1 Institute of Laboratory Medicine, Clinical Chemistry and Molecular Diagnostics, University Hospital Leipzig, Paul-List-Str. 13-15, D-04103 Leipzig, Germany.
2 Section of Hepatology, Department of Gastroenterology and Rheumatology, University Hospital Leipzig, Liebigstr. 20, D-04103 Leipzig, Germany.
3 Anesthesiology and Intensive Care Medicine, University Hospital Greifswald, Ferdinand-Sauerbruch-Str., D-17475 Greifswald, Germany.
4 Institute of Laboratory Medicine, Microbiology and Clinical Pathobiochemistry, University Hospital OWL, Hospital Lippe, Röntgenstr. 18, D-32756 Detmold, Germany.

✉ Correspondence: Sebastian Gibb <>

Last updated: 2022-12-19

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1 Introduction

Liver cirrhosis is the terminal result of the fibrotic remodeling of liver tissue due to chronic damage. This end-stage of liver disease is usually irreversible, and the only available therapy is liver transplantation. However, the shortage of grafts for transplantation from deceased donors requires risk stratification and precise and fair allocation rules. The allocation of liver transplantation in most countries is based on disease severity determined by the model of end-stage liver disease (MELD) (Malinchoc et al. 2000; Wiesner et al. 2003; Organ Procurement and Transplantation Network 2021). The MELD score estimates patients’ 3-month mortality risk based on laboratory results, namely bilirubin, creatinine, and the international normalized ratio (INR). The MELD score has been extended by the sodium level (MELD-Na score) because this was found to be an important additional risk factor in liver cirrhosis (Kim et al. 2008; Organ Procurement and Transplantation Network 2021). Recently MELD 3.0 was introduced adding a factor for female sex, albumin and interactions between bilirubin and sodium and between albumin and creatinine (Kim et al. 2021). The MELD was initially developed to predict the survival of patients undergoing transjugular intrahepatic portosystemic shunts. It was subsequently revalidated to predict mortality risk in patients awaiting a liver transplantation. Although the MELD score should be an objective allocation score, creatinine and INR are highly dependent on the laboratory methods used (Trotter et al. 2004; Cholongitas et al. 2007). In addition women are disadvantaged in MELD-Na (Sealock et al. 2022). Patients with identical disease states can have very different MELD scores and thus receive different priority levels on the liver transplantation waiting list. Furthermore, for acute-on-chronic liver failure, for example, the MELD score often underestimates the mortality risk (Hernaez et al. 2020).

There have been some attempts to use the data extracted from more than 300,000 electronic medical records from two hospitals in the United States to improve the MELD score (Kartoun et al. 2017). The derived MELD-Plus7 and MELD-Plus9 risk scores add albumin, white blood cell count, total cholesterol, age, and length of stay to the MELD-Na variables. Despite their published prediction improvement, the MELD-Plus scores are not yet used for transplant allocation.

As shown by the MELD-Plus risk and MELD 3.0 scores, better predictive scores often need more variables and are more complicated. To reduce the risk of overlooking or incorrectly calculating and interpreting the results, clinical decision support systems may be used and could improve patient safety. The research project on digital laboratory medicine (AMPEL) develops a clinical decision support system based on laboratory diagnostics that should support clinical practitioners in interpreting laboratory results and taking the necessary medical interventions (Eckelt et al. 2020).

This study aims to find clinical and laboratory values that improve on the risk stratification for liver transplantation of the classical MELD, MELD-Na, MELD 3.0, and MELD-Plus scores and that might be implemented as part of the AMPEL clinical decision support system.

2 Material and methods

2.1 Study population

In a retrospective cohort study we followed 778 consecutive patients, who were recruited during the evaluation process for liver transplantation at University Hospital Leipzig from November 2012 to June 2015. For each patient, we recorded 44 variables, including age, sex, etiology of liver disease, complications as listed in Table 3.1, and 25 laboratory measurements.

Flowchart showing inclusion and exclusion of records.

Figure 2.1: Flowchart showing inclusion and exclusion of records.

Version Author Date
68ef9aa Sebastian Gibb 2022-07-22
83e3c7a Sebastian Gibb 2022-07-19

We excluded 124 patients from our analysis (Figure 2.1). One was younger than 18 years, 24 had had a liver transplant before and in 99 cases the follow-up data were missing or invalid.

The Ethics Committee at the Leipzig University Faculty of Medicine approved the retrospective usage of the data for our study (reference number: 039/14ff).

2.2 MELD scores

MELD and MELD-Na were calculated as described in Organ Procurement and Transplantation Network (2021) using the following formulas: \(MELD = 10 * (0.957 \ln(creatinine [mg/dL]) + 0.378 \ln(bilirubin [mg/dL]) + 1.120 * \ln(INR) + 0.643)\), Creatinine, bilirubin and INR values lower than 1.0 mg/dL were set to 1.0 mg/dL. The maximum allowed creatinine was 4.0 mg/dL. If the patients received dialysis, creatinine was set to 4.0 mg/dL. For MELD-Na, MELD was calculated as above and recalculated if greater than 11 using: \(MELD\text{-}Na = MELD_i + 1.32 * (137 - Na [mmol/L]) - (0.033 * MELD_i * (137 - Na [mmol/L]))\)

Serum sodium values lower than 125 mmol/L or higher than 137 mmol/L were set to 125 mmol/L and 137 mmol/L, respectively.

MELD 3.0 was calculated as described in kim2021:

\[ \begin{aligned} MELD3 = 1.33 (if female) &+ \\ 4.56 &* \ln(bilirubin [mg/dL]) + \\ 0.82 &* (137 - Na [mmol/L]) - 0.24 * (137 - Na [mmol/L]) * \ln(bilirubin [mg/dL]) + \\ 9.09 &* \ln(INR) + \\ 11.14 &* \ln(creatinine [mg/dL]) + \\ 1.85 &* (3.5 - albumin [g/dL]) - 1.83 * (3.5 - albumin [g/dL]) * \ln(creatinine [mg/dL]) + 6 \end{aligned} \] In contrast to MELD-Na the maximum allowed creatinine was set to 3.0 mg/dL.

The MELD-Plus7 risk score was calculated as described in Kartoun et al. (2017): $$ \[\begin{aligned} L = 8.53499496 &+ \\ 2.59679650 &* \log_{10}(1 + creatinine [mg/dL]) + \\ 2.06503238 &* \log_{10}(1 + bilirubin [mg/dL]) + \\ 2.99724802 &* \log_{10}(1 + INR) - \\ 6.47834101 &* \log_{10}(1 + sodium [mmol/L]) - \\ 6.34990436 &* \log_{10}(1 + albumin [g/dL]) + \\ 1.92811726 &* \log_{10}(1 + wbc [th/cumm]) + \\ 0.04070442 &* age [years] \end{aligned}\]

$

\[MELD\text{-}Plus = \frac{\exp(L)}{1 + \exp(L)}\]

The MELD-Plus9 score was ignored because the length of stay information was not available for our cohort, and the model itself was not superior to MELD-Plus7 in its original publication (Kartoun et al. 2017).

2.3 Data processing and machine-learning

All data processing, statistical, and machine-learning analyses were performed using R version 4.2.0 (R Core Team 2022). Prior to the analyses, all laboratory values were zlog transformed to approximate a normal distribution as described in Hoffmann et al. (2017) and implemented in Gibb (2021).

\[ z = (\log(x) - \frac{\log(LL) + \log(UL)}{2}) * \frac{3.92}{\log(UL) - \log(LL)} \]

where \(LL\) and \(UL\) are the lower and upper age-, and sex-related reference limits of the corresponding laboratory diagnostic, respectively. Missing laboratory measurements were replaced with a zlog value of zero. In a similar manner, where information about complications or comorbidities was missing, we treated them as not present.

We compared 13 different statistical and machine-learning algorithms using the mlr3 framework (Lang et al. 2019, 2022; Sonabend et al. 2021; Sonabend, Kiraly, and Lang 2022). The algorithms used were designed for analysis of survival data: Cox proportional hazards regression model (Cox 1972; Terry M. Therneau and Patricia M. Grambsch 2000; Therneau 2022); penalized regressions, namely, two different implementations of the lasso (least absolute shrinkage and selection operator) regression (Tibshirani 1997; Simon et al. 2011; Friedman et al. 2022; J. J. Goeman 2010; J. Goeman et al. 2022), two different implementations of the ridge regression (Simon et al. 2011; Friedman et al. 2022; J. J. Goeman 2010; J. Goeman et al. 2022), and the elastic net regression (Simon et al. 2011; Friedman et al. 2022); two different random forest implementations (Wright and Ziegler 2017; Wright, Wager, and Probst 2021; H. Ishwaran et al. 2008; Hemant Ishwaran and Kogalur 2020); extreme gradient boosting (T. Chen and Guestrin 2016; Tianqi Chen et al. 2022); two different support vector machines (Belle et al. 2011; Fouodo 2018); and two neural networks (Katzman et al. 2018; Kvamme, Borgan, and Scheel 2019; Sonabend 2022).

We used nested resampling to avoid feature- and model-selection-bias to obtain reliable metrics to choose the best model. We thus applied a 5-fold inner and 3-fold outer cross-validation that was repeated 10 times. We searched the hyperparameter space using a grid search with a resolution of 10. The models were evaluated using the concordance index, which is a measure of rank correlation between predicted and observed events (Harrell 1982). Subsequently, we selected the model with the highest median concordance index. If multiple models were comparable, we chose the simpler (more penalized) one.

After selecting the final model, we trained and validated it as described in Harrell, Lee, and Mark (1996). Briefly, we developed our model using a 3-fold cross-validation that was repeated 10 times and finally predicted survival at 90 days. The predictions were sorted and grouped into equal-sized intervals so that there were 50 patients in each interval. For each group, the mean survival probability and the difference to the Kaplan-Meier estimate was calculated. The same procedure was repeated for 200 bootstrap samples. Subsequently, the differences between predicted survival and Kaplan-Meier estimates of the bootstrap samples were averaged and added to the original model difference to obtain a bias-corrected estimate between predicted and observed survival.

The final model was compared against the MELD, MELD-Na, MELD 3.0 and MELD-Plus7 scores using the area under the time-dependent receiver operating characteristic curve (AUROC) based on the nonparametric inverse probability of censoring weighting estimator (IPCW) Paul Blanche (2019). Testing was applied as described in P. Blanche, Dartigues, and Jacqmin-Gadda (2013). A \(p < 0.05\) was considered a statistically significant difference.

Further we determined the variable importance by counting how often the variable was chosen during the feature selection in the bootstrap process described above and by the logrank value returned by one random forest implementation (Wright, Wager, and Probst 2021).

Summary tables were built using the gtsummary package (Sjoberg et al. 2021, 2022).

3 Results

3.1 Baseline characteristics

Table 3.1: Baseline characteristics.
Values are given as median (lower quartile, upper quartile) or n (percent).
AIH, autoimmune hepatitis; ALAT, alanine aminotransferase; ALF, acute liver failure; ASAT, aspartate aminotransferase; CLI, chronic liver insufficiency; GIB, gastrointestinal bleeding; HBV, hepatitis B virus; HCV, hepatitis C virus; IL-6, interleukin 6; INR, international normalized ratio; LTx, liver transplantation; NASH, non-alcoholic steatohepatitis; PBC, primary biliary cirrhosis; PSC, primary sclerosing cholangitis; SBP, spontaneous bacterial peritonitis
Characteristic Female, N = 240 Male, N = 414 Overall, N = 654
General
Follow-up time [days] 181 (17, 411) 198 (54, 378) 191 (38, 384)
Age 56 (51, 64) 58 (52, 63) 58 (52, 64)
LTx 20 (8.3%) 40 (9.7%) 60 (9.2%)
Laboratory measurements
Total bilirubin [µmol/L] 21 (10, 49) 26 (14, 51) 24 (13, 50)
Cystatin C [mg/L] 1.31 (1.04, 1.80) 1.32 (1.08, 1.76) 1.32 (1.07, 1.79)
(Missing) 2 5 7
Creatinine [µmol/L] 73 (58, 91) 85 (71, 110) 80 (65, 104)
INR 1.20 (1.06, 1.50) 1.22 (1.10, 1.44) 1.21 (1.09, 1.46)
(Missing) 1 1 2
Sodium [mmol/L] 138.8 (135.4, 141.0) 138.0 (135.0, 140.1) 138.1 (135.2, 140.4)
(Missing) 5 4 9
WBC [exp 9/L] 6.7 (4.7, 8.8) 6.2 (4.6, 7.8) 6.3 (4.7, 8.3)
(Missing) 10 13 23
IL-6 [pg/mL] 10 (5, 36) 14 (6, 47) 13 (6, 42)
(Missing) 27 29 56
Albumin [g/L] 41 (35, 46) 38 (33, 43) 39 (34, 45)
(Missing) 2 4 6
Total protein [g/L] 71 (63, 76) 71 (65, 76) 71 (65, 76)
(Missing) 2 4 6
Cholesterine [mmol/L] 4.64 (3.41, 5.56) 4.28 (3.34, 5.15) 4.40 (3.34, 5.31)
ALAT [µkat/L] 0.29 (0.21, 0.42) 0.36 (0.23, 0.56) 0.33 (0.22, 0.48)
(Missing) 2 8 10
ASAT [µkat/L] 0.68 (0.49, 1.05) 0.81 (0.61, 1.23) 0.77 (0.55, 1.16)
(Missing) 3 5 8
MELD
MELD score 10 (7, 18) 12 (9, 17) 11 (8, 17)
(Missing) 2 1 3
MELD-Na score 10 (7, 19) 12 (9, 20) 11 (8, 20)
(Missing) 5 4 9
MELD Category
[6,9] 111 (47%) 146 (36%) 257 (40%)
[10,20) 71 (30%) 163 (40%) 234 (36%)
[20,30) 28 (12%) 77 (19%) 105 (16%)
[30,40) 21 (8.9%) 17 (4.1%) 38 (5.9%)
[40,52) 4 (1.7%) 7 (1.7%) 11 (1.7%)
(Missing) 5 4 9
MELD 3.0 score 12 (8, 20) 12 (9, 19) 12 (8, 19)
(Missing) 8 8 16
Entities
Cirrhosis 203 (85%) 391 (94%) 594 (91%)
(Missing) 1 0 1
ALF 6 (2.5%) 2 (0.5%) 8 (1.2%)
CLI 30 (12%) 21 (5.1%) 51 (7.8%)
Etiology (more than 1 per patient possible)
Ethyltoxic 114 (48%) 297 (72%) 411 (63%)
HBV 4 (1.7%) 16 (3.9%) 20 (3.1%)
HCV 17 (7.1%) 28 (6.8%) 45 (6.9%)
AIH 22 (9.2%) 9 (2.2%) 31 (4.7%)
PBC 17 (7.1%) 0 (0%) 17 (2.6%)
PSC 5 (2.1%) 11 (2.7%) 16 (2.4%)
NASH 17 (7.1%) 31 (7.5%) 48 (7.3%)
Cryptogenic 36 (15%) 32 (7.7%) 68 (10%)
Complications (more than 1 per patient possible)
Dialysis 14 (5.9%) 19 (4.6%) 33 (5.1%)
(Missing) 1 1 2
GIB 58 (24%) 104 (25%) 162 (25%)
HCC 18 (7.5%) 103 (25%) 121 (19%)
SBP 31 (13%) 60 (15%) 91 (14%)
(Missing) 0 1 1
Mortality
Within 7 days 16 (7.2%) 18 (4.5%) 34 (5.5%)
Within 30 days 25 (12%) 31 (8.1%) 56 (9.4%)
Within 90 days 32 (16%) 49 (13%) 81 (14%)
Within 365 days 39 (20%) 61 (18%) 100 (18%)

In this study, we analyzed a cohort of 654 patients evaluated for liver transplantation (Tab. 3.1). Of these, 414 (63%) were men. The median (IQR) follow-up times was 191 (38, 384) days. Within the follow-up time, 60 (9.2%) patients received a liver transplant and were censored for the analysis beyond this time point. The median (IQR) age of the cohort was 58 (52, 64) years.

Most of the patients presented with cirrhosis (594 (91%)). The remaining patients had acute liver failure (8 (1.2%)) or chronic liver insufficiency (51 (7.8%)). At evaluation time, the median (IQR) MELD, MELD-Na and MELD 3.0 scores were 11 (8, 17), 11 (8, 20), and 12 (8, 19), respectively. Within 90 days, 81 (14%) patients had died. In nearly two thirds of all patients (411 (63%)), alcohol was the main cause of their end-stage liver disease. The remaining patients had viral infections - hepatitis B (20 (3.1%)) or C (45 (6.9%)) - autoimmune autoimmune (31 (4.7%)), primary sclerosing cirrhosis (16 (2.4%)), primary biliary cirrhosis (17 (2.6%)), unknown causes (non-alcoholic steatohepatitis (48 (7.3%)), or cryptogenic hepatitis (68 (10%))). The most common complications among all patients were gastrointestinal bleedings in 162 (25%) patients, followed by hepatocellular carcinoma (HCC) in 121 (19%) and spontaneous bacterial peritonitis (SBP) in 91 (14%) patients. Just 33 (5.1%) patients required renal dialysis.

3.2 MELD scores

We divided our cohort into 5 MELD-Na-score risk categories, with 257, 234, 105, 38, and 11 patients, respectively. As shown in Table 3.2, our observed 90-day mortality was 1.2 to 2.2 times higher than the predicted one (VanDerwerken et al. 2021). Only in the group with the lowest MELD-Na scores was the mortality much lower.

Table 3.2: Observed vs. MELD-Na-expected 90-day mortality. MELD-Na mortality values are taken from VanDerwerken et al. (2021) and the mean value was calculated for each MELD-Na category. All patients censored before day 90 are ignored for the calculation of the MELD-Na-expected deaths. SMR, Standardized mortality ratio = observed deaths/expected deaths.
MELD-Na category Observed deaths (n) Expected deaths (n) Standardized mortality ratio (SMR) Observed mortality (%) Expected mortality (%)
[6,9] 1 5.8 0.2 0.5 2.8
[10,20) 9 6.9 1.3 4.5 3.7
[20,30) 37 17.0 2.2 40.9 22.0
[30,40) 23 16.2 1.4 87.5 64.6
[40,52) 6 5.1 1.2 100.0 84.4

3.3 AMPEL MELD

The penalized regression and random forest models resulted in a similar high median performance in the benchmark process. In favour of simpler models, we chose a lasso-based approach for the final model development. The classical Cox model, the data and computational intense algorithms extreme gradient boosting, the support vector machines and the neural networks yielded a worse performance.

Table 3.3: Model coefficients
Coefficient
IL-6 0.193
Total protein -0.081
INR 0.067
Cholinesterase -0.037
Cystatin C 0.026
Direct bilirubin 0.010

The resulting AMPEL model of end-stage liver disease (AMELD) uses 6 predictors. Besides the classical MELD variables INR and (direct) bilirubin, the lasso regression selected cystatin C over creatinine, as well as IL-6, total protein, and cholinesterase.

Table 3.4: Underlying survival function; S0: baseline survival estimate
t [days] 2 7 30 90 180 365
S0 (t) 0.9967 0.9912 0.9816 0.9661 0.9546 0.9489

The 90-day survival estimate of a given patient can be calculated as shown in (3.1).

\[\begin{align} S &= S_{0,90}^{\exp{LP}} \\ &= 0.9661 ^{\exp{( 0.1929 * zlog(\text{IL-6})-0.0805 * zlog(\text{Total protein})+0.0667 * zlog(\text{INR})-0.0368 * zlog(\text{Cholinesterase})+0.026 * zlog(\text{Cystatin C})+0.0098 * zlog(\text{Direct bilirubin}) )}} \tag{3.1} \end{align} \]

where \(S_{0}\) is the baseline survival estimate from 3.4 and \(LP\) is the linear predictor of the coefficients in 3.3.

3.4 Model comparison

Receiver operating characteristic (ROC) curve. Area under the time-dependent ROC curve (AUC) based on the nonparametric inverse probability of censoring weighting estimate (IPCW) for AMELD, MELD, MELD-Na, MELD 3.0, MELD-Plus7, as described in [@blanche2013].

Figure 3.1: Receiver operating characteristic (ROC) curve. Area under the time-dependent ROC curve (AUC) based on the nonparametric inverse probability of censoring weighting estimate (IPCW) for AMELD, MELD, MELD-Na, MELD 3.0, MELD-Plus7, as described in (P. Blanche, Dartigues, and Jacqmin-Gadda 2013).

Version Author Date
5235082 Sebastian Gibb 2022-11-30
65d58c4 Sebastian Gibb 2022-07-18
ebe29cf Sebastian Gibb 2022-06-16
8035219 Sebastian Gibb 2022-06-15
Table 3.5: Test comparison between AUCROC for MELD-Na and AMELD according to P. Blanche, Dartigues, and Jacqmin-Gadda (2013) at day 2, 7, 30, 90, 180, 365.\(p\)-values are shown as non-adjusted and adjusted for multiple testing.
t=2 t=7 t=30 t=90 t=180 t=365
Non-adjusted \(p\)-values 0.27 0.15 0.33 0.03 0.02 0.33
Adjusted \(p\)-values 0.75 0.52 0.84 0.15 0.08 0.84

AMELD offers the best AUROC 0.961 (95% CI, 0.942-0.980) of all competitors. However, after correction for multiple testing, the difference against the second-best model, MELD 3.0 (AUROC 0.936 (95% CI, 0.910-0.963)), is not statistical significant (\(p = 0.15\)) (see Table 3.5 for complete comparison).

Calibration of AMELD in comparison to MELD, MELD-Na, MELD 3.0 and MELD-Plus7. The points mark the mean predicted survival of 50 patients per interval against their observed mean survival. The error bars correspond to the 95% confidence interval of the survival estimate.

Figure 3.2: Calibration of AMELD in comparison to MELD, MELD-Na, MELD 3.0 and MELD-Plus7. The points mark the mean predicted survival of 50 patients per interval against their observed mean survival. The error bars correspond to the 95% confidence interval of the survival estimate.

Version Author Date
5235082 Sebastian Gibb 2022-11-30
83e3c7a Sebastian Gibb 2022-07-19
65d58c4 Sebastian Gibb 2022-07-18
ebe29cf Sebastian Gibb 2022-06-16
8035219 Sebastian Gibb 2022-06-15

Fig. 3.2 depicts the calibration curve for AMELD and the competing MELD scores. While the prediction for low-risk patients is similar to other scores, AMELD predicts the medium-risk patients more accurately.

3.5 Variable importance

The AMELD selected features IL-6, total protein, INR, cholinesterase, cystatin C, and direct bilirubin are the 6 highest ranked features in the bootstrap process. In the random forest logrank they are among the 12 highest ranked features out of 42 features. Sodium and albumin introduced by MELD-Na and MELD 3.0 are on position 18 and 12 for the bootstrap and 20 and 5 for the random forest variable importance ranking, respectively (see ??, ?? for the complete rankings).

4 Discussion

In this retrospective analysis of 654 consecutive patients who were recruited during the evaluation process for liver transplantation at University Hospital Leipzig, we developed a new model to predict 90-day survival probability. Our new model, AMELD, incorporates synthesis and inflammatory markers and may improve the prediction over previous published MELD scores.

Although the Organ Procurement and Transplantation Network recommends the use of MELD-Na over MELD, the sodium does not add any information to the score. Neither in the bootstrap selection nor in the variable importance of a random forest model does the sodium gain any important weight (in bootstrap selection rank 18 of 42 and in a random forest variable importance rank 20 of 42, see ??, ??). In addition, sodium levels can be affected by diuretic therapy, and the discrimination performance of MELD-Na has already been shown by Kartoun et al. (2017) to be insignificantly different from the classical MELD. Consequently it is not a component of our model.

The albumin included in MELD 3.0 is part of the total protein that has throughout higher rankings in both variable importance measurements (12 vs. 2 in the bootstrap selection and 5 vs. 1 in the random forest variable importance, see ??, ??). Using total protein instead of albumin as synthesis marker offers more information about additional globulins and especially coagulation factors that are incompletely measured by INR.

It has been shown that women receive median lower scores in MELD-Na and therefore are less likely to receive an urgent listing for liver transplantation (Sealock et al. 2022). MELD 3.0 tries to circumvent this by adding 1.33 to the score for femal sex. To address sexual differences in laboratory measurements we applied the zlog transformation (Hoffmann et al. 2017) in our study. This transformation also yields comparable laboratory measurements across different clinical laboratories and methods, as well as reducing the influence of age- and sex-related differences, which could improve the objectivity of the allocation process. The already nearly normal scaled zlog-transformed laboratory measurements allow us to avoid the sample-dependent scaling prior to model development. Both should increase the external applicability of our approach.

Our model, AMELD, uses 6 predictors. Three of these - INR, (direct) bilirubin, and cystatin C - are identical or similar to the laboratory measurements utilized in the classical MELD. The direct bilirubin selected by our approach and the total bilirubin in MELD are highly correlated (Spearman correlation: 0.96) and therefore interchangeable.

In our feature selection process, cystatin C was chosen instead of creatinine. This is in line with recent studies that show a better prediction of mortality for cystatin C in unselected and critically ill patients (Helmersson-Karlqvist, Ärnlöv, and Larsson 2016; Helmersson-Karlqvist et al. 2021).

Furthermore AMELD, extends MELD by the additional synthesis parameters total protein and cholinesterase, and most importantly the inflammatory marker IL-6.

The latter is an example where results from machine-learning can aid in finding clinically meaningful patterns and guide further research. Systemic inflammatory response syndrome is an independent risk factor for poor outcomes in patients with cirrhosis (Thabut et al. 2007). However, neither MELD, MELD-Na, nor MELD 3.0 took inflammation into account. By contrast, IL-6 is the most important variable in our model. Even if IL-6 is excluded, the algorithms select CRP as one of the most important variables, which highlights the important role of inflammation in the prognosis of patients with end-stage liver disease. We and other researchers have already shown that adding inflammatory markers, namely IL-6 or CRP, to the classical MELD score increases the accuracy of the 90-day mortality prediction (Remmler et al. 2017; Cervoni et al. 2016).

Besides laboratory measurements, we investigated 17 other items of clinical data, but none were chosen in our model-selection process. Kartoun et al. (2017) also used the lasso approach and did not select any clinical data. In retrospective analyses in particular, the clinical data are often not detailed enough to provide valuable information.

In our benchmark of 13 different machine-learning algorithms we have seen that the more complex algorithms, such as boosting, support vector machines, and neural networks, perform worse than simpler ones. This may be due to additive effects that favor regression models or due to our relatively small sample size. It has been shown that in machine-learning more than 200 events per predictor variable are required to achieve good prediction performance (Ploeg, Austin, and Steyerberg 2014).

4.1 Limitations

Our study has several limitations. Principally, it is a single-center, retrospective analysis lacking an external validation cohort. The data were collected during the evaluation process for liver transplantation at University Hospital Leipzig. There was no controlled follow-up process. We excluded all patients who had already undergone liver transplantation, which could artificially lower the disease severity of the cohort. Furthermore, most of our patients suffered from ethyltoxic liver cirrhosis (63%), which may limited the transfer to other etiologies.

With a median MELD-Na score of 11, our cohort was healthier than those in previous studies that reported a score of 14-18.5 (Kim et al. 2008; Kartoun et al. 2017; VanDerwerken et al. 2021). However, the 90-day mortality rate of 81 (14%) was comparable to the mortality rates seen in earlier studies ranging from 6% to 30% (Malinchoc et al. 2000; Kim et al. 2008; Kartoun et al. 2017). Although our cohort was healthier, with a medium mortality rate, the classical MELD score underestimates the observed mortality by 1.2 to 2.2 times. Unfortunately, our sample size was low in the high-risk patient category, resulting in a poor but better than MELD-based prediction performance by our AMELD for very ill patients.

5 Conclusion

In conclusion, we have developed a new model to predict the 90-day survival of patients during the evaluation process for liver transplantation. Our model, AMELD, extends the classical MELD predictors INR, (direct) bilirubin, and cystatin C (instead of creatinine) by using the synthesis parameters total protein and cholinesterase and, most importantly, the inflammatory marker IL-6. Using these six laboratory measurements, AMELD may improve the prediction over previous published MELD scores. For wider adoption, a prospective multi-center study for model recalibration and validation is needed.

5.1 Acknowledgments

We thank the whole AMPEL team for their support, Stefan Kemnitz for his technical support regarding the use of the high-performance computing (HPC) cluster at the University of Greifswald and Bernd Klaus for helpful discussions about survival analysis and proofreading the manuscript.

The calculations were conducted using the HPC cluster at University of Greifswald. In 2018, the average carbon efficiency of the German power grid was 0.471 kgCO2eq/kWh (Icha, Lauf, and Kuhs 2021). A single run of the complete calculation pipeline took roughly 96 hours of computation on an Intel(R) Xeon(R) E5-2650 v4 and Intel(R) Xeon(R) Gold 6240 CPU (thermal design power: 105 and 150 W). The total estimated emissions were at least 6.77 kgCO2eq (ignoring development, test runs, etc.). This is equivalent to 44 km driven by an average car (Allekotte et al. 2021).

5.2 Research funding

The study was supported by the AMPEL project (www.ampel.care). This project is co-financed through public funds according to the budget decided by the Saxon State Parliament under RL eHealthSax 2017/18 grant number 100331796. The funder provided support in the form of salaries for author SG but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

5.3 Author contributions

Funding was acquired by TK. The study was conceptualized by SG and TK. The data were acquired by TK. The data were analyzed and processed by SG. Visualization was produced by SG. The original drafts of the manuscript were written by SG and TK. Drafts were edited and reviewed by SG, TB, AH, BI, and TK. The project was supervised by TK. All authors have accepted responsibility for the entire content of this manuscript and have approved its submission.

5.4 Competing interests

TB recieved grants or research support from Abbvie, BMS, Gilead, MSD/Merck, Humedics, Intercept, Merz, Norgine, Novartis, Orphalan, Sequana Medical. TB received honoraria or consultation fees/advisory board from Abbvie, Alexion, Bayer, Gilead, GSK, Eisai, Enyo Pharma, Falk Foundation, HepaRegeniX GmbH, Humedics, Intercept, Ipsen, Janssen, MSD/Merck, Novartis, Orphalan, Roche, Sequana Medical, SIRTEX, SOBI, and Shionogi TB participated in a company sponsored speaker’s bureau for Abbvie, Alexion, Bayer, Gilead, Eisai, Intercept, Ipsen, Janssen, MedUpdate GmbH, MSD/Merck, Novartis, Orphalan, Sequana Medica, SIRTEX, and SOBI. All other authors state no conflict of interest.

5.6 Ethical approval

Research involving human subjects complied with all relevant national regulations and institutional policies, as well as the tenets of the Helsinki Declaration (as revised in 2013), and was approved by the Ethics Committee at the Leipzig University Faculty of Medicine (reference number: 039/14ff).

5.7 Data and software availability

The complete code and reproducible analysis can be found at https://ampel-leipzig.github.io/ampel-leipzig-meld/. In addition, all data are available in the ameld R package (Gibb 2022) at https://github.com/ampel-leipzig/ameld DOI for further investigation.

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sessionInfo()
R version 4.2.0 (2022-04-22)
Platform: x86_64-unknown-linux-gnu (64-bit)

Matrix products: default
BLAS/LAPACK: /gnu/store/ras6dprsw3wm3swk23jjp8ww5dwxj333-openblas-0.3.18/lib/libopenblasp-r0.3.18.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] grid      stats     graphics  grDevices utils     datasets  methods  
[8] base     

other attached packages:
 [1] gtsummary_1.6.0   consort_1.0.1     timeROC_0.4       ameld_0.0.31     
 [5] survival_3.3-1    glmnet_4.1-4      Matrix_1.4-1      viridis_0.6.2    
 [9] viridisLite_0.4.0 mlr3viz_0.5.9     ggplot2_3.3.6     targets_0.12.1   

loaded via a namespace (and not attached):
 [1] fs_1.5.2                 bbotk_0.5.3              rprojroot_2.0.3         
 [4] mlr3pipelines_0.4.1      mlr3proba_0.4.11         numDeriv_2016.8-1.1     
 [7] tools_4.2.0              backports_1.4.1          bslib_0.3.1             
[10] utf8_1.2.2               R6_2.5.1                 mlr3_0.13.3             
[13] colorspace_2.0-3         withr_2.5.0              mlr3misc_0.10.0         
[16] tidyselect_1.1.2         gridExtra_2.3            processx_3.5.3          
[19] compiler_4.2.0           git2r_0.30.1             cli_3.3.0               
[22] ooplah_0.2.0             gt_0.6.0                 lgr_0.4.3               
[25] bookdown_0.26            sass_0.4.1               scales_1.2.0            
[28] checkmate_2.1.0          mvtnorm_1.1-3            pec_2022.05.04          
[31] callr_3.7.0              palmerpenguins_0.1.0     commonmark_1.8.0        
[34] mlr3tuning_0.13.1        stringr_1.4.0            digest_0.6.29           
[37] mlr3extralearners_0.5.37 rmarkdown_2.14           param6_0.2.4            
[40] paradox_0.9.0            set6_0.2.4               pkgconfig_2.0.3         
[43] htmltools_0.5.2          parallelly_1.31.1        highr_0.9               
[46] fastmap_1.1.0            rlang_1.0.2              shape_1.4.6             
[49] jquerylib_0.1.4          generics_0.1.2           jsonlite_1.8.0          
[52] dplyr_1.0.9              magrittr_2.0.3           Rcpp_1.0.8.3            
[55] munsell_0.5.0            fansi_1.0.3              lifecycle_1.0.1         
[58] stringi_1.7.6            whisker_0.4              yaml_2.3.5              
[61] parallel_4.2.0           dictionar6_0.1.3         listenv_0.8.0           
[64] promises_1.2.0.1         crayon_1.5.1             lattice_0.20-45         
[67] splines_4.2.0            knitr_1.39               ps_1.7.0                
[70] pillar_1.7.0             timereg_2.0.2            igraph_1.3.1            
[73] uuid_1.1-0               base64url_1.4            future.apply_1.9.0      
[76] codetools_0.2-18         glue_1.6.2               evaluate_0.15           
[79] broom.helpers_1.7.0      data.table_1.14.2        vctrs_0.4.1             
[82] httpuv_1.6.5             foreach_1.5.2            distr6_1.6.9            
[85] tidyr_1.2.0              gtable_0.3.0             purrr_0.3.4             
[88] future_1.26.1            xfun_0.31                prodlim_2019.11.13      
[91] later_1.3.0              tibble_3.1.7             iterators_1.0.14        
[94] workflowr_1.7.0          lava_1.6.10              globals_0.15.0          
[97] ellipsis_0.3.2