by transforming the input variable dataset by a mathematical function into a 'higher dimension' in which separation is much easier (feature map = input variables dataset). The basis of this new heuristic is that classification of a seemingly chaotic input space is possible when one increases dimensionality and thereby finds a separating plane. Copyright permission from V.P. Bioinformatics (Improved Outcomes Software, Kingston, ON, Canada).

Figure 2

Outliers for the prediction of the tacrolimus blood concentration for the three models. MLR, multiple linear regression; RBF SVR, radial basis function support vector regression (nonlinear support vector regression); SVR, support vector regression. *'s represent extreme values (values more extreme than 3*IQR).

Figure 3

Correlation of real and predicted tacrolimus blood concentrations for the linear support vector regression model.

Figure 4

Correlation of real and predicted tacrolimus blood concentrations for the radial basis function support vector regression model.

Figure 5

Correlation of real and predicted tacrolimus blood concentrations for the multiple linear regression model.

Figure 6

Bland-Altman plot for comparison of linear support vector regression (SVR) (a) and multiple linear regression (MLR) (b): x-axis = difference (linear SVR and MLR) = a - b; y-axis = mean of linear SVR and MLR = (a + b)/2. If two models are the same, all datapoints are represented around one point. However, in this figure, there is a considerable amount of spread between the datapoints of the linear SVR method and the MLR method which is a graphical illustration of the statistical difference found between these two methods.