Bayesian prediction for liver fibrosis staging: Combined use of elastography and serum fibrosis markers

Authors


  • Potential conflict of interest: Nothing to report.

To the Editor:

Liver elastography, using ultrasound transient elastography (UTE) or magnetic resonance elastography (MRE), and serum fibrosis markers have been used separately to predict liver fibrosis stage in chronic liver disease.1, 2 Combined use of elastography and fibrosis markers may be a superior method. Algorithms for combined use of serum markers and elastography have been proposed, with specific cut-off values being used in the decision trees.3-5 However, a cut-off value for staging always involves a compromise between sensitivity and specificity. The use of Bayesian prediction to stage liver fibrosis involves calculating the stage based on elastographic or serum biomarker measures (see Appendix). The probability of a certain fibrosis stage can be calculated after obtaining the stiffness value of the patient's liver or the aspartate aminotransferase-to-platelet ratio index (APRI) value.

Table 1 shows the results of fibrosis stage prediction in 20 patients who underwent liver resection and had elastography (both MRE and UTE) and serum fibrosis biomarkers before surgery. Histological fibrosis stage is shown by the METAVIR score. Respective cut-off values for the APRI, UTE, and MRE were 0.5, 5.2, and 3.2 kPa for significant fibrosis (≥F2) and 2.0, 12.9, and 4.6 kPa for cirrhosis (F4).6, 7 Accuracy of fibrosis staging was compared between APRI and APRI with UTE and between APRI and APRI with MRE using Bayesian methods. The Bayesian method successfully combined APRI and UTE/MRE, with a significant increase in accuracy; the decision-tree cut-off method failed to increase accuracy after combining elastography with APRI.

Table 1. Preliminary Results of 20 Patients in Whom Histological Fibrosis Stage Was Confirmed
For Significant Fibrosis (≥F2)APRIAPRI+UTEAPRI+MRE
Cut-off method   
 Accuracy (%)75 (15/20)80 (16/20)70 (14/20)
 P value versus APRIControl0.3170.706
Bayesian method   
 Accuracy (%)60 (12/20)80 (16/20)80 (16/20)
 P value versus APRIControl0.0460.046
For cirrhosis (F4)APRIAPRI+UTEAPRI+MRE
Cut-off method   
 Accuracy (%)65 (13/20)65 (13/20)65 (13/20)
 P value versus APRIControl1.0001.000
Bayesian method   
 Accuracy (%)60 (12/20)65 (13/20)90 (18/20)
 P value versus APRIControl0.3170.014

An advantage of Bayesian prediction over the cut-off method is its applicability over a range of conditions. Once the mean and standard deviation (SD) of various elastographic and serum fibrosis markers have been determined, a combinational probability estimate can be obtained for the fibrosis stage. Furthermore, the Bayesian prediction provides probabilities, rather than a yes/no decision (Fig. 1), allowing the predicted stage to be questioned if the associated probability is too low. The Bayesian method also allows weighting of the different methods. A small SD indicates a method with high validity, and the Bayesian prediction reflects the SD in the probability.

Figure 1.

Two representative cases are shown. Case 1, with histological fibrosis (stage F3), had an APRI of 1.65, indicating significant fibrosis, but not cirrhosis. A value of 16.0 kPa, by UTE, indicated cirrhosis, whereas noncirrhosis, but significant fibrosis, were suggested by a 3.6-kPa value by MRE. Staging discordance was observed in the combined APRI and UTE using the cut-off method. As shown in the bar graph, the Bayesian method depicts the probability of each fibrosis stage. In case 2, the Bayesian method simply suggested that the APRI result would be equivocal.

A limitation of this approach is the assumed normal distribution of values returned by each method. However, the use of Bayesian prediction, incorporating relevant findings from the available methods, is a promising technique for accurate liver fibrosis staging.

Appendix

A Bayesian prediction model for liver fibrosis staging, including a detailed explanation of the model, is available at http://yamarad.umin.ne.jp/bayesian/.

Utaroh Motosugi M.D.*, Tomoaki IChicahua M.D.*, Tsutomu Araki M.D.*, Masanori Matsuda M.D.†, HHideki Fujii M.D.†, Nobuyuki Enomoto M.D.‡, * Department of Radiology University of Yamanashi, Yamanashi, Japan, † First Department of Surgery, University of Yamanashi, Yamanashi, Japan, ‡ First Department of Internal Medicine, University of Yamanashi, Yamanashi, Japan.

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