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Impact of waiting time on post-transplant survival for recipients with hepatocellular carcinoma: a natural experiment randomized by blood group

  • Berend R. Beumer
    Affiliations
    Erasmus MC Transplant Institute, Department of Surgery, Division of HPB & Transplant Surgery, University Medical Centre Rotterdam, Rotterdam, The Netherlands
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  • Wojciech G. Polak
    Affiliations
    Erasmus MC Transplant Institute, Department of Surgery, Division of HPB & Transplant Surgery, University Medical Centre Rotterdam, Rotterdam, The Netherlands
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  • Robert A. de Man
    Affiliations
    Erasmus MC Transplant Institute, Department of Gastroenterology and Hepatology, University Medical Centre Rotterdam, Rotterdam, The Netherlands
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  • Herold J. Metselaar
    Affiliations
    Erasmus MC Transplant Institute, Department of Gastroenterology and Hepatology, University Medical Centre Rotterdam, Rotterdam, The Netherlands
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  • David van Klaveren
    Affiliations
    Department of Public Health, Erasmus MC - University Medical Centre, Rotterdam, The Netherlands
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  • Jeremy Labrecque
    Affiliations
    Department of Epidemiology, Erasmus MC - University Medical Centre, Rotterdam, The Netherlands
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  • Author Footnotes
    1 The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, a worldwide license to the Publishers and its licensees in perpetuity, in all forms, formats and media (whether known now or created in the future), to i) publish, reproduce, distribute, display and store the Contribution, ii) translate the Contribution into other languages, create adaptations, reprints, include within collections and create summaries, extracts and/or, abstracts of the Contribution, iii) create any other derivative work(s) based on the Contribution, iv) to exploit all subsidiary rights in the Contribution, v) the inclusion of electronic links from the Contribution to third party material where-ever it may be located; and, vi) license any third party to do any or all of the above.
    Jan NM. IJzermans
    Correspondence
    Corresponding author. . Phone: 010-7032396 , Erasmus MC Transplant Institute, Dr. Molewaterplein 40, 3015 GD Rotterdam, Department of Surgery RG-219
    Footnotes
    1 The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, a worldwide license to the Publishers and its licensees in perpetuity, in all forms, formats and media (whether known now or created in the future), to i) publish, reproduce, distribute, display and store the Contribution, ii) translate the Contribution into other languages, create adaptations, reprints, include within collections and create summaries, extracts and/or, abstracts of the Contribution, iii) create any other derivative work(s) based on the Contribution, iv) to exploit all subsidiary rights in the Contribution, v) the inclusion of electronic links from the Contribution to third party material where-ever it may be located; and, vi) license any third party to do any or all of the above.
    Affiliations
    Erasmus MC Transplant Institute, Department of Surgery, Division of HPB & Transplant Surgery, University Medical Centre Rotterdam, Rotterdam, The Netherlands
    Search for articles by this author
  • Author Footnotes
    1 The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, a worldwide license to the Publishers and its licensees in perpetuity, in all forms, formats and media (whether known now or created in the future), to i) publish, reproduce, distribute, display and store the Contribution, ii) translate the Contribution into other languages, create adaptations, reprints, include within collections and create summaries, extracts and/or, abstracts of the Contribution, iii) create any other derivative work(s) based on the Contribution, iv) to exploit all subsidiary rights in the Contribution, v) the inclusion of electronic links from the Contribution to third party material where-ever it may be located; and, vi) license any third party to do any or all of the above.
Open AccessPublished:November 21, 2022DOI:https://doi.org/10.1016/j.jhepr.2022.100629

      Highlights

      • Blood groups create a natural randomized controlled trial with treatment arms receiving different waiting times, while being equal in terms of the distribution of confounders
      • For patients with hepatocellular carcinoma waiting harms post-transplant survival
      • Simulation shows that the test-of-time could be useful to increase the utility of scarce donor livers but should likely not exceed 8 months.

      Abstract

      Background & Aims

      When listing for liver transplantation we can transplant as soon as possible or introduce a test-of-time to better select patients, as the tumor’s biological behavior is observed. Knowing the degree of harm caused by time itself is essential to advise patients and decide on the maximum duration of the test-of-time. Therefore, we investigated the causal effect of waiting time on post-transplant survival for patients with HCC.

      Methods

      We analyzed the UNOS-OPTN dataset and exploited a natural experiment created by blood groups. Relations between variables and assumptions were described in a causal graph. Selection bias was addressed by inverse probability weighting. Confounding was avoided using instrumental variable analysis, with an additive hazards model in the second stage. The causal effect was evaluated as a contrast between if all patients waited 2 months instead of 12 months. Upper bounds of the test-of-time were evaluated for probable scenarios by means of simulation.

      Results

      F-statistic of the first stage was 86.3. The effect of waiting 12 months versus 2 months corresponded with a drop in overall survival of 5.07% 95%CI [0.277; 9.69] and 8.33% 95% CI [0.47; 15.60] at 5- and 10-years post-transplant, respectively. The median survival dropped by 3.41 years from 16.21 years 95%CI [15.98; 16.60] for those waiting 2 months to 12.80 years 95%CI [10.72; 15.90] for those waiting 12 months.

      Conclusions

      From a patient’s perspective the choice between ablate-and-wait versus immediate transplantation is in favor of immediate transplantation. From a policy perspective, the extra waiting time can be used to increase the utility of scarce donor livers. However, the duration of the test-of-time is bounded, and it likely shouldn’t exceed 8 months.

      Lay summary

      This research found that waiting is harmful for liver cancer patients. Furthermore, our simulation showed that a preoperative observational period can be useful to ensure good donor liver allocation, but that its duration should not exceed 8 months.

      Graphical abstract

      Keywords

      Abbreviations

      AFP
      Alpha-fetoprotein
      ALBI score
      Albumin-bilirubin score
      ATE
      Average treatment effect
      CDF
      Cumulative density function
      HCC
      Hepatocellular carcinoma
      IPW
      Inverse probability weighting
      IV
      Instrumental variable
      LT
      Liver transplantation
      LRT
      Loco-regional therapy
      OPTN
      Organ Procurement and Transplantation Network
      OS
      Overall survival
      UNOS
      United Network for Organ Sharing

      Authors contributions

      Beumer had the original idea. Beumer, IJzermans, Polak, De Man, Metselaar, Labrecque, and Van Klaveren designed the study. Beumer, IJzermans and Polak helped in the organization of the study and the collection of the data. Beumer performed the statistical analysis which was checked by Van Klaveren and Labrecque. Beumer wrote the first version of the manuscript. The manuscript was critically reviewed and improved upon by all co-authors. IJzermans as guarantor accepts the full responsibility for the work and the conduct of the study, had access to the data, and controlled the decision to publish.

      Conflict of interest statement

      All authors have completed the ICMJE uniform disclosure form at http://www.icmje.org/disclosure-of-interest/and declare: no support from any organization for the submitted work; no financial relationships with any organizations that might have an interest in the submitted work in the previous three years; no other relationships or activities that could appear to have influenced the submitted work.

      Introduction

      Patients with Hepatocellular carcinoma (HCC) that are eligible for liver transplantation (LT) are placed on a waiting list as a donor liver is not instantly available. How this waiting list should be organized is a continuous topic of fierce debate. In the past two decades high quality research was aimed at answering major questions like: which subset of patients should be placed on the waiting list? What is the best way to treat patients prior to transplantation? And how do we prioritize high-risk patients to reduce waiting list mortality? Continued research on these major topics will keep advancing the discussion on how to best organize clinical care. Although there is a growing consensus about these major topics, a question fundamental to organizing the waiting list remains controversial. Namely, how much does the waiting cost a patient with HCC in terms of post-transplant survival
      • Everhart J.E.
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      INCREASED WAITING TIME FOR LIVER TRANSPLANTATION RESULTS IN HIGHER MORTALITY1.
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      Liver transplant waiting time does not correlate with waiting list mortality: implications for liver allocation policy.
      ?
      Knowing the cost of waiting is essential to determine the maximum size of the waiting list, or to confidently expand it. Additionally, the use of the so-called test-of-time is increasingly promoted
      • Roberts J.P.
      • Venook A.
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      Hepatocellular carcinoma: ablate and wait versus rapid transplantation.
      ,
      • Kulik L.
      • Abecassis M.
      Living donor liver transplantation for hepatocellular carcinoma.
      . The rationale of this policy is that in the perioperative observation period patients with the most aggressive forms of cancer are filtered out, hereby improving the allocation of scarce donor livers, and increasing the average post-transplant survival. However, the merit of this allocation policy depends on whether the possible harm of the additional waiting time endured by the full population can be offset with the better allocation of a fraction of the livers. Lastly, knowledge on the cost of waiting can aid transplant clinicians to recommend treatment for patients with multiple options. Patients with more treatment options are often diagnosed in an earlier stage with good liver function leading to a low ranking in the waiting list. Knowing the cost of waiting helps clinicians to identify a threshold at which resection or ablation is the better strategy compared to bridging therapy and eventually transplantation.
      Establishing the causal effect of waiting time is, however, complicated by the prioritization schemes. To reduce waiting list mortality, the waiting list is currently organized such that the patients with the lowest liver function get transplanted first

      OPTN-UNOS. OPTN Bylaws effective Dec 6 2021. Allocation of Livers and Liver-intestines2021.

      . Therefore, a naive survival comparison of patients transplanted within 6 months versus those transplanted after more than 6 months, or a variation thereof, is guaranteed to result in downward biased estimates. In extreme cases, it would appear that waiting is beneficial. A further complicating feature is that socioeconomic mechanisms play an important role, crippling almost all empirical studies. Namely, it is known that patients with lower socioeconomic status are more often inactive on the waiting list due to, for example, problems with their insurance, incomplete screening, or medical non-compliance
      • Bryce C.L.
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      • Roberts M.S.
      The effect of race, sex, and insurance status on time-to-listing decisions for liver transplantation.
      . Additionally, lower frequency of check-up visits leads to a slower escalation of their priority in the waiting list if their liver function decreases. Even though a randomized controlled trial is the golden standard to avoid these biases, in this case it is less preferred due to ethical considerations and the time and expenditures involved. Studying natural experiments in large national datasets may offer a valid alternative to a to a prospective RCT, avoiding confounding altogether.
      In this case, blood groups create a natural randomized controlled trial with treatment arms that are equal in composition of (unobserved) confounders but differ with regard to waiting time. Key is that blood groups are determined at conception and follow the fundamental laws of inheritance
      • Haycock P.C.
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      . Therefore, they can be expected to be independent of confounders. In other words, patients or doctors cannot choose the blood group. Additionally, the blood group itself does not directly influence the severity of the HCC, liver function, complications, or survival. The blood groups, however, do directly influence a patient’s time to transplant. This is caused by the fact that patients with blood group AB can in case of emergency accept a donor organ from blood group A, B, AB, or O. While patients with blood group O can only receive a donor organ from blood group O. Therefore, the blood group could be used as an instrument for waiting time in an instrumental variable analysis. Hence, our research aim is to analyze the natural randomized controlled trial created by blood groups and estimate the causal effect of waiting time on postoperative overall survival for transplanted HCC patients.

      Patients and methods

      Data

      The reporting of this retrospective observational cohort study adheres to the STROBE guidelines (Supplementary Table 1)
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      . The protocol for this study was approved by the Medical Ethics Committee of Erasmus MC, Erasmus University Medical Centre, Rotterdam, the Netherlands (MEC-2020-0779), and adheres to the declaration of Helsinki. The data was supplied by the United Network for Organ Sharing (UNOS) of the Organ Procurement and Transplantation Network (OPTN) as of December 2, 2021. This study analyzed patients with HCC listed for LT in the period between 2000-2019. The records of patients were excluded if: the blood group or follow-up data was missing; patients were younger than 18 at the time of listing; the record did not describe the first transplantation; if the patient received a multi-organ transplantation; or if the patient received a living donor liver transplantation. Furthermore, the information from multiple listings (e.g., due to hospital transfers) was aggregated for the relevant variables. Most importantly, waiting time was recalculated as the time difference between the date of first listing, out of all listings, and the date of transplantation.

      Outcome measures

      The primary outcome measure was overall survival (OS), defined as the time in days between the date of LT and the date of death or last follow-up. The primary aim was to estimate the average treatment effect (ATE) of waiting, defined as the change in hazard rate due to increase in waiting time by one day. To aid interpretation, the secondary aim was to estimate the difference in 5-year OS between if all patients waited 2 months instead of 12 months, which approximately correspond to the first and last quartile of the waiting time distribution. In addition, we investigated if tumor number, tumor size, alpha-fetoprotein (AFP), or the albumin-bilirubin (ALBI) score moderated the treatment effect. Lastly, for the test-of-time simulation we will evaluate the effect of waiting by taking the difference of the average lifetimes, defined as the area under the survival curve

      Efron B. The two sample problem with censored data. Paper presented at: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability1967.

      .

      Causal graph

      Relations between variables were described in a causal graph and were based on expert opinion (Figure 1). Variables that cover similar information and that share similar arrangements are grouped for clarity. An introduction to causal graphs can be found in supplement 1. In addition, the rationale and a more detailed version of our causal graph are provided in Supplementary Fig. 1. The causal graph shows that the relationship between waiting time and survival is biased by multiple mechanisms. More specifically, the dropout from the waiting list induces selection bias, as only those without the most aggressive sub-types and good liver function make it to the liver transplantation. In the analysis of post-transplant survival, by definition, only patients that received the transplantation are analyzed. Hereby we necessarily condition on the variable dropout depicted in the graph by the shading in gray. Furthermore, we can observe that socioeconomic status is a common cause of waiting time and survival. The variables inactivity, intermediate liver function and socioeconomic status are not observed. Therefore, these paths cannot be blocked by means of conditioning and confounding remains. In the causal graph these backdoor paths are highlighted in red. Further, it should be noted that pre-operative loco-regional therapy (LRT) acts as a mediator, potentially modifying the effect of the waiting time. Rather than focusing on the isolated effect of waiting time, this research will evaluate the total effect of waiting time. Hereby the effect of the LRT is absorbed into our measurement. Assuming pre-operative LRT is not harming patients, this will result in a conservative estimate of the isolated effect of waiting.
      Figure thumbnail gr1
      Figure 1Causal graph. Legend : The causal graph guiding the analysis identifying the harm of the waiting time. Abbreviations: Liver function (LF), intermediate (interm.)

      Statistical analysis

      For the descriptive statistics, discrete data was represented in absolute numbers and percentages. Continuous data was represented using the first, second and third quartiles. Covariate balance over the blood groups was assessed using the standardized mean difference and the Kolmogorov-Smirnov statistic with thresholds 0.25 and 0.1, respectively
      • Rubin D.B.
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      . Missing values were addressed using multiple imputation. As the fraction of missing data was 10% the missing values were imputed 20 times with each imputation receiving 20 iterations
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      . Estimates from the repeated analysis were pooled using the Rubin Rules

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      Van Buuren S. Flexible imputation of missing data. CRC press; 2018.

      .
      Selection bias resulting from conditioning on patients that received a transplantation was addressed using inverse probability weighting (IPW)
      • Hernán M.A.
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      • Robins J.M.
      A structural approach to selection bias.
      . The probability that a patient drops-out is estimated using a logistic regression model that included the variables: Gender, Age, BMI, Functional Status, Life support, Level of education, Ethnicity, Insurance type, Transplant region, ALBI score (last), MELD score (last), Encephalopathy, Ascites, Cirrhosis, Tumor number (last), Tumor size (last), Total tumor size (last), log10(AFP).
      Confounding bias was avoided using instrumental variable (IV) analysis, which is explained in supplement 2
      • Angrist J.D.
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      • Angrist J.D.
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      . The four essential IV assumptions are credible for the following reasons. First, the independence assumption was unlikely to be violated by the fact that the blood group of the child is exclusively determined by random selection of the parental alleles. Important to note, however, is that although the allele selection is random, there are slight differences in the distribution of A, B, and O alleles across transplant regions and ethnic groups. To ensure that no open backdoor paths exist the variables transplant region and ethnicity are absorbed into the conditioning set. Secondly, the relevance assumption was supported by the asymmetry in the compatible blood groups between donors and recipients. For example, a recipient with blood group AB can potentially receive a donor liver from someone with blood group AB, A, B, or O, while a recipient with blood group O can only receive a donor liver from a donor with blood group O. This results in that even if a recipient with blood group O is the highest on the waiting list he or she might need to wait longer until a suitable organ is available in comparison to a recipient with blood group AB. Empirically, the relevance assumption will be assessed using the F-statistic of the first stage which corresponds to the strength of the association between the bloodgroup and waiting time. By rule of thumb the F-statistic should be above 10 for the first stage to have sufficient strength

      Staiger DO, Stock JH. Instrumental variables regression with weak instruments. National Bureau of Economic Research Cambridge, Mass., USA; 1994.

      . Thirdly, the exclusion assumption was justified as, to the best of our knowledge, no studies exist which describe a direct or indirect oncogenic interaction between the blood group antigen and the hepatocytes. In extension, there is no evidence that the blood group is related to HCC recurrence, metastasis, or mortality in any other way. In addition, after appropriate matching of donor and recipients, the blood group is not correlated to primary graft dysfunction or rejection. An overview of the addressed and avoided backdoor paths is shown in Supplementary Fig. 1. Lastly, the monotonicity assumption is warranted. Although, the waiting times vary between individuals it never increases if a patient were, hypothetically, assigned a more favorable blood group
      • Angrist J.D.
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      . The validity of this assumption will be empirically assessed by plotting the cumulative density function (CDF) of the waiting time stratified per blood group.
      To estimate the treatment effect of waiting we used two-stage predictor substitution
      • Tchetgen E.J.T.
      • Walter S.
      • Vansteelandt S.
      • Martinussen T.
      • Glymour M.
      Instrumental variable estimation in a survival context.
      . The first stage consisted of a linear regression model in which waiting time was regressed on the blood group, transplant region, and ethnicity. In the second stage an additive hazards model was used to regress the time-to-event information on the predicted value of the first stage, transplant region, and ethnicity
      • Aalen O.O.
      A linear regression model for the analysis of life times.
      . Standard errors were obtained using bootstrap resampling. Heterogeneity in the treatment effect was investigated on a variable-by-variable basis for which the population was subsetted based on the quartiles. For the lowest and highest subset the instrumental variable analysis was repeated. More formally the IV analysis was extended with the addition of interaction terms to investigate if the ATE was moderated by tumor number, tumor size, AFP, or the ALBI score, which were measured prior to listing.
      Lastly, we performed a post-hoc simulation to investigate the conditions under which the test-of-time results in a survival benefit given the causal effect of waiting time on post-transplant survival. For this, following the rationale of the test-of-time
      • Roberts J.P.
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      Schwartz M, Florman S. Optimal Liver Allocation for Hepatocellular Carcinoma: Hurry up AND wait, but which one when? Vol 14: Wiley Online Library; 2014:1479-1480.

      ,
      • Mehta N.
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      • Lee D.
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      Wait time of less than 6 and greater than 18 months predicts hepatocellular carcinoma recurrence after liver transplantation: proposing a wait time “sweet spot”.
      , the population of patients was viewed as a mixture of patients with aggressive, and non-aggressive HCC. The derivation of the upper bound is presented in Supplement 3. Only the cost of waiting was studied and quantified in this research. For the other components we used credible ranges to calculate the upper bound. More specifically, for the difference in average lifetime between patients with aggressive and non-aggressive HCC we used a range of 7 to 16 years; for the proportion of aggressive cases without the test-of-time we used a range of 2 to 30 percent; and lastly, we used a range of 10 to 70 percent for the reduction of aggressive cases with the test-of-time.

      Results

      Of the in total 273,134 patients in the UNOS dataset 45,694 patients were included in the study. All included patients were used in the IPW model, and 32,000 patients that had undergone transplantation entered the IV analysis (Supplementary Fig. 2). Of the included patients the median waiting time was 7.4 months with an IQR of 12 months. The descriptive statistics, stratified by blood group, showed no major disbalance in important confounders across the blood groups (Table 1). Blood groups were not uniformly distributed across different ethnicities. Furthermore, differences across the blood groups exist in terms of waiting time, dropout rate, and post-transplant survival. A more detailed overview of the covariate balance statistics for each blood group contrast is presented in Supplementary Fig. 3.
      Table 1Descriptive characteristics stratified per blood group.
      ABBAOSMD (max)KS (max)
      n179758771681821202
      Period n (%)[2000,2005]268 (15)966 (16)2642 (16)3391 (16)0.0420.015
      (2005,2010]458 (25)1435 (24)4119 (24)5258 (25)0.0250.011
      (2010,2015]596 (33)1926 (33)5485 (33)6872 (32)0.0160.008
      (2015,2020]475 (26)1550 (26)4572 (27)5681 (27)0.0180.008
      MaleMissing0 (0)0 (0)0 (0)0 (0)--
      n (%)1404 (78)4513 (77)13061 (78)16165 (76)0.0450.019
      AgeMissing (%)0 (0)0 (0)0 (0)0 (0)--
      Q1 | Q2 | Q355 | 60 | 6454 | 59 | 6454 | 59 | 6454 | 59 | 640.0660.037
      Height (m)Missing (%)3 (0)29 (0)59 (0)58 (0)0.0580.003
      Q1 | Q2 | Q3165 | 173 | 180165 | 173 | 178167 | 173 | 180165 | 173 | 1780.1090.046
      Weight (kg)Missing (%)3 (0)30 (1)64 (0)63 (0)0.0590.003
      Q1 | Q2 | Q372 | 84 | 9770 | 82 | 9673 | 85 | 9873 | 84 | 970.1480.025
      Ethnicity n (%)Missing (%)0 (0)0 (0)0 (0)0 (0)--
      White1163 (65)3157 (54)12105 (72)12908 (61)0.3810.183
      Black175 (10)840 (14)1043 (6)2149 (10)0.2700.081
      Hispanic146 (8)772 (13)2398 (14)4359 (21)0.3610.124
      Asian292 (16)1045 (18)1056 (6)1433 (7)0.3620.125
      Native American1 (0)15 (0)90 (1)182 (1)0.1230.008
      Pacific Islander10 (1)15 (0)46 (0)45 (0)0.0610.003
      Multiracial10 (1)33 (1)80 (0)126 (1)0.0160.001
      Meld scoreMissing (%)18 (1)47 (1)188 (1)198 (1)0.0330.003
      Q1 | Q2 | Q38 | 11 | 158 | 11 | 158 | 11 | 158 | 11 | 150.0350.025
      ALBI scoreMissing (%)13 (0.7)29 (0.5)115 (0.7)119 (0.6)0.0290.002
      Q1 | Q2 | Q3-2.4 | -1.9 | -1.4-2.4 | -1.9 | -1.3-2.3 | -1.8 | -1.3-2.3 | -1.8 | -1.30.1060.032
      Tumor nr n (%)Missing438 (24)1105 (19)3126 (19)3868 (18)0.1540.061
      11032 (57)3622 (62)10337 (61)13196 (62)0.0150.018
      2234 (13)849 (14)2449 (15)3053 (14)
      390 (5)282 (5)856 (5)1024 (5)
      40 (0)13 (0)39 (0)45 (0)
      >=53 (0)6 (0)11 (0)16 (0)
      Tumour size (cm)Missing (%)438 (24)1105 (19)3126 (19)3868 (18)0.1540.061
      Q1 | Q2 | Q32 | 2 | 32 | 2 | 32 | 2 | 32 | 2 | 30.0220.028
      log10(AFP) (ng/mL)Missing (%)546 (30.4)1473 (25.1)4220 (25.1)5318 (25.1)0.1210.053
      Q1 | Q2 | Q30.7 | 1 | 1.60.7 | 1 | 1.60.7 | 1 | 1.60.7 | 1 | 1.60.0350.024
      LRTMissing465 (26)1388 (24)3905 (23)5109 (24)0.0620.027
      n (%)916 (69)3278 (73)9496 (74)11849 (74)0.1090.049
      Waiting time (months)Missing (%)0 (0)0 (0)0 (0)0 (0)--
      Q1 | Q2 | Q31 | 3 | 82 | 7 | 133 | 8 | 153 | 8 | 160.3290.252
      DropoutMissing22 (1)126 (2)438 (3)594 (3)0.1080.016
      n (%)304 (17)1428 (25)4470 (27)6159 (30)0.2970.128
      n146543061185714372
      Med. FU [95%CI] (yr)6 [5.8 - 6.3]5.9 [5.8 - 6]5.9 [5.9 - 6]5.9 [5.8 - 6]
      DeathMissing0 (0)0 (0)0 (0)0 (0)
      n (%)402 (27)1205 (28)3512 (30)4317 (30)
      Med. OS [95%CI] (yr)14.5 [13.5 - NA]14.3 [12.9 - 15.9]12.7 [12.3 - 13.3]12.8 [12.3 - 13.3]
      5 yr OS [95%CI]0.75 [0.73 - 0.78]0.75 [0.74 - 0.77]0.74 [0.73 - 0.75]0.74 [0.73 - 0.74]
      Legend Table 1 –The main characteristics stratified by blood group. Tumor number, Tumor size, Meld score, ALBI score, and AFP represent the measurement at listing. Abbreviations: Alpha fetoprotein (AFP); Body mass index (BMI); Model for end stage liver disease (Meld), Albumin bilirubin score (ALBI score), Follow up (FU), Overall survival (OS), Median (Med), Quantile (Q), Standardized mean difference (SMD), Kolmogorov-Smirnov (KS).
      In the first stage the mean waiting time at each of the levels of the instrument was significantly different with respect to the reference category (AB). Furthermore, the F-statistic of 86.3 indicated that the blood group as an instrument is sufficiently associated with waiting time to be used in instrumental variable analysis. The underlying source of variation was confirmed to be the asymmetric blood group compatibility (Supplementary Table 2). This results in an over representation of patients with AB and B in the first quartile, and in the last quartile more patients with blood groups O and A are left (Figure 2). The empirical cumulative distribution functions did not show any evidence that the monotonicity assumption was violated, as the lines overlap at the extremes but do not cross (Supplementary Fig. 4).
      Figure thumbnail gr2
      Figure 2Waiting time distribution. Legend : The distribution of the waiting time on the linear scale (A) and on the logarithmic scale (B).
      The IV analysis indicates that waiting longer reduces post-transplant survival (Figure 3). The time varying estimates were increasing, and the confidence bounds did not include the zero line. The estimation of the time constant effect, γ*10−4, was estimated to be 0.44 (95%CI [0.12; 0.76], p < 0.001). On the survival scale, the effect of waiting 12 months versus 2 months corresponded with a drop in overall survival of 5.07% 95%CI [0.277; 9.69] at 5-year post transplantation and 8.33% 95% CI [0.47; 15.60] at 10 years post transplantation. The median survival dropped by 3.41 years from 16.21 years 95%CI [15.98; 16.60] for those waiting 2 months to 12.80 years 95%CI [10.72; 15.90] for those waiting 12 months and the difference in mean lifetime was 1.36 years 95%CI[0.26; 2.34].
      Figure thumbnail gr3
      Figure 3Average treatment effect of waiting time. Legend : The average treatment effect of waiting time on post-transplant survival. Panel (A) shows the time constant and time varying cumulative hazard function for waiting time. In panel (B) the cumulative coefficient for waiting time is translated to the survival scale and shows a contrast between if all patients wait 2 months versus 12 months.
      Table 2 shows the descriptive statistics regarding the heterogeneity of the treatment effect. All estimates indicate a higher impact of waiting on patients that were in the highest quartile (I.e., to those more ill) in comparison to patients that were in the lowest quartile (I.e., to those less ill). However, due to the reduction in sample size the confidence intervals of the ATE in the subgroups increased. The estimate for waiting time in the Q4 subgroup of tumor number is the only subset in which the subgroup ATE is significantly different from zero with γ*10−4 of 1.03 95%CI[0.10; 1.79]. The heterogeneous treatment effect was more formally investigated using interaction terms shown in Table 3. These are all positive, in concordance with that more ill patients are harmed more by waiting. However, none of the interaction terms attained statistical significance. The tests therefore remain inconclusive with respect to whether the harm of waiting is equal for all, or if some patients are more affected.
      Table 2Heterogenous treatment comparison of quantiles.
      Q1Q4
      LevelFγ*10-4 [95%CI]Δ5 yr OS %LevelFγ*10-4 [95%CI]Δ5 yr OS %
      Tumor number1630.17 [-0.22; 0.55]1.872241.03 [0.10; 1.97]11.8
      Tumor size (cm)1.8320.35 [-0.34; 1.04]4.022.9240.54 [-0.19; 1.27]6.0
      log10(AFP)0.7240.28 [-0.32; 0.88]3.381.59250.62 [-0.19; 1.44]6.4
      ALBI score-2.37310.39 [-0.16; 0.94]4.7-1.33180.43 [-0.37; 1.24]4.6
      Legend Table 2: The harm of waiting for each of the variables within the lowest and the highest subgroup based on the quartiles. Abbreviations: Alpha fetoprotein (AFP), Albumin bilirubin score (ALBI score), Overall survival (OS).
      Table 3Heterogenous treatment effect regression.
      γ * 10-4[95%CI]p value
      W0.38[0.06; 0.82]0.004
      W*tumor number0.48[-0.27; 1.20]0.115
      Tumor number70[26; 114]<0.001
      W*tumor size0.08[-0.48; 0.64]0.938
      Tumor size0.12[-0.55; 0.79]<0.001
      W*log10(AFP)0.12[-0.55; 0.79]0.908
      log10AFP120[82; 160]<0.001
      W*ALBI0.11[-0.65; 0.87]0.936
      ALBI81[20; 140]<0.001
      Legend Table 3: The regression with interaction terms to study the heterogenous effect of waiting. Abbreviations: Alpha fetoprotein (AFP), Albumin bilirubin score (ALBI score).
      The results of the simulation investigating the conditions under which test-of-time results in a survival benefit are presented in Supplementary Tables 3 and 4. The simulation shows that given a proportion of aggressive cases of 12% and a reduction of 50% with the test-of-time, the upper bound of the waiting time is 3 to 8 months, with the point estimate depending on the difference in average survival between the aggressive and non-aggressive cases. Beyond this upper bound, the harm of waiting is no longer compensated by the improved allocation of donor livers.

      Discussion

      The aim of our research was to estimate the causal effect of waiting time on post-transplant survival. We conclude that for transplant patients with HCC waiting is harmful, with an estimated loss of 5% overall survival at 5-year after transplantation and a drop of 3.41 years in median survival if a patient waits 12 instead of 2 months. We reason that the impaired survival could be biologically explained by the increased time at risk for micro metastatic spread. This is in line with our subgroup analysis indicating that a large tumor burden is likely to aggravate the harm of waiting. Although our research by itself does not recommend a specific liver transplant policy, it does provide essential information needed to formulate conditions which policies need to meet in order to result in a net benefit. These conditions necessarily need to consider both the impact of dropout and the post-transplant survival. In this research we focused on the latter and are hereby closer to answering the question whether the harm of all patients having to wait longer can be offset by the improved allocation of a fraction of the livers. Besides quantifying the harm of waiting on post-transplant survival, to the best of our knowledge, we provide the first causal graph in the field. This graph represents a model of reality and simultaneously explicates our assumptions. The graph is an important starting point for all future empiric liver transplantation research in order to avoid spurious results.
      In the literature, the effect of waiting time on survival is studied from two different perspectives. Despite that the perspectives are linked, they are, and should be treated as, distinct. The first perspective is concerned with the causal effect on a patient. That perspective is studied here. The second perspective is concerned with the measurement of the association. Most of the research focuses on the second perspective
      • Lai Q.
      • Lerut J.
      • Study E.H.C.L.T.E.
      Waiting time and transplantation for hepatocellular cancer: A balance between tempus fugit and carpe diem.
      . All these studies find that waiting longer is associated with improved post-transplant survival
      • Roberts J.P.
      • Venook A.
      • Kerlan R.
      • Yao F.
      Hepatocellular carcinoma: ablate and wait versus rapid transplantation.
      ,
      • Halazun K.J.
      • Patzer R.E.
      • Rana A.A.
      • Verna E.C.
      • Griesemer A.D.
      • Parsons R.F.
      • et al.
      Standing the test of time: outcomes of a decade of prioritizing patients with hepatocellular carcinoma, results of the UNOS natural geographic experiment.
      • Salvalaggio P.
      • Felga G.
      • Axelrod D.
      • Della Guardia B.
      • Almeida M.
      • Rezende M.
      List and liver transplant survival according to waiting time in patients with hepatocellular carcinoma.
      • Schlansky B.
      • Chen Y.
      • Scott D.L.
      • Austin D.
      • Naugler W.E.
      Waiting time predicts survival after liver transplantation for hepatocellular carcinoma: A cohort study using the U nited N etwork for O rgan S haring registry.
      • Samoylova M.L.
      • Dodge J.L.
      • Yao F.Y.
      • Roberts J.P.
      Time to transplantation as a predictor of hepatocellular carcinoma recurrence after liver transplantation.

      San Miguel C, Vilchez A, Villegas T, Granero K, Becerra A, Lopez M, et al. Influence of waiting list in recurrence disease of hepatocellular carcinoma. Paper presented at: Transplantation proceedings2015.

      or no harm
      • Palmer W.C.
      • Lee D.
      • Burns J.
      • Croome K.
      • Rosser B.
      • Patel T.
      • et al.
      Liver transplantation for hepatocellular carcinoma: impact of wait time at a single center.
      ,
      • Hogen R.
      • Lo M.
      • DiNorcia J.
      • Ji L.
      • Genyk Y.
      • Sher L.
      • et al.
      More than just wait time? Regional differences in liver transplant outcomes for hepatocellular carcinoma.
      . Many acknowledge that the cause of this association has no oncological basis. They explain the association by the fact that the patients with the most aggressive HCC do not make it to the transplantation and are thus filtered out of the post-transplant survival analysis. This leads to an important difference between the two perspectives. Given a different waiting time policy, for a patient the causal effect of 1 month of extra waiting stays the same, while the strength of the association measured changes depending on the degree of dropout that is characteristic to a particular waiting policy. Given this, we join the formulation of Metha et al.
      • Mehta N.
      • Heimbach J.
      • Lee D.
      • Dodge J.L.
      • Harnois D.
      • Burns J.
      • et al.
      Wait time of less than 6 and greater than 18 months predicts hepatocellular carcinoma recurrence after liver transplantation: proposing a wait time “sweet spot”.
      in that this association should be seen as a perceived risk of transplanting patients too early and not as an actual risk for the patient itself. It is, namely, possible that all patients are harmed by waiting longer but that the measured average post-transplant survival increases due to the shifting proportion of aggressive/non-aggressive cases. Despite this, previous studies addressed the selection bias due to dropout only by means of performing an additional intention-to-treat analysis. Although, the intention-to-treat analysis allows for the inclusion of all patients, it describes a less defined treatment or exposure. In this case the treatment becomes a mixture of waiting time only, and waiting time followed by transplantation. Yet the proportion of these is again dependent on the waiting policy, hereby distorting the measurement of the causal effect.
      In addition, because these studies did not use a causal graph, it remains unclear if they sufficiently accounted for confounding bias, as illustrated by the widely varying conditioning sets. The study of Halazun et al.
      • Halazun K.J.
      • Patzer R.E.
      • Rana A.A.
      • Verna E.C.
      • Griesemer A.D.
      • Parsons R.F.
      • et al.
      Standing the test of time: outcomes of a decade of prioritizing patients with hepatocellular carcinoma, results of the UNOS natural geographic experiment.
      addressed confounding in more detail by investigating survival differences between long and short waiting time regions. They suggested a natural experiment was exploited. Hereby implying that patients are randomly assigned to either a long or short waiting time region, resulting in an equal distribution of confounders. However, it remains unclear if the composition of patients was actually comparable, as for example socio-economic factors also differ from region to region and do affect survival. As the socio-economic factors were not part of their conditioning set, confounding biases are still present. Therefore, the causal claim of their research was not well supported. Even though the considerations were more complex, involving equal access and the utility of scarce donor organs, the consensus of the associational studies played an important role in the adoption of the mandatory 6-month waiting policy by the UNOS.
      Several authors did, however, study the first perspective using causal inference. Recently, Nagai et al. used a before-after study design to investigate the mandatory 6-month waiting policy
      • Nagai S.
      • Kitajima T.
      • Yeddula S.
      • Salgia R.
      • Schilke R.
      • Abouljoud M.S.
      • et al.
      Effect of mandatory 6‐month waiting period on waitlist and transplant outcomes in patients with hepatocellular carcinoma.
      . Their primary aim was to investigate waiting list mortality and dropout, however, as a secondary outcome they also investigated post-transplant outcomes. The authors reported that the policy change had no effect on the post-transplant mortality. However, a few limitations, inherent to the before-after study design, made interpretation of their results more difficult. The before-after study design was likely biased by trends in the post-transplant survival. As the inclusion period spanned more than 5 years, and improvements in terms of imaging and clinical care were not controlled for, the estimates are likely biased toward the null (I.e., the group with a longer waiting time got an improved medical treatment in comparison with the group that waited shorter). Furthermore, apart from changes in the treatment technique, the composition of the before and after group changed. The authors anticipated a higher dropout rate and better post-transplant outcomes, due to exclusion of the most aggressive HCC during the extended waiting period. However, their results showed both lower dropout and better post-transplant survival in the group which experienced the mandatory 6-months waiting policy. Care could have been improved, but Nagai et al. speculated that after the policy change doctors became more reluctant to place patients with advanced disease on the waiting list, knowing that exception points are only assigned after 6 months of waiting. In their analysis they did not address the trends in treatment outcomes or the multitude of selection processes. In addition, they recommended that a longer follow-up was needed to study post-transplant survival in more detail.
      An alternative causal inference technique is to exploit the exogenous variation in a treatment created by an instrumental variable. The research by Everhart et al. was the first to analyze the survival of patients stratified by blood group
      • Everhart J.E.
      • Lombardero M.
      • Detre K.M.
      • Zetterman R.K.
      • Wiesner R.H.
      • Lake J.R.
      • et al.
      INCREASED WAITING TIME FOR LIVER TRANSPLANTATION RESULTS IN HIGHER MORTALITY1.
      . The analysis was, however, limited to stratification. Several other aspects of the study are problematic for identifying the harm of waiting in terms of survival for HCC patients. Most importantly, the study described patients treated two decades ago (1990-1993) and indications for transplantation and the waiting list policy have changed since. For this reason, their study also did not include patients with HCC and is therefore not representative. Further, their sample size of 673 patients was limited. In addition, the logistic model they used to study time-to-event data was likely biased due to more frequent censoring of patients with a longer survival. Later, Howard expanded on the work of Everhart et al. and used blood groups as an instrument in a two-stage regression approach
      • Howard D.
      The impact of waiting time on liver transplant outcomes.
      . However, this analysis did not focus on post-transplant survival, but on graft failure within 3 months post-transplant. Our research extends the use of blood groups as an instrumental variable for post-transplant survival.
      A strength of our analysis is that hereby our results are subject to minimal (unobserved) confounding. In addition, selection bias was addressed using IPW and missing values were imputed using multiple imputation. Important to note, however, is that our research has several limitations. First is that the causal graph presented here is our view on reality and we realize that undoubtedly more detail can be added. In the graph the most important simplification we made was that the complexities involved with waiting time being a time varying treatment were simplified to where it is being assigned at once and at listing. We recognize that in reality the waiting time of a patient is not known at the time of listing and that the waiting time depends on intermediate examinations of which the frequency is tailored to the individual patient.
      Another limitation is that our analysis of the heterogeneous treatment effect involves parametric assumptions. Although we expect changes in the treatment effect to be smooth it is not necessarily linear. Alternatives such as performing the analysis using a subset, kernel smoothing, or K-nearest neighbours are more flexible. However, for this research we valued the ability of interaction terms to test if the treatment effect changed relative to the average treatment effect. Yet we acknowledge that the power of interaction terms to detect heterogeneity is limited.
      Our work can be extended in several ways. Our research was quantitative in nature, determining how much waiting harms post-transplant survival. A qualitative research focusing on why waiting harms survival should be performed in a dataset with high quality data regarding follow-up, recurrence and metastatic spread. Another future study, with a more advanced instrumental variable analysis, could unentangle the isolated effects of LRT and waiting time on survival. In the current study the total or combined effect is analyzed, but quantification of the isolated effect is certainly of value. Furthermore, we advise to repeat the analysis in a non-American dataset and investigate the transportability of our results.
      Overall, we conclude that for transplant candidates with HCC a prolonged waiting period is harming their post-transplant survival. From a patient’s perspective, all else equal, the choice between first LRT and eventually transplantation versus immediate transplantation is in favor of immediate transplantation, due to the harm of the waiting time. Yet we stress that the reduction in survival is limited compared to the survival gain from liver transplantation. From a policy perspective, we realize that extra waiting time can be desirable such that more biologically aggressive cancers are filtered out and the utility of the scarce donor livers is increased. Among all suggestions for selection criteria the ones incorporating (a variation of) the test-of-time might be the most fair. Nevertheless, the duration of the test-of-time is bounded, and we highlight that more research is needed to identify the optimal waiting time.

      Data Availability Statement

      The data of this study were supplied by United Network for Organ Sharing as the contractor for the Organ Procurement and Transplantation Network in December 2020. The patient level data are available at this institution upon reasonable request.

      Statistical Script

      The R source file is available as online supplement entitled: Effect of waiting time on survival - blood group IV - UNOS.R

      Transparency statement

      Beumer and IJzermans, as the lead authors, affirm that the manuscript is an honest, accurate, and transparent account of the study; that no important aspects of the study have been omitted.

      Disclaimer

      The data reported here have been supplied by the United Network for Organ Sharing as the contractor for the Organ Procurement and Transplantation Network. The interpretation and reporting of these data are the responsibility of the author(s) and in no way should be seen as an official policy of or interpretation by the OPTN or the U.S. Government.

      Acknowledgements

      Dr. Naghi, Dr. O’Neill, and Mrs. Fresina are gratefully acknowledged for proofreading the manuscript.

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