Prediction Model for Graft Survival After Liver Transplantation Using Aspartate Aminotransferase, Total Bilirubin and Coagulation Factor: ABC Model

Jinsoo Rhu Samsung Medical Center, Sungkyunkwan University School of Medicine Jong Man Kim (  yjongman21@gmail.com ) Samsung Medical Center, Sungkyunkwan University School of Medicine Kyunga Kim Samsung Medical Center Heejin Yoo Samsung Medical Center Gyu-Seong Choi Samsung Medical Center, Sungkyunkwan University School of Medicine Jae-Won Joh Samsung Medical Center, Sungkyunkwan University School of Medicine


Introduction
Liver transplantation (LT) is a life-saving procedure for patients with acute or chronic liver failure and malignancy such as hepatocellular carcinoma. However, due to organ shortage, LT can only be performed in a limited number of patients. Nevertheless, LT is not always successful, and 2.7 to 6.9% of liver grafts develop graft dysfunction. [1][2][3] Dysfunction of the graft, whether the cause is primary or secondary, can lead to death or need for additional liver transplantation. Currently in the United States, the Organ Procurement and Transplant Network (OPTN) set an urgent listing criteria for primary nonfunction of a transplanted liver within 7 days of implantation. 4 The recipients should be in an anhepatic phase or should have aspartate aminotransferase (AST) ≥3000 U/L and one or both of the following: international normalized ratio (INR) of prothrombin time ≥ 2.5, or acidosis, de ned as arterial pH ≤7.30 or venous pH ≤7.25 and/or lactate ≥4 mmol/L. However, the criteria of OPTN seem restrictive, and many patients who do not ful ll the criteria experience graft failure.
Therefore, we designed this study to build a prediction model for predicting allograft survival of which endpoint has been de ned as retransplantation of the liver or death due to graft dysfunction with three goals. First, to design both living donor liver transplantation (LDLT) and deceased donor liver transplantation (DDLT) models to predict graft survival using common laboratory tests. The second goal is to compare the predictability with other known models. The third goal is to internally validate the prediction model. The calculating model designed for predicting graft survival will be abbreviated as ABC model by including AST, TB, and INR of prothrombin time which is a coagulation factor.

Patients
The study population consisted of adult patients who underwent LT in Samsung Medical Center during the period of 2004 to 2018. Pediatric LTs were excluded, while both living donor and deceased donor LTs of adult recipients were included. No organs from executed prisoners were used Data collection Patient data of demographics, LT surgery, and post-transplantation course including laboratory values of AST, TB, and INR were collected from the date of transplantation to the 7 th day post-transplantation.

Graft failure
Graft failure was de ned as failure of the liver allograft, either primary or secondary, due to complications that required re-LT or resulted in death of the recipient. The date of graft failure was de ned as the date of re-LT or death. Deaths from causes other than liver failure were not de ned as graft failure.
Post-transplantation laboratory values AST, TB, and INR were used to predict graft survival. Laboratory values during the rst week were used. Since laboratory values during the early posttransplantation period can be in uenced by pre-transplantation conditions, some modi cations were made. TB and INR levels from the day of LT to post-LT day 2 were not used for the prediction model since TB and INR gradually decrease along the post-LT course even in successful LT. Therefore, for the prediction model, maximum level of AST during the rst week (AST max7 ), maximum level of TB from days 3 to 7 post-LT (TB max3-7 ), and maximum INR from days 3 to 7 post-LT (INR max3-7 ) were used to predict graft survival.

Statistical analysis
The prediction models were built using variables that are clinically familiar and relevant. Two models each for LDLT and DDLT were constructed. After building the models, the two models were compared to MEAF score and EAD criteria by comparing C-index and time dependent area-under-the-curve (AUC) at 2 weeks and 4 weeks. 14,15 MEAF score was calculated based on the previous study reported by Pareja et al. 15 The comparing process was performed using R packages 'compareC' and 'timeROC'. Validation process for the chosen modeling process was performed. Internal validation using 20time repeated 5-fold cross-validations were performed using R package 'survAUC' to calculate the C-statistic and AUC estimator proposed by Uno et al. 16 Calibration plot was drawn to validate the models through 1000 bootstrap resamples of the same size as the original data. Decision curve analysis to evaluate the clinical usefulness of the models was performed by drawing a decision curve computing the net bene t, and the range of positive net bene t was analyzed.
Statistical analyses were performed using SPSS 20.0 (IBM, Chicago, IL, USA), SAS v9.4 (SAS Institute Inc, Cary, NC, USA), and R 3.6.1 (R Foundation for Statistical Computing, Vienna, Austria) using packages 'rmda' for decision curve analysis and 'rms' for drawing a calibration plot.

Ethical approval
This study was approved by the Institutional Review Board (IRB) of Samsung Medical Center (IRB No. 2020-02-013).

Informed consent
The need for informed consent was waived by the IRB of Samsung Medical Center due to the retrospective nature of this study. Investigational methods used in this study were implemented in accordance with the relevant guidelines and regulations of the IRB.

Prediction model using multivariable Cox regression
To build the best model for prediction, laboratory values were analyzed using univariable and multivariable models. Log 2 -transformation was performed to increase the predictability by changing the variable to a normal distribution.    Figure 1C) Time-dependent AUC at 4 weeks of the ABC model (AUC=0.94, CU=0.89-1.00) was signi cantly higher compared to those of MEAF score (AUC=0.82, CI=0.68-0.96, P=0.02) and EAD criteria (AUC=0.81, CI=0.74-0.88, P<0.001, Figure 1D).
The predicted survival probabilities from Cox proportional hazards model for a set of covariates X may be estimated by the equation below where S 0 (t) is

Calibration plot
Calibration plots of ABC models at 2 weeks and 4 weeks through 1000 bootstrap resamples were performed. Figure 2 shows the calibration plots of ABC models for both LDLT and DDLT. The predicted probability and actual survival probability showed relatively competent calibration for ABC models for LDLT and DDLT.

Decision curve analysis
To evaluate the clinical usefulness of ABC model, decision curves were computed to calculate the net bene t. Figure 3 shows the decision curves of ABC models for LDLT and DDLT. For both 2 weeks and 4 weeks, and for both LDLT and DDLT, the decision curve constantly calculated above the zero-bene t line, showing bene cial expectation of the models.

Time-dependent AUC curves of ABC model
Time-dependent AUC curves of ABC models were illustrated in Figure 4. When the reference line was set as AUC of 0.75, the time-dependent AUCs were calculated to be above the reference line until 1 year in LDLT, and around 250 days in DDLT.

Discussion
Due to improvement in surgical skills, optimization of immunosuppression, and postoperative intensive care, the outcome of LT has improved throughout the decades, and graft failure rate has signi cantly decreased. However, there are still recipients who experience graft dysfunction and require appropriate decision making to undergo re-transplantation. Nevertheless, new competent liver grafts for those experiencing graft dysfunction are not always available, creating an urgent need for re-transplant criteria. The criteria of OPTN are utilized as guidance in allocating deceased donor livers although they are limited in allocating new grafts for patients with potential graft failure. Several studies have built a prediction model for graft failure. Although such studies showed improvement in prediction, there is no consensus on a de nite model for predicting graft failure. This study was designed to build a prediction model for graft survival using simpli ed variables among the largest studied cohort.
Nonfunctioning livers usually show a similar pattern of laboratory values. AST and ALT peak at day 1 and 2 post-LT, respectively, and gradually decrease thereafter; there can be additional peaks when the graft is injured by mechanisms such as hypotension. The pattern is similar in successful grafts, but maximum AST and ALT indicate extent of graft injury. On the other hand, TB level changes slowly and gradually increases along the clinical course in failing grafts. The initial TB level is dependent on pre-LT TB level and transfusions, which are performed intensely during the initial post-LT period. Therefore, both successful and failing LTs show a decreasing pattern in the initial period, while failing LTs then show gradual increase. Patterns of INR level are most similar between successful and failing grafts, although the levels are higher in nonfunctioning grafts and remain higher during the post-LT course. However, the time point and level of the peak may vary among LT cases. Therefore, peak AST after LT and maximum TB and INR after the early post-LT period are important regardless of day. This is why we built a model to choose the maximum AST of the post-LT period and maximum values of TB and INR starting from day 3 post-LT.
ABC model was built based on LT data from 1153 LDLT and 359 DDLTs. The AUCs of the prediction models were 0.96 and 0.98 in predicting graft failure within 2 weeks and 0.93 and 0.94 in predicting graft failure within 4 weeks, for LDLT and DDLT, respectively. ABC model is also very intuitive by including the maximum values of AST, TB, and INR during the rst week and during the rst 2 weeks for predicting graft failure within 2 weeks and 4 weeks, respectively. The model was compared to previously published models, such as MEAF score and EAD criteria. By comparing the C-index and timedependent AUC at 2 weeks and 4 weeks, ABC model showed superior outcome compared to the other two models.
Prediction probability can be calculated easily if the clinician knows the maximum AST, TB, and INR during the post-LT period, by inserting the values to our supplementary Excel document, which is well-calibrated to the retrospective cohort of our institution.
The limitation of our study is that it is based on data from a single institution. The model was based on a cohort of was performed predominantly with LDLTs and number of cases included in the DDLT model was 359 cases. Nevertheless, our study showed high validity during internal validation; therefore, good results during external validation with other cohorts is expected.
The currently applied criteria for primary nonfunction as suggested by OPTN served as a good decision tool. However, the criteria were quite restrictive; in countries like the Republic of Korea where donation from deceased donors is relatively lower than in other countries, many patients with graft failure are unable to undergo re-LT. Our prediction model provides objective data on the probability of graft survival, which can guide patient selection in those requiring urgent re-LT even the rst week after LT.