ORIGINAL ARTICLE. Sarah K. Alver, 1 Douglas J. Lorenz, 1 Michael R. Marvin, 2 and Guy N. Brock 1 SEE EDITORIAL ON PAGE 1321 ORIGINAL ARTICLE 1343

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1 ORIGINAL ARTICLE Projected Outcomes of 6-Month Delay in Exception Points Versus an Equivalent Model for End-Stage Liver Disease Score for Hepatocellular Carcinoma Liver Transplant Candidates Sarah K. Alver, 1 Douglas J. Lorenz, 1 Michael R. Marvin, 2 and Guy N. Brock 1 1 Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, Louisville, KY; and 2 Department of Transplantation and Liver Surgery, Geisinger Medical Center, Danville, PA The United Network for Organ Sharing (UNOS) recently implemented a 6-month delay before granting exception points to liver transplantation candidates with hepatocellular carcinoma (HCC) to address disparity in transplantation access between HCC and non-hcc patients. An HCC-specific scoring scheme, the Model for End-Stage Liver Disease equivalent (MELD EQ ), has also been developed. We compared projected dropout and transplant probabilities and posttransplant survival for HCC and non-hcc patients under the 6-month delay and the MELD EQ using UNOS data from October 1, 2009, to June 30, 2014, and multistate modeling. Overall (combined HCC and non-hcc) wait-list dropout was similar under both schemes and slightly improved (though not statistically significant) compared to actual data. Projected HCC wait-list dropout was similar between the MELD EQ and 6-month delay at 6 months but thereafter started to differ, with the 6-month delay eventually favoring HCC patients (3-year dropout 10.0% [9.0%-11.0%] for HCC versus 14.1% [13.6%-14.6%]) for non-hcc) and the MELD EQ favoring non-hcc patients (3-year dropout 16.0% [13.2%-18.8%] for HCC versus 12.3% [11.9%-12.7%] for non-hcc). Projected transplant probabilities for HCC patients were substantially lower under the MELD EQ compared to the 6-month delay (26.6% versus 83.8% by 3 years, respectively). Projected HCC posttransplant survival under the 6-month delay was similar to actual, but slightly worse under the MELD EQ (2-year survival 82.9% [81.7%-84.2%] versus actual of 85.5% [84.3%-86.7%]). In conclusion, although the 6-month delay improves equity in transplant and dropout between HCC and non-hcc candidates, disparity between the 2 groups may still exist after 6 months of wait-list time. Projections under the MELD EQ, however, appear to disadvantage HCC patients. Therefore, modification to the exception point progression or refinement of an HCC prioritization score may be warranted. Liver Transplantation AASLD. Received December 3, 2015; accepted June 7, SEE EDITORIAL ON PAGE 1321 Abbreviations: AFP, alpha-fetoprotein; CI, confidence interval; HCC, hepatocellular carcinoma; ln(afp), natural log of alpha-fetoprotein; LT, liver transplantation; MELD, Model for End-Stage Liver Disease; MELD EQ, Model for End-Stage Liver Disease equivalent; OPTN, Organ Procurement and Transplantation Network; UNOS, United Network for Organ Sharing. Address reprint requests to Guy N. Brock, Ph.D., Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, 485 E. Gray Street, Louisville, KY Telephone: ; FAX: ; guy.brock@osumc.edu Additional supporting information may be found in the online version of this article. The Model for End-Stage Liver Disease (MELD) scoring system is used as part of the criteria for liver transplantation (LT) allocation. Previously under Organ Procurement and Transplantation Network (OPTN) policies, transplant candidates with hepatocellular carcinoma (HCC) stage T2 lesions initially received a MELD score equivalent to a 15% risk of 3- month mortality. Additional points equivalent to a 10% increase in mortality risk were given every 3 months thereafter, until the patient received a transplant or became unsuitable for transplant based on their HCC progression. (1) Under this system, patients with HCC exceptions have had higher transplant rates and lower dropout ORIGINAL ARTICLE 1343

2 LIVER TRANSPLANTATION, October 2016 compared to patients without HCC. To address this, a delay of 6 months before granting exception points to HCC patients has recently been implemented. A secondary aim of this delay was to avoid transplanting HCC patients with aggressive tumors who may have a high recurrence risk after transplant. Under the delay, candidates will be listed at their laboratory MELD scores until the second 3- month extension, at which time they will be assigned 28 points and continue with the scheduled progression of exception points. These exception points will be capped at 34 so that these patients are not candidates for default regional sharing with the regional MELD 35 sharing policy. (4) Other methods for addressing this disparity between HCC and non-hcc patients have been proposed, including equivalent MELD scores for HCC patients. (5-10) These scores were meant to reflect mortality risk for HCC patients more accurately than scheduled progression of exception points. Toso et al. (11) described them in a recent publication. Another alternative score, the Model for End-Stage Liver Disease equivalent (MELD EQ ), was derived by determining dropout hazard rates based on established HCC characteristics as well as laboratory MELD and then equating this risk to that of non-hcc patients to find the corresponding equivalent MELD score. (10) Incidentally, the MELD EQ also included a wait-list time factor derived as part of the scoring system which increased an HCC patient s score after 6 months on the waiting list. Because it is on the same scale as the laboratory MELD score for non-hcc patients, it could be used comparably. The main objective of the current study was to compare the projected effect of the 6-month delay to rates (2,3) Guy N. Brock is currently affiliated with the Department of Biomedical Informatics and Center for Biostatistics, The Ohio State University, College of Medicine, Columbus, OH. The content is the responsibility of the authors alone and does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the US government. Copyright VC 2016 by the American Association for the Study of Liver Diseases. View this article online at wileyonlinelibrary.com. DOI /lt Potential conflict of interest: Nothing to report. prioritization using MELD EQ scores on HCC and non-hcc dropout and transplant probabilities. These projections for HCC patients were studied for the MELD EQ in its original publication, (10) and projections for transplant rates and mortality under the delay were previously studied by Heimbach et al. (12) using simulation methods. However, the current study compares outcomes under both approaches and uses more recent United Network for Organ Sharing (UNOS) data. Additionally, we compared actual posttransplant survival for HCC and non-hcc patients with that projected under the 6-month delay and the MELD EQ. Furthermore, whereas the previous MELD EQ study only evaluated projected effects on HCC patients, the current study includes projections for non-hcc patients as well. Though the earlier study by Heimbach et al. (12) demonstrated improved equity between HCC and non-hcc patients using the 6-month delay, the effects of the delay on patients in various dropout risk strata were not specifically examined. Using UNOS data and multistate modeling, we evaluated projected wait-list dropout and transplant probabilities for both HCC and non-hcc patients in varying risk strata under the 6-month delay and the MELD EQ scoring system. Patients and Methods DATA Data were obtained on all patients who were added to the UNOS LT waiting list on or after October 1, 2009, based on OPTN data as of June 30, 2014, and who were at least 18 years old at the time of initial listing. We excluded patients with exceptions other than HCC and restricted the non-hcc data set to patients with no exceptions. Patients listed as status 1A or 1B and HCC patients who were missing HCC-related covariate data were also excluded. IRB approval was not required per University of Louisville policy as OPTN data is one of the approved sources of publicly available data. OUTCOMES AND COVARIATES The main outcomes studied included actual and projected dropout and transplant probabilities for HCC and non-hcc patients based on the prior practice of scheduled progression of exception points, the 6- month delay, and prioritization using MELD EQ scores. The covariates used in the MELD EQ model 1344 ORIGINAL ARTICLE

3 LIVER TRANSPLANTATION, Vol. 22, No. 10, 2016 were the natural log of alpha-fetoprotein (ln[afp]), laboratory MELD, maximum tumor size, and number of tumors. Dropout was defined as removal from the waiting list due to death, determined medically unsuitable, or too sick for transplant. Transplant was defined as having received transplant for any reason. Those who remained on the waiting list or were removed due to improvement were considered censored. Additional outcomes included actual and projected posttransplant survival for HCC and non-hcc patients under the MELD EQ and the 6-month delay. STATISTICAL METHODS The MELD EQ was calculated for all HCC patients at each follow-up time using the following equation: MELD EQ 51:143 3 MELD11:324 3 lnðafpþ 11:438 3 number of tumors11:194 3max tumor size1cðtþ; where cðtþ5 13:70 for t < 6 months and cðtþ5 6:85 for t 6 months MELD, alpha-fetoprotein (AFP, in ng/ml), and tumor characteristics were updated for each patient at each time point. If the laboratory MELD score was greater than the calculated MELD EQ, the MELD EQ score was taken to be the laboratory MELD. Observations were categorized into ranges based on their MELD EQ and laboratory MELD scores. These ranges included < 12, 12-15, 16-21, 22-27, and Scores of 22 and above were categorized based on the previous exception points granted at 3-month intervals and then combined due to sparse data in the higher-risk groups. These categories were used as the transient states in a nonparametric multistate model for dropout and transplant probabilities, using the R package mssurv. (13) Figure 1 displays a schematic diagram of the multistate model. In a multistate model, patients can transition between the transient states at any time but cannot transition out of the terminal states. Briefly, our multistate model consists of 5 transient states (the MELD/MELD EQ risk categories, labeled states 1-5) and 2 terminal states of wait-list dropout (state 6) and transplantation (state 7). The multistate model was used to calculate probabilities for transplant and waitlist dropout (terminal states) for each risk category FIG. 1. Schematic diagram of multistate model. Transient states consisting of MELD or MELD EQ ranges are represented by circles, whereas the terminal states of dropout and transplant are represented by rectangles. Transitions are possible between any of the transient states and another transient state (light lines), and from any transient state to the terminal states (bold lines). Transitions to the dropout/transplant states are of primary interest. (transient states). The model accounts for transitioning between these states prior to dropout or transplant, as well as transitioning directly to the terminal states. Dropout and transplant probabilities were modeled for HCC patients. One model was fitted for HCC patients stratified by laboratory MELD ranges for comparison with the 6-month delay and another with stratification using MELD EQ. A similar model was constructed for non-hcc patients. Actual dropout and transplant probabilities were obtained from these models. We also examined HCC posttransplant survival among several strata of the components of the MELD EQ, and overall posttransplant survival for HCC and non-hcc patients. Kaplan- Meier survival estimates, Cox proportional hazard models, and the log-rank test were used for this comparison. All data analysis and statistical calculations were performed usingsas,version9.4(sasinc.,cary,nc)andr,version (R Project, Vienna, Austria). PROJECTED OUTCOMES The projection estimates assume that HCC and non- HCC patients with the same MELD/equivalent MELD strata are transplanted at the same hazard rate. This is similar to our previous projection method (10) and is based on a technique that has been used to perform causal inference in multistate models. (14,15) However, here we modify the approach to account for the potential impact on non-hcc ORIGINAL ARTICLE 1345

4 LIVER TRANSPLANTATION, October 2016 patients as well. This is done by assuming that the total number of available organs remains fixed and that organs are redistributed across strata according to non-hcc rates. Essentially, the conditional probability that an HCC patient in a given risk strata receives an organ is assumed to be equal to that of a non-hcc patient in the equivalent strata. The organs are redistributed to risk strata consisting of HCC and non-hcc patients grouped together, and the probability that an organ goes to an HCC patient is then equal to the fraction of HCC patients in that strata. The technical details for the projection method and underlying assumptions are given in the Supporting Text. The projected transplant hazards were calculated as above for both the 6-month delay model and the MELD EQ model. For projections under the 6-month delay, we resumed use of the actual transplant hazards in the Aalen-Johansen estimator after 6 months to reflect reverting to scheduled exception point progression. For projections under the MELD EQ, we calculated the probabilities using projected transplant hazards through 18 months. To project outcomes for patients under the MELD EQ given a patient is still on the list after 6 months, we made separate calculations for 6-18 months from listing. Calculations were made in an analogous fashion using the non-hcc multistate model, the MELD EQ HCC multistate model, and projected transplant hazards as described in the previous paragraphs. However, transition times starting at 6 months from listing were used. Overall projected and actual dropout and transplant probabilities at 6, 12, 18, 24, and 36 months since time of listing were calculated using the multistate models for the 6-month delay, the MELD EQ, and the previous scheme. The variances of these estimates for actual probabilities were obtained using the bootstrap option in the R package mssurv, (13) with 200 iterations, and were used to construct normal 95% confidence intervals (CIs). For projected overall probabilities, 500 bootstrap iterations of the projected estimates were performed and checked graphically for normality. Standard deviations were used to construct normal 95% CIs. Projected posttransplant survival for HCC and non- HCC patients was also calculated under the 6-month delay and the MELD EQ. These projected survival estimates were obtained by calculating the projected proportion of transplants performed in each risk stratum under each scheme. The ratio of the actual proportion TABLE 1. Outcomes at Last Follow-up for HCC and Non- HCC Patients Outcome HCC Non-HCC Censored 1837 (23.2) 16,633 (47.7) Dropout 452 (5.7) 3700 (10.6) Transplanted 5629 (71.0) 13,895 (39.9) Improved 10 (0.1) 640 (1.8) Total ,868 NOTE: All data are given as n (%). to projected proportion for each stratum was then used to weight each individual in the projected Kaplan- Meier survival curve. Standard errors of the Kaplan- Meier curve were calculated based on these weighted subjects. Results ACTUAL AND PROJECTED WAIT-LIST OUTCOMES A total of 7931 patients were listed with HCC exceptions and 34,868 patients with standard MELD scores during the time frame between October 1, 2009 and June 30, Three HCC patients were missing HCC-related covariate data, leaving 7928 for analysis. Table 1 shows the numbers and percentages of HCC and non-hcc patients who were censored, dropped out, received transplant, or improved as of last followup. Compared to non-hcc, HCC patients had a higher percentage of transplantation (71.0% versus 39.9%) and a lower percentage of dropout (5.7% versus 10.6%). Figure 2 displays actual and projected dropout and transplant probabilities for patients stratified by their laboratory MELD ranges during 0-18 months from listing. As expected, the transplant probabilities under previous allocation are similar for HCC patients regardless of MELD score range (solid lines in Fig. 2A). The separation in projected transplant probabilities by dropout risk strata under the 6-month delay is much more distinct compared to the previous allocation, though curves start converging on each other after 6 months (Fig. 2B). There is some differentiation in actual dropout probabilities for HCC patients stratified by laboratory MELD, though not as clear as that for non-hcc patients (Fig. 2C). Dropout probabilities for HCC patients with MELD scores of <22 are projected to increase slightly (solid lines in Fig. 2D versus Fig. 2C) though patients with higher MELD scores are expected to have reduced dropout probabilities. For 1346 ORIGINAL ARTICLE

5 LIVER TRANSPLANTATION, Vol. 22, No. 10, 2016 FIG. 2. Actual and projected time to transplant and dropout for non-hcc and HCC patients stratified by laboratory MELD score (0-18 months). Time is from 0 to 18 months after listing. Solid lines indicate the probability of transplant/ dropout for HCC patients under the previous scheme (A,C) and projected under the 6-month delay in assigning exception points (B,D). Dashed lines indicate the corresponding probability curves for non-hcc patients. The number at risk for HCC patients at baseline and at 6 and 12 months is given in the upper part of panel C. non-hcc patients, dropout probabilities are projected to be slightly reduced for those with MELD scores of >15 (dashed lines in Fig. 2C versus Fig. 2D). Projections under the MELD EQ are very similar to those for the 6-month delay for the first 6 months of listing, as seen by comparing Figs. 2 and 3 for the first 6 months shown. During these first 6 months, the MELD EQ score is equivalent to the laboratory MELD score for 93% of observations. Table 2 shows the similarity of the distributions of the MELD EQ and laboratory MELD for HCC patients at listing. Under the MELD EQ model, projected transplant probabilities are much more defined according to risk strata compared to projections under the 6-month delay (solid lines in Fig. 3B versus Fig. 2B). A slight increase in projected transplant probabilities is seen under this scheme at 6 months, as the MELD EQ assigns 6.85 more points at 6 months after listing. Under the MELD EQ, dropout probabilities for HCC patients are projected to increase for those with scores of <22 and decrease for those with scores of 22 (solid lines in Fig. 3C,D). However, matching between projected dropout probabilities for HCC and non-hcc patients under the MELD EQ is subpar, particularly for the (projected HCC dropout far exceeds non-hcc) and (projected HCC dropout far below non-hcc) ranges. Non-HCC transplant probabilities are projected to increase slightly for all strata under this model (cf. dashed lines in Fig. 3A versus Fig. 3B), whereas non-hcc dropout would decrease slightly for all but the lowest stratum (Fig. 3C versus Fig. 3D). Figure 4 shows actual and projected transplant and dropout probabilities for HCC and non-hcc patients starting at 6 months after listing and going to 18 months. These curves reflect the probability of ORIGINAL ARTICLE 1347

6 LIVER TRANSPLANTATION, October 2016 FIG. 3. Actual and projected time to transplant and dropout for 0 to 18 months after listing for HCC patients stratified by MELD EQ score and non-hcc patients by MELD. Time is from 0 to 18 months after listing. Solid lines indicate the probability of transplant/dropout for HCC patients under the previous scheme (A,C) and projected under the MELD EQ scoring system (B,D). Dashed lines indicate the corresponding probability curves for non-hcc patients. The number at risk for HCC patients at baseline and at 6 and 12 months is given in the upper part of panel C. transplant or dropout for a patient given if the patient is still on the waiting list at 6 months. During this time frame, projected transplant probabilities under the MELD EQ match those for non-hcc patients in corresponding ranges well (Fig. 4B). However, projected dropout probabilities for HCC patients under this scheme exceed the levels for the corresponding non-hcc strata (Fig. 4D). Compared with actual TABLE 2. Frequency Distributions of the MELD EQ and Laboratory MELD Scores for HCC Patients at Initial Listing Score Ranges HCC MELD EQ HCC Laboratory MELD (60.0) 4889 (61.7) (26.2) 2017 (25.4) (12.1) 911 (11.5) (1.6) 102 (1.3) (0.1) 9 (0.1) NOTE: All data are given as n (%) of patients out of 7928 total HCC patients. dropout (Fig. 4C), projected probabilities would again be reduced for HCC patients with MELD EQ scores of 22 but increased for those with scores of <22. For non-hcc patients, projected dropout probabilities are similar to actual for MELD < 16 and reduced for MELD 16 (dashed lines in Fig. 4D versus Fig. 4C). The results displayed in Figs. 2 and 3 are aggregated and summarized in Table 3, which gives overall dropout and transplant probabilities under prior practice and projected for the 6-month delay and the MELD EQ at 6, 12, 18, 24, and 36 months after listing. Overall projected dropout and transplant probabilities for HCC patients under the 6-month delay and MELD EQ are similar at 6 months, but thereafter start to differ. The projected HCC transplant probabilities for the 6- month delay converge to prior actual probabilities starting at 18 months (70.2% versus 81.0%, respectively), whereas the projected transplant under the MELD EQ remains quite low even at 3 years (16.6%) ORIGINAL ARTICLE

7 LIVER TRANSPLANTATION, Vol. 22, No. 10, 2016 FIG. 4. Actual and projected time to transplant and dropout for 6 to 18 months after listing for HCC patients stratified by MELD EQ score and non-hcc patients by MELD. Time is from 6 months until 18 months after listing. The curves reflect the probability, given a patient is still on the waiting list at 6 months, of transplant or dropout under the previous scheme (A,C) and those projected under the MELD EQ scoring system (B,D). Solid lines represent probabilities for HCC patients whereas dashed lines represent those for non-hcc patients. The number at risk for HCC patients at 6, 9, 12, and 15 months is given in the upper part of panel C. In contrast, projected HCC dropout is not dissimilar (based on overlapping 95% CIs) between the 6-month delay and MELD EQ until approximately 24 months. At 3 years, the difference in projected HCC dropout between the 2 systems is most stark (16.0% for MEL- D EQ versus 10.0% for 6-month delay). Conversely, projected dropout and transplant probabilities for non-hcc patients are most favorable under the MELD EQ system, with lower projected overall dropout (12.3% versus 14.1% for the 6-month delay at 3 years) and higher projected transplant probabilities (58.5% versus 54.9% under the 6-month delay at 3 years). This counterbalance results in a wash in total (combined HCC and non-hcc) projected dropout and transplant probabilities for the 2 systems (second and third columns of Table 3C). The MELD EQ results in better equity of total projected dropout between HCC and non-hcc patients until 2 years after listing, but at 3 years the projected dropout for HCC patients under the MELD EQ becomes notably higher. Although currently few HCC patients remain on the waiting list that long, because a large number of HCC candidates are projected to still be on the waiting list at 3 years under the MELD EQ, this would be an important consideration under that scheme. ACTUAL AND PROJECTED POSTTRANSPLANT SURVIVAL A potential limitation of the MELD EQ could be reduced posttransplant survival because it assigns higher priority for larger tumor size, greater number of tumors, and higher AFP. To investigate this, we examined posttransplant mortality using a multivariate Cox proportional hazards model for several ranges of the covariates that comprise the MELD EQ. These covariates and levels were laboratory MELD (stratified into the same ranges described earlier), AFP (0-10, , ORIGINAL ARTICLE 1349

8 LIVER TRANSPLANTATION, October 2016 TABLE 3. Overall Dropout/Transplant Probabilities for HCC and Non-HCC Patients, Actual and Projected With Prioritization Under the 6-Month Delay and MELDEQ Scoring System at 6, 12, 18, 24, and 36 Months Wait-list Time A. HCC Patients Dropout Transplant Actual 6-Month Delay MELDEQ Actual 6-Month Delay MELDEQ 6 months 3.7% (3.3%-4.1%) 4.6% (4.0%-5.2%) 4.5% (4.0%-5.1%) 43.3% (42.2%-44.5%) 8.2% (7.8%-8.6%) 8.5% (8.1%-9.0%) 12 months 5.6% (5.1%-6.2%) 7.7% (6.9%-8.5%) 8.4% (7.5%-9.3%) 66.3% (65.2%-67.4%) 45.9% (44.3%-47.5%) 16.5% (15.8%-17.2%) 18 months 6.4% (5.9%-7.0%) 9.0% (8.1%-9.9%) 10.8% (9.6%-12.0%) 81.0% (79.9%-82.0%) 70.2% (68.5%-71.9%) 21.6% (20.7%-22.5%) 24 months 6.7% (6.1%-7.3%) 9.4% (8.5%-10.3%) 12.2% (10.7%-13.8%) 85.9% (85.0%-86.8%) 78.3% (76.9%-79.8%) 24.0% (23.1%-25.0%) 36 months 7.0% (6.4%-7.7%) 10.0% (9.0%-11.0%) 16.0% (13.2%-18.8%) 89.2% (88.4%-90.0%) 83.8% (82.5%-85.1%) 26.6% (25.5%-27.8%) B. Non-HCC Patients Dropout Transplant Actual 6-Month Delay MELD EQ Actual 6-Month Delay MELD EQ 6 months 7.7% (7.4%-8.0%) 7.0% (6.7%-7.3%) 7.0% (6.8%-7.3%) 36.0% (35.5%-36.5%) 41.2% (40.7%-41.7%) 41.1% (40.6%-41.7%) 12 months 10.2% (9.8%-10.5%) 9.1% (8.8%-9.4%) 8.9% (8.6%-9.2%) 42.7% (42.2%-43.3%) 46.8% (46.3%-47.4%) 49.8% (49.3%-50.3%) 18 months 11.9% (11.5%-12.3%) 10.7% (10.3%-11.1%) 10.2% (9.9%-10.6%) 46.4% (45.8%-47.0%) 50.1% (49.6%-50.7%) 54.5% (54.0%-55.0%) 24 months 13.3% (12.8%-13.7%) 12.0% (11.6%-12.4%) 11.2% (10.8%-11.6%) 48.7% (48.0%-49.4%) 52.2% (51.6%-52.8%) 56.5% (55.9%-57.0%) 36 months 15.5% (15.0%-16.0%) 14.1% (13.6%-14.6%) 12.3% (11.9%-12.7%) 51.6% (50.9%-52.4%) 54.9% (54.3%-55.6%) 58.5% (57.8%-59.1%) C. Total (HCC and non-hcc) Dropout Actual 6-Month Delay MELD EQ 6 months 7.0% (6.6%-7.3%) 6.6% (6.2%-6.9%) 6.6% (6.2%-6.9%) 12 months 9.3% (8.9%-9.7%) 8.9% (8.5%-9.3%) 8.8% (8.4%-9.2%) 18 months 10.9% (10.5%-11.3%) 10.4% (9.9%-10.8%) 10.3% (9.8%-10.8%) 24 months 12.1% (11.6%-12.5%) 11.5% (11.0%-12.0%) 11.4% (10.8%-12.0%) 36 months 14.0% (13.4%-14.5%) 13.3% (12.7%-13.9%) 13.0% (12.1%-13.9%) NOTE: The numbers shown are the estimated probabilties and their 95% CIs ORIGINAL ARTICLE

9 LIVER TRANSPLANTATION, Vol. 22, No. 10, 2016 FIG. 5. Posttransplant survival for HCC patients stratified by AFP ranges. The dashed line is a Kaplan-Meier survival curve for patients with AFP 0-10 ng/ml, the light line is a survival curve for those with AFP ng/ml, and the bold line is a survival curve for those with AFP > 500 ng/ml. The numbers at risk for each group at 0, 1, 2, and 3 years are shown at the bottom of the figure. and >500 ng/ml), number of tumors (2 and >2), and maximum tumor size (<1 and 1 cm). The results of this model were not significant (P 0.07) for any covariate except AFP. For AFP, the hazard ratios for posttransplant mortality compared to the baseline group (AFP, 0-10 ng/ml) were 1.67 (95% CI, ; P < 0.001) and 2.80 (95% CI, ; P < 0.001) for AFP ranges of and >500 ng/ml, respectively. Kaplan-Meier survival curves for these ranges of AFP are displayed in Fig. 5. Additionally, we calculated projected posttransplant survival for HCC and non-hcc patients under the MELD EQ and the 6-month delay (Table 4). For HCC patients, projected posttransplant survival under the 6-month delay is very similar to actual posttransplant survival. Under the MELD EQ, projected posttransplant survival for HCC patients is approximately 1%-2% lower than actual survival at each time point, though this difference is not statistically significant after 2 years. For non-hcc patients and for the combined HCC and non-hcc group, projected survival is very similar under all 3 schemes. The total numbers of organs allocated to HCC patients versus non-hcc patients under each scheme are also displayed in the bottom rows of Table 4A,B. Table 5 shows the overall proportion of organs allocated to each risk stratum (out of the total allocated to HCC patients) under prior practice (actual) and projected under the MELD EQ and 6-month delay. These proportions are relatively similar between actual practice and the 6-month delay. However, the projected proportions under the MELD EQ differ markedly from the other 2 scenarios, with a large reduction in allocation to patients with MELD EQ scores of < 16 and an increase in allocation to scores in the range. Those in the highest MELD EQ stratum (28-40), however, would still be a lower proportion relative to the lowest risk strata (<16) under the MELD EQ. Discussion In this study, we evaluated projections for dropout probabilities, transplant probabilities, and posttransplant survival under the recently implemented 6-month delay for granting exception MELD points to HCC patients and compared these to prioritization based on the MELD EQ. Although the 6-month delay will improve equity of transplant probabilities between HCC and non-hcc patients for the first 6 months on the waiting list, our results show that reverting to scheduled exception point progression after 6 months appears to advantage HCC patients. Additionally, reverting to exception points after 6 months still treats all HCC patients as having the same dropout risk regardless of tumor characteristics or laboratory MELD. Dropout was projected to increase under the delay for HCC patients with MELD scores of <22 but was projected to decrease for both HCC and non-hcc patients with MELD scores of 22. This increase in dropout for lower HCC risk groups is in contrast to the original study describing the derivation of the MELD EQ. (10) In that study, it was projected that patients with MELD EQ scores of 15 would not be adversely affected by the 6-month delay, whereas those with higher scores could be adversely affected in terms of dropout probability. It was noted that the advantage to HCC patients was not universal because dropout probabilities for lower-risk HCC patients (MELD EQ 15) were lower than their non-hcc counterparts, whereas their transplant probabilities were higher. The opposite (higher dropout, lower transplant) was true for patients in higher MELD EQ ORIGINAL ARTICLE 1351

10 LIVER TRANSPLANTATION, October 2016 TABLE 4. Overall Posttransplant Survival, 95% CI and Total Number Transplanted for HCC and Non-HCC Patients, Actual and Projected Under the 6-Month Delay and MELD EQ Scoring System at 1, 2, 3, and 4 Years Following Transplant A. HCC Patients Actual 6-Month Delay MELD EQ 1 year 92.0% (91.2%-92.8%) 91.7% (90.9%-92.5%) 90.2% (89.3%-91.1%) 2 years 85.5% (84.3%-86.7%) 85.3% (84.1%-86.5%) 82.9% (81.7%-84.2%) 3 years 80.9% (79.4%-82.5%) 80.8% (79.3%-82.4%) 79.1% (77.5%-80.7%) 4 years 72.0% (68.8%-75.2%) 71.9% (68.7%-75.2%) 70.0% (66.5%-73.7%) Total number of transplants 5598 (28.9% of total) 2945 (15.1% of total) 973 (5.1% of total) B. Non-HCC Patients Actual 6-Month Delay MELD EQ 1 year 88.4% (87.9%-89.0%) 88.5% (87.9%-89.0%) 88.5% (87.9%-89.1%) 2 years 84.4% (83.7%-85.1%) 84.4% (83.7%-85.1%) 84.5% (83.8%-85.2%) 3 years 80.6% (79.7%-81.5%) 80.6% (79.7%-81.5%) 80.7% (79.8%-81.6%) 4 years 75.7% (74.3%-77.1%) 75.7% (74.3%-77.1%) 75.8% (74.4%-77.2%) Total number of transplants 13,803 (71.1% of total) 16,574 (84.9% of total) 18,196 (94.9% of total) C. Total (HCC and Non-HCC Patients Combined Group) Actual 6-Month Delay MELD EQ 1 year 89.4% (89.0%-89.9%) 88.9% (88.5%-89.4%) 88.6% (88.1%-89.1%) 2 years 84.7% (84.1%-85.3%) 84.5% (83.9%-85.1%) 84.4% (83.8%-85.0%) 3 years 80.7% (80.0%-81.5%) 80.6% (79.9%-81.4%) 80.6% (79.9%-81.4%) 4 years 74.9% (73.6%-76.2%) 75.3% (74.0%-76.5%) 75.6% (74.4%-76.8%) Total number of transplants* 19,401 19,519 19,169 *Total projected transplants under each scheme are through 4.3 years wait-list time. The projection method requires using event times common to both HCC and non-hcc groups, so projected totals will not have an exact match with actual totals. Actual posttransplant survival could not be calculated for 31 HCC patients and 92 non-hcc patients due to missing follow-up times. ranges. Although this appears to still be the case for transplant probabilities, dropout for most HCC groups in the current study appears to be lower than in the original MELD EQ study. Overall HCC dropout probabilities in our study were found to be 3.7% at 6 months and 5.6% at 12 months, whereas in the earlier study they were 4.7% at 6 months and 7.2% at 12 months. (10) Although we found that dropout probabilities would increase somewhat for HCC patients under both the 6-month delay and the MELD EQ, the magnitude of this increase was much smaller than that of the projected decrease in HCC transplant probabilities. This was particularly evident under the MELD EQ.Results from Heimbach et al. (12) also suggested that increased mortality rates may not accompany decreased transplant rates for HCC patients. Other investigators have looked at the balance between waiting time, wait-list dropout, posttransplant survival, and equity of transplant rates, and they found that increased waiting time was TABLE 5. Proportions of Transplanted Organs to Each Risk Stratum, Actual and Projected Under the 6-Month Delay and MELD EQ Scoring System HCC MELD/MELD EQ Range Percent of Total HCC Transplantation, Actual Percent of Total HCC Transplantation, Projected for 6-Month Delay Percent of Total HCC Transplantation, Projected for MELD EQ < % 49.9% 13.1% % 26.1% 15.7% % 17.3% 37.4% % 5.4% 24.2% % 1.4% 9.5% NOTE: The risk stratum displayed is at the last follow-up prior to transplant. The strata reflect MELD scores for projections under the 6-month delay and MELD EQ scores for actual and projected under MELD EQ ORIGINAL ARTICLE

11 LIVER TRANSPLANTATION, Vol. 22, No. 10, 2016 associated with either improved overall survival (while on the waiting list and after transplant) or posttransplant survival. (16-18) However, Roayaie and Roayaie point out that although increased waiting time was associated with longer posttransplant survival, waiting too long begins to remove patients who would have done well after transplant. (19) Given that our projections indicate only 27% of HCC patients being transplanted at 3 years under the MELD EQ, this is a concern for prioritization under that scheme. A related limitation of our study is that actual dropout rates for HCC patients in the UNOS data may not be representative of those rates in other populations. Investigators using data from sources other than UNOS have reported HCC dropout percentages ranging from 7.8% to 20% at varying wait-list times. (6,8,9,18) The observed HCC dropout percentage in our study was only 7.0% at 3 years, at the low end of the spectrum. To further address this concern, we performed a sensitivity analysis to simulate a possible worst-case scenario for HCC patients when delaying their transplant. Here, the dropout hazard for HCC patients in each risk strata was doubled relative to their actual HCC dropout hazard starting at 6 months. Our simulations under this scenario (see Supporting Table) indicated the MELD EQ performed poorly (25.6% dropout for HCC patients at 3 years), whereas the 6- month delay remained fairly robust (only 14.9% dropout for HCC patients at the same time). Another potential concern with prioritization schemes based on HCC characteristics is that those highest risk patients who are assigned higher priority could also be those with worse posttransplant survival. In our projections, HCC posttransplant survival under the MELD EQ was slightly worse than actual though this difference was not statistically significant after 2 years. Because we did find that posttransplant survival was significantly worse for those with higher AFP, perhaps a cap on points for patients with extremely elevated AFP (eg, at an AFP of 500 ng/ml) is warranted. However, only 2.5% of transplanted HCC patients had an AFP above 500 ng/ml. The MELD EQ does not match corresponding non- HCC MELD risk score categories well when considering time from initial listing, particularly for the highest MELD EQ category (28-40, cf. Fig. 3). We investigated the 9 patients in this category at listing and found that nearly all of them (8/9) had MELD EQ 5 MELD at listing (eg, laboratory MELD was equal to or higher than MELD EQ ). For the majority of these patients (6/9), their final wait-list MELD score was at least 10 points lower than their initial MELD (with no change or improvement in tumor characteristics or AFP levels), suggesting that initial wait-list MELD was either incorrect or unusually high. This could explain the low dropout probability observed for these patients (4 underwent transplantation, 2 died, and 3 were still on the waiting list at last follow-up). Another aspect is that the projections for Fig. 3 used time from listing as time zero, whereas the projections in the original MELD EQ article used time from entering a given risk strata as time zero. The reason for this change was to enable comparisons with the 6-month delay. Because the MELD EQ assigns more points once a patient has been on the waiting list for 6 months, it is likely that some of the higher risk patients identified in the earlier study had already been on the list for 6 months or more. In fact, the noted low dropout probability for the MELD EQ group disappears when considering time from 6 months onward on the waiting list (cf. Fig. 4). Here the MELD EQ strata have much more sensible alignment with the MELD strata, although the projected HCC dropout exceeds the target non-hcc levels. Predicting wait-list dropout is inherently more difficult among HCC patients compared to other patients awaiting LTs. The MELD EQ has a lower predictive accuracy compared to the chemical MELD score in non-hcc patients even in the original derivation sample. (10) This underlying disease progression that is difficult to characterize with tumor characteristics alone is reflected in the difference between the underlying dropout hazards for HCC and non-hcc patients (HCC patients have a steeper dropout hazard compared to non-hcc patients in our experience, data not shown). We approximated this difference in the original MELD EQ derivation by a jump in score of 6 points at 6 months. There may be a bigger difference that needs to be modeled by a bigger jump in points at, eg, 2 and 3 years, and this is reflected in the projected low transplant rates for HCC patients under the MELD EQ at these times. However, this is difficult to estimate with current data given the low numbers of HCC patients on the waiting list at later time points (only 90 HCC patients on the waiting list at 3 years in this current study, from a starting cohort of 7928 patients). Some of this difference in underlying hazard rate might be related to local tumor recurrence (eg, after ablative therapy) of HCC patients. Currently, all tumors are scored the same way in the MELD EQ regardless of whether it is a local recurrence or not, and this is a noted limitation. In fact, to our knowledge ORIGINAL ARTICLE 1353

12 LIVER TRANSPLANTATION, October 2016 none of the other previously developed HCC risk scores (7-9) make this differentiation either. Any future reformulation of an HCC risk score would need to consider this as a potential risk factor. One of the central assumptions for our projections is that of exchangeability (see description in Supporting Text). That is, conditional on the same set of tumor characteristics, MELD score, and AFP, an HCC patient who was transplanted at a given time is exchangeable with one that is still on the waiting list. Although there is justification for this assumption conditional on risk score and based on how HCC patients were previously prioritized, other factors unaccounted for in the model (eg, physician assessment of patient severity of illness) might cast this assumption into doubt. Strengths of our study include that we examined projected dropout, transplant, and posttransplant survival of the 6-month delay and the MELD EQ and that we studied these effects among different HCC dropout risk strata. Although equalizing HCC and non-hcc dropout and transplant probabilities overall is the primary goal, part of this objective is to prioritize those patients who most urgently need and can benefit the most from transplantation. Studying outcomes for each stratum based on a score using HCC characteristics can help identify those patients and help to further calibrate HCC-based scores. Taking all the data into consideration (projected wait-list dropout, transplant, and posttransplant survival), our projections currently support the 6-month delay as a better overall choice for prioritizing HCC patients than the MELD EQ. Although overall (combined HCC and non-hcc) wait-list dropout was similar under both schemes, projected longterm transplant probabilities for HCC patients were substantially lower under the MELD EQ (26.6% at 3 years) compared to the 6- month delay (83.8% at 3 years). This translated eventually into a more favorable wait-list dropout for non- HCC patients under the MELD EQ (16.0% projected dropout for HCC versus 12.3% for non-hcc at 3 years). Using the MELD EQ is also projected to decrease posttransplant survival for HCC patients by 1 to 2 percentage points compared to the 6-month delay. However, reverting to the current exception point progression after the 6-month delay is projected to still favor HCC patients (10.0% projected dropout at 3 years for HCC patients versus 14.1% for non-hcc). 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