A Model to Predict Survival in Patients with End-Stage Liver Disease
Comparision against MELD, MELD-Na, MELD-Plus7.
Sebastian Gibb1,2,✉, and Thorsten Kaiser1
2021-10-20
Abstract
Background: TODO
Methods: TODO
Results: TODO
Conclusion: TODO
1 Institute of Laboratory Medicine, Clinical Chemistry and Molecular Diagnostics, University Hospital Leipzig, Paul-List-Str. 13-15, D-04103 Leipzig, Germany.
2 Anesthesiology and Intensive Care Medicine, University Hospital Greifswald, Ferdinand-Sauerbruch-Straße, D-17475 Greifswald, Germany.
✉ Correspondence: Sebastian Gibb <mail@sebastiangibb.de>
Last updated: 2021-10-20
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ampel-leipzig-meld/
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| Rmd | 28ad932 | Sebastian Gibb | 2021-10-19 | feat: describe zlog in more detail |
| html | df8964f | Sebastian Gibb | 2021-10-15 | chore: rebuild site |
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| html | c66640c | Sebastian Gibb | 2021-09-14 | feat: first nnet tests |
| html | afa48d9 | Sebastian Gibb | 2021-08-07 | chore: rebuild site |
| Rmd | d32f7b3 | Sebastian Gibb | 2021-08-07 | fix: gtsummary compact theme |
| Rmd | ebf878b | Sebastian Gibb | 2021-08-07 | fix: observed vs expected mortality table |
| Rmd | 4ec3d40 | Sebastian Gibb | 2021-08-04 | feat: add table 1 and table observed vs expected mortality |
| Rmd | e41dd8c | Sebastian Gibb | 2021-08-03 | feat: add flowchart and discussion notes |
| Rmd | 523c286 | Sebastian Gibb | 2021-08-02 | refactor: use bookdown::html_document2 instead of workflowr::wflow_html to allow crossreferences |
| html | 3aab3e1 | Sebastian Gibb | 2021-08-01 | chore: rebuild site |
| Rmd | 91bfbd2 | Sebastian Gibb | 2021-08-01 | feat: add first article draft with pandoc filters |
1 Introduction
Liver cirrhosis is the terminal result of fibrotic remodeling of liver tissue due to chronic damage. An organ failure is often irreversible and the only available therapy is liver transplantation. However, the shortage in grafts for transplantation from deceased donors requires risk stratification and precise 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 the patients’ 3-month mortality risk based on laboratory results, namely bilirubin, creatinine and international normalized ratio (INR). In general the MELD score is extended by the sodium level (MELD-Na score) as this was found to be an important additional risk factor in liver cirrhosis (Kim et al. 2008; Organ Procurement and Transplantation Network 2021). The MELD was initially developed for predicting the survival of patients undergoing transjugular intrahepatic portosystemic shunts. Afterwards it was revalidated for predicting mortality risk in patients awaiting a liver transplantation. Although the MELD score should be an objective allocation score especially the creatinine and INR are highly dependent on the utilized laboratory methods (Trotter et al. 2004; Cholongitas et al. 2007). Patients with identical disease state could have very different MELD scores and thus get different priority on the liver transplantation waiting list. Furthermore often, e.g. for acute-on-chronic liver failure, the MELD score 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 score add albumin, white blood cell count, age and total cholesterol and length of stay to the MELD-Na variables. Despite its published prediction improvement the MELD-Plus scores are not used for transplant allocation yet.
As depicted by MELD-Plus risk 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 the laboratory results and taking the necessary medical interventions (Eckelt et al. 2020).
This study aims to find clinical and laboratory values that improve the risk stratification for liver transplantation over classical MELD, MELD-Na and MELD-Plus scores and could 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 the University Hospital of Leipzig from November 2012 to Juni 2015. For each patient we recorded 44 variables. Among them are age, sex, etiology of liver disease, complications as listed in Table 3.1 and 25 laboratory measurements.
Figure 2.1: Flowchart Inclusion/Exclusion.
We excluded 124 patients from our analysis (Figure 2.1). One was younger than 18 years. 24 had a liver transplantation 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 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.
The MELD-Plus7 risk score was calculated as described in Kartoun et al. (2017): \[ \begin{aligned} L = 8.53499496 &+ \\ 2.59679650 &* \log_{10}(1 + creatinine [mg/dl]) + \\ 2.06503238 &* \log_{10}(1 + bilirubin [mg/dl]) + \\ 2.99724802 &* \log_{10}(1 + INR) - \\ 6.47834101 &* \log_{10}(1 + sodium [mmol/l]) - \\ 6.34990436 &* \log_{10}(1 + albumin [g/l]) + \\ 1.92811726 &* \log_{10}(1 + wbc [th/cumm]) + \\ 0.04070442 &* age [years] \end{aligned} \]
\[MELD\text{-}Plus = \frac{\exp(L)}{1 + \exp(L)}\]
The MELD-Plus9 score was ignored because the length of stay information was not available for our cohort and the model itself wasn’t 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 4.1.1 (R Core Team 2021). Prior to the analyses all laboratory values were zlog transformed 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 reference limit of the corresponding laboratory diagnostic, respectively. Missing laboratory measurements were replaced with a zlog value of zero. In similar manner if information about complications or comorbidities were missing we treat them as not present.
We compared 12 different statistical and machine learning algorithms using the mlr3 framework (Lang et al. 2019, 2021; Sonabend et al. 2021; Sonabend, Kiraly, and Lang 2021). The used algorithms are designed for analysis of survival data: Cox proportional hazards regression model (Cox 1972; Terry M. Therneau and Patricia M. Grambsch 2000; Therneau 2021), 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. 2021; J. J. Goeman 2010; J. Goeman et al. 2018), tow different implementations of the ridge regression (Simon et al. 2011; Friedman et al. 2021; J. J. Goeman 2010; J. Goeman et al. 2018), and the elastic net regression (Simon et al. 2011; Friedman et al. 2021), 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 (Chen and Guestrin 2016; Chen et al. 2021), two different support vector machines (Belle et al. 2011; Fouodo 2018) and a neural network (Katzman et al. 2018; Sonabend 2021).
To choose the best model we used nested resampling to avoid feature- and model-selection-bias. Therefore, we applied a 2-fold inner and a 2-fold outer cross-validation that was repeated 1 times. Subsequently we selected the model with the highest median concordance index (Harrell 1982). If multiple models were comparable we chose the simpler (more penalized) one.
TODO: selected final model, analysis, feature selection
Summary tables were built using the gtsummary package (Sjoberg, Whiting, et al. 2021; Sjoberg, Curry, et al. 2021).
3 Results
3.1 Baseline characteristics
| 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, 1.45) |
| (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 Category | |||
| [6,9] | 111 (47%) | 146 (35%) | 257 (39%) |
| [10,20) | 80 (34%) | 196 (47%) | 276 (42%) |
| [20,30) | 30 (13%) | 50 (12%) | 80 (12%) |
| [30,40) | 12 (5.0%) | 14 (3.4%) | 26 (4.0%) |
| [40,52) | 5 (2.1%) | 7 (1.7%) | 12 (1.8%) |
| (Missing) | 2 | 1 | 3 |
| MELD-Na score | 10 (7, 19) | 12 (9, 20) | 11 (8, 20) |
| (Missing) | 5 | 4 | 9 |
| MELD-Plus7 risk score | 0.04 (0.02, 0.09) | 0.05 (0.03, 0.11) | 0.04 (0.02, 0.11) |
| (Missing) | 17 | 18 | 35 |
| 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 analysed a cohort of 654 patients evaluated for liver transplantation (Tab. 3.1). 414 (63%) of them 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 an acute liver failure (8 (1.2%)) or a chronic liver insufficiency (51 (7.8%)). At evaluation time the median (IQR) MELD and MELD-Na score were 11 (8, 17) and 11 (8, 20), respectively. Within 90 days 81 (14%) patients died. In nearly two third of all patients alcohol was the main cause (411 (63%)) of their end-stage liver disease. The remaining patients had viral infections (hepatitis B and C viruse 20 (3.1%) and 45 (6.9%), respectively), autoimmune processes (autoimmune hepatitis 31 (4.7%), primary sclerosing cirrhosis 16 (2.4%)), primary biliary cirrhosis 17 (2.6%) or unknown causes (non-alcoholic steatohepatitis 48 (7.3%) and 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 a renal dialysis.
3.2 MELD scores
According to Wiesner et al. (2003) we divided our cohort into 5 MELD-score risk categories, with 257, 276, 80, 26, and 12 patients, respectively. As shown in Table 3.2 our observed 90 day mortality was 1.4 to 2.9 times higher than the predicted one. Just in the group with the lowest MELD scores the mortality was much lower.
| MELD category | Observed deaths (n) | Expected deaths (n) | Standardized mortality ratio (SMR) | Observed mortality (%) | Expected mortality (%) |
|---|---|---|---|---|---|
| [6,9] | 1 | 4.0 | 0.3 | 0.5 | 1.9 |
| [10,20) | 21 | 13.0 | 1.6 | 8.9 | 6.0 |
| [20,30) | 34 | 11.6 | 2.9 | 51.0 | 19.6 |
| [30,40) | 18 | 10.0 | 1.8 | 92.8 | 52.6 |
| [40,52) | 6 | 4.3 | 1.4 | 100.0 | 71.3 |
r <- bmrk_results$clone()
id <- grep("^scale", x = r$learners$learner_id, invert = TRUE, value = TRUE)
r$filter(task_id = "zlog_eldd", learner_id = id)
autoplot(r) +
geom_boxplot(aes(fill = learner_id)) +
geom_jitter(position = position_jitter(0.2)) +
scale_fill_viridis(discrete = TRUE) +
theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
Figure 3.1: Benchmark results of machine learning algorithms.
| Version | Author | Date |
|---|---|---|
| df8964f | Sebastian Gibb | 2021-10-15 |
TODO: mention best ml algorithm (3.1)
4 Discussion
In this retrospective analysis of 654 consecutive patients, who were recruited during the evaluation process for liver transplantation at the University Hospital of Leipzig we compared 12 different statistical and machine learning algorithms.
…
- higher mortality than predicted, compare Hernaez et al. (2020)
- adding sodium doesn’t add much/any discrimination information
- as already seen in Kartoun et al. (2017)
- Kartoun et al. (2017) uses > 60 variables mostly clinical stuff, just few laboratory values, none of the clinical stuff remains
- general low sample size thus simpler models/fewer predictors are preferred.
- comparison of different predictors of MELD-Plus7 (+MELD-Plus9) vs our features
- 90 day mortality post discharge
- poorer performance in own validation set (lower and more uniform disease severity, also lower MELD)
- machine learning algorithms worse than statistical learning (lower c-index, higher variance/instability)
- additive effects (favour statistical models)
- low sample size, for ML more than 200 events per predictor variable necessary (Ploeg, Austin, and Steyerberg 2014)
- national register required
4.1 Limitations
- comparable mortality?
- retrospective analysis
- single center
- unknown cause of death (death with vs of end-stage liver disease)
- bias caused by LTx censorship?
5 References
sessionInfo()R version 4.1.1 (2021-08-10)
Platform: x86_64-unknown-linux-gnu (64-bit)
Matrix products: default
BLAS/LAPACK: /gnu/store/bs9pl1f805ins80xaf4s3n35a0x2lyq3-openblas-0.3.9/lib/libopenblasp-r0.3.9.so
locale:
[1] LC_CTYPE=de_DE.UTF-8 LC_NUMERIC=C
[3] LC_TIME=de_DE.UTF-8 LC_COLLATE=de_DE.UTF-8
[5] LC_MONETARY=de_DE.UTF-8 LC_MESSAGES=de_DE.UTF-8
[7] LC_PAPER=de_DE.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=de_DE.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] gtsummary_1.5.0 ameld_0.0.12 survival_3.2-13 viridis_0.6.1
[5] viridisLite_0.4.0 mlr3viz_0.5.7 ggplot2_3.3.5 targets_0.8.0
loaded via a namespace (and not attached):
[1] fs_1.5.0 RColorBrewer_1.1-2 bbotk_0.4.0
[4] rprojroot_2.0.2 mlr3proba_0.4.1 mlr3pipelines_0.3.6-1
[7] mlr3learners_0.5.0 tools_4.1.1 backports_1.2.1
[10] utf8_1.2.2 R6_2.5.1 mlr3_0.12.0
[13] DBI_1.1.1 colorspace_2.0-2 withr_2.4.2
[16] mlr3misc_0.9.4 tidyselect_1.1.1 gridExtra_2.3
[19] processx_3.5.2 compiler_4.1.1 git2r_0.28.0
[22] cli_3.0.1 ooplah_0.1.0 gt_0.3.1
[25] lgr_0.4.3 labeling_0.4.2 sass_0.4.0
[28] bookdown_0.24 scales_1.1.1 checkmate_2.0.0
[31] callr_3.7.0 palmerpenguins_0.1.0 commonmark_1.7
[34] mlr3tuning_0.9.0 stringr_1.4.0 digest_0.6.28
[37] mlr3extralearners_0.5.9 rmarkdown_2.11 param6_0.2.3
[40] paradox_0.7.1 set6_0.2.3 pkgconfig_2.0.3
[43] htmltools_0.5.2 parallelly_1.28.1 highr_0.9
[46] fastmap_1.1.0 htmlwidgets_1.5.4 rlang_0.4.11
[49] rstudioapi_0.13 farver_2.1.0 visNetwork_2.1.0
[52] jquerylib_0.1.4 generics_0.1.0 jsonlite_1.7.2
[55] dplyr_1.0.7 magrittr_2.0.1 Matrix_1.3-4
[58] Rcpp_1.0.7 munsell_0.5.0 fansi_0.5.0
[61] lifecycle_1.0.1 stringi_1.7.4 whisker_0.4
[64] yaml_2.2.1 grid_4.1.1 parallel_4.1.1
[67] dictionar6_0.1.3 listenv_0.8.0 promises_1.2.0.1
[70] crayon_1.4.1 lattice_0.20-45 splines_4.1.1
[73] knitr_1.34 ps_1.6.0 pillar_1.6.3
[76] igraph_1.2.6 uuid_0.1-4 codetools_0.2-18
[79] glue_1.4.2 evaluate_0.14 data.table_1.14.0
[82] broom.helpers_1.4.0 vctrs_0.3.8 httpuv_1.6.3
[85] distr6_1.6.2 gtable_0.3.0 purrr_0.3.4
[88] tidyr_1.1.3 future_1.22.1 assertthat_0.2.1
[91] xfun_0.26 later_1.3.0 tibble_3.1.4
[94] workflowr_1.6.2 DiagrammeR_1.0.6.1 globals_0.14.0
[97] ellipsis_0.3.2