development and validation of a model predicting graft survival after liver transplantation

ORIGINAL ARTICLE

Development and Validation of a ModelPredicting Graft Survival After LiverTransplantationGeorge N. IoannouDivision of Gastroenterology, Department of Medicine, Hepatitis C Resource Center, Health ServicesResearch and Development, and Research Enhancement Award Program, Veterans Affairs Puget SoundHealth Care System, Seattle, WA, and Division of Gastroenterology, Department of Medicine, University ofWashington, Seattle, WA

This study aimed to develop and validate a comprehensive model that predicts survival after liver transplantation based onpretransplant donor and recipient characteristics. Complete data were available from the United Network for Organ Sharing for20,301 persons who underwent liver transplantation in the United States between 1994 and 2003. Proportional-hazardsregression was used to identify the donor and recipient characteristics that best predicted survival and incorporate thesecharacteristics in a multivariate model. A data-splitting approach was used to compare survival predicted by the model to theobserved survival in samples not used in the derivation of the model. A model was derived using 4 donor characteristics (age,cold ischemia time, gender, and race/ethnicity) and 9 recipient characteristics (age, body mass index, model for end-stage liverdisease score, United Network for Organ Sharing priority status, gender, race/ethnicity, diabetes mellitus, cause of liverdisease, and serum albumin) that adequately predicted survival after liver transplantation in patients without hepatitis C virus,and a slightly different model was used for patients with hepatitis C virus. The models illustrate that variations in bothpretransplant donor and recipient characteristics have a large effect on posttransplant survival. In conclusion, the modelspresented here can be used to derive scores that are proportional to the excess risk of graft loss after liver transplantation forpotential donors, recipients, or donor/recipient combinations. The models may be used to inform liver transplant candidates andtheir doctors what posttransplant survival would be expected when a given donor is offered and may be particularly helpful formarginal or high-risk donors. Liver Transpl 12:1594-1606, 2006. © 2006 AASLD.

Received August 29, 2005; accepted February 2, 2006.

See Editorial on 574

One of the main limitations of liver transplantation astreatment of end-stage liver disease is the scarce supplyof liver donors relative to the number of patients in needof liver transplantation.1 According to the United Net-work for Organ Sharing (UNOS), 6,168 liver transplantswere performed in the United States in 2004, and

17,895 patients are currently waiting for liver trans-plantation. This imbalance between supply and de-mand is likely to get even worse, since the number oftransplants per year has remained relatively stable inthe United States in recent years, whereas the numberof patients on the waiting list has been increasing dra-matically.2

One way to increase the availability of organs for livertransplantation is to expand the criteria that are used

Abbreviations: UNOS, United Network for Organ Sharing; HCV, hepatitis C virus; MELD, model for end-stage liver disease; BMI, bodymass index; SOLD, score of liver donor.Supported by the American College of Gastroenterology, Junior Faculty Development Award, Veterans Affairs Northwest Hepatitis CResource Center, and Veterans Affairs Puget Sound Health Care System Research Enhancement Award Program. Supported in partby Health Resources and Services Administration contract 231-00-0115.This research was based on data derived from the United Network for Organ Sharing on October 6, 2003. The content is theresponsibility of the author alone and does not necessarily reflect the views or policies of the Department of Health and HumanServices.Address reprint requests to George Ioannou, MD, MS, Veterans Affairs Puget Sound Health Care System, Gastroenterology, S-111-Gastro, 1660S. Columbian Way, Seattle, WA 98108. Telephone: 206-277-3136; FAX: 206-764-2232; E-mail [email protected]

DOI 10.1002/lt.20764Published online in Wiley InterScience (www.interscience.wiley.com).

LIVER TRANSPLANTATION 12:1594-1606, 2006

© 2006 American Association for the Study of Liver Diseases.

to determine whether an organ from a potential liverdonor is acceptable for liver transplantation. Unfortu-nately, no such universally accepted criteria exist. In-stead, individual transplant programs use different,and often poorly defined, criteria to determine whetherto use the liver of a potential liver donor for transplan-tation. Such criteria include donor age, donor high-riskbehavior, the degree of steatosis on liver biopsy, coldischemia time, “down time,” and the macroscopic ap-pearance of the liver.

In addition to donor characteristics, many recipientcharacteristics are important predictors of posttrans-plant survival. The aim of this study was to identifydonor and recipient characteristics that are importantpredictors of graft survival following liver transplanta-tion and to use these predictors to develop and validatea survival model using data from UNOS. Such a modelcould determine risk scores based on donor, or recipi-ent, or donor/recipient characteristics that would bedirectly related to expected posttransplant survival.These risk scores may be used together with data on theexpected mortality on the transplant waiting list, todetermine whether or not a liver should be used fortransplantation, or to form the basis for future discus-sions on “expanding” donor criteria to try to address theimbalance between supply and demand in liver trans-plantation. In addition, donor/recipient scores may beused by physicians to stratify liver transplantationsinto “high risk” (lower graft survival and higher risk ofposttransplant complications) and “low risk” (highergraft survival and lower risk of posttransplant compli-cations). Finally, these risk scores may be used in thefuture to inform liver transplant candidates and theirdoctors what posttransplant survival would be ex-pected when a given donor is offered and may be par-ticularly helpful for marginal or high-risk donors

PATIENTS AND METHODS

Data Collection

Transplant centers and organ procurement organiza-tions in the United States are required to submit toUNOS3 standardized data collection forms, includingthe Transplant Candidate Registration Form, whichcontains patient information at the time of listing forliver transplantation; the Deceased Donor RegistrationForm, which contains information on all consented re-covered and nonrecovered donors; the Transplant Re-cipient Registration Form, which includes the patientstatus at discharge, pretransplant and posttransplantclinical information, and treatment data; and theTransplant Recipient Follow-up Form, which is gener-ated 6 months posttransplant and on each subsequenttransplant anniversary and includes patient status andclinical and treatment information. These forms arecurrently submitted to UNOS electronically, and theinformation is entered into a single Standard Trans-plant Analysis and Research file, which includes 1record per transplant event and the most recent fol-low-up information on patient status as of the date that

the file was created. The Standard Transplant Analysisand Research file created by UNOS on October 6, 2003,was kindly provided to the author for this study.

Patient Population

Data were available from UNOS for 52,845 patientsaged � 18 years who underwent orthotopic liver trans-plantation in the Unites States between 1987 and 2003.The analysis was limited to 38,811 liver transplanta-tions that occurred after April 1, 1994, because poten-tially important variables such as donor alcohol use,donor weight, recipient diabetes status, and cold isch-emia time were not routinely recorded prior to that date.We excluded patients who had donors under 10 (n �519) or over 75 (n � 508) years of age, living donors (n �1,249), split-liver donors (n � 564), non-heart-beatingdonors (n � 328), or donors with a serum sodium con-centration �170 mmol/L (n � 591). We excluded pa-tients with multiple simultaneous organ transplanta-tion (n � 1,171), previous liver transplantation (n �3,219), or no available follow-up records after trans-plant (n � 658), leaving 30,004 participants in the uni-variate analyses. In addition, 9,703 patients were ex-cluded from the multivariate analyses becauseinformation was missing on 1 or more of the covariatesleaving 20,301 in the current analysis including 6,477with hepatitis C viral (HCV) infection.

Survival Modeling

Cox proportional hazards regression was used to modelgraft survival after liver transplantation using a num-ber of prognostic variables.4 Graft failure was definedas liver failure (with or without retransplantation) orpatient death from any cause. The variable for graftfailure as defined above (“gstatus”) is provided in theUNOS Standard Transplant Analysis and Research file.Time was measured from the date of liver transplanta-tion to the date of liver failure, death, or last follow-up(variable “gtime” in the UNOS Standard TransplantAnalysis and Research file). Patients who remainedalive without liver failure were censored at the time theywere last traced alive.

Univariate survival analyses were initially performedto identify donor and recipient characteristics that weresignificant predictors of survival at a P � 0.05 level fromthe following list of a priori chosen potential predictors.

a. Donor characteristics: body mass index (calculatedas the weight in kilograms divided by the square ofthe height in meters) categorized as 15 to �25, 25 to�30, 30 to �35, 35 to �40, and 40 to �55 kg/m2;age; cold ischemia time; presence of diabetes melli-tus or hypertension; history of alcohol dependency,race/ethnicity (categorized as white, black and Afri-can American, Hispanic, and other); gender; ciga-rette use (�20 pack years ever or not); degree ofsteatosis on liver biopsy (categorized as 0-19%, 20-35%, and �35%); laboratory values immediatelyprior to organ donation, including serum creatinine,

SURVIVAL MODEL FOR LIVER TRANSPLANTATION 1595

LIVER TRANSPLANTATION.DOI 10.1002/lt. Published on behalf of the American Association for the Study of Liver Diseases

aspartate aminotransferase, alanine aminotransfer-ase, and total bilirubin; and intravenous or otherdrug use in the 6 months prior to organ donation.

b. Recipient characteristics: UNOS urgency status(categorized as status 1 [fulminant hepatic failure,or immediate hepatic artery thrombosis or graft non-function after liver transplantation] or other); modelfor end-stage liver disease (MELD) score at the timeof transplantation calculated using the formulaMELD � [(0.957 � ln(creatinine) � 0.378 � ln(bil-irubin) � 1.120 � ln(international normalized ra-tio) � 0.6] � 10,5,6 where the international normal-ized ratio was approximated as the prothrombintime/12.5 when not available; serum albumin at thetime of transplantation; liver disease (categorized ashepatitis C [� hepatitis B], hepatitis B, alcoholiccirrhosis, primary biliary cirrhosis, cryptogenic cir-rhosis, hepatocellular carcinoma or cholangiocarci-noma, and other); gender; race/ethnicity (catego-rized in the same way as for donors); body massindex (at the time of liver transplantation, catego-rized in the same way as for donors), diabetes mel-litus, and time period of liver transplantation (cate-gorized into 4 periods from 1994 to 2003 each with aquarter of the total number of transplantations).

Modeling of Predictors

All categorical variables were modeled as dummy vari-ables. For continuous variables we considered stan-dard transformations (logarithmic, square, square root)as well as categorization into 5 categories based on thevalues of the 25th, 50th, 75th, and 90th centiles. Thelikelihood ratio test was used to determine which rep-resentation best predicted survival.

Selection of Predictors for Multivariate Model

To pick a small subset of donor and recipient charac-teristics that adequately predicted survival, we usedboth forward stepwise and backward elimination selec-tion methods. Specifically, all characteristics that weresignificant (P � 0.05) in univariate analyses were en-tered into a multivariate model. We then eliminatedfrom the model all donor variables that were not statis-tically significant in the multivariate analysis. Each ofthe eliminated variables was then individually added tothe model of the significant variables and was kept if itwas statistically significant or if its inclusion affectedthe value of the coefficients of other variables by morethan 20%.

Region of Transplantation

Transplant centers and organ procurement organiza-tions in the United States belong to 1 of 11 geographicaltransplant regions. Because transplant survival mayvary by region, all multivariate analyses were stratifiedon geographical region. Stratifying by region yieldsequal coefficients for each predictor across regions butwith baseline hazard unique to each region. Informa-

tion on the center or hospital at which transplantationwas performed is not available.

Etiology of Liver Disease

Preliminary analyses suggested that there were largedifferences in the models derived for patients with HCVinfection compared to patients without HCV infectionand that a single model could not adequately predictsurvival in both groups. Hence, models were derivedseparately for persons with and without HCV.

Model Validation

A data-splitting approach was used in which the data-set was randomly divided into 10 equal model valida-tion groups, each containing 10% of the population.7

For each group, a model predicting survival was fit tothe remaining 90% of the population (the model-build-ing group) using the process described above. Thismodel was then used to predict survival in the 10% ofthe population not involved in the derivation of themodel. The Cox proportional hazards model takes thefollowing standard form:

S(t,X) � S0(t)exp(aX1 � bX2 � ..zXn), where S (t,X) is thepredicted survival at time t of a person with values X1 toXn for each of “n” predictors of survival, and S0(t) is the“baseline” survival at time t in persons who have “base-line” (that is, zero) values for each predictor. The sum(aX1 � bX2 � ..zXn) is also known as the risk score.Risk scores were calculated using models derived fromthe model building groups for each person in the modelvalidation group. Persons were divided into 3 non-over-lapping risk score groups using the values correspond-ing to the 33rd and 66th centile. For each group themean risk score was calculated and then used to cal-culate the predicted survival using the formula above.The observed survival for each group was computedusing the Kaplan-Meier method. Observed and pre-dicted survivals were compared graphically.

RESULTS

The donor and recipient characteristics of the patientsincluded in or excluded from the current analysis areshown in Table 1. Liver transplantations excluded fromthe current analysis because of missing data had verysimilar characteristics except for a longer mean cold isch-emia time, a higher proportion of status 1 patients, and aslightly different geographical regional distribution.

Predictors of Survival After LiverTransplantation in Patients Without HCVInfection

The following donor characteristics were significantpredictors of graft survival in univariate analyses: age,cold ischemia time, diabetes mellitus, history of alcoholdependence, gender, race/ethnicity, terminal serumaspartate aminotransferase, alanine aminotransferase,total bilirubin, and creatinine. All recipient character-istics described in the Patients and Methods section

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were significant in univariate analyses. In a multivari-ate model that included only the donor and recipientcharacteristics significant in univariate analyses, allrecipient variables were significant except gender andperiod of transplantation as well as the following donorvariables: age, cold ischemia time, gender, and race/ethnicity. The multivariate model was then limited tothese variables, all of which remained significant. Ad-ditional variables were individually added to this model,none of which was significant. However, addition ofrecipient gender did modify substantially the values ofthe coefficients of other predictors, hence this was in-

cluded in the final model. For the continuous variables,survival was best predicted (as demonstrated by thelikelihood ratio test) with categorization of cold isch-emia time, recipient age and recipient albumin, linearMELD score and squaring of donor age. Thus, for pa-tients without HCV the variables retained in the finalmultivariate model included 4 donor characteristics(age, cold ischemia time, gender, and race/ethnicity)and nine recipient characteristics (age, body mass in-dex [BMI], MELD score, status at time of transplanta-tion, gender, race/ethnicity, diabetes mellitus, cause ofliver disease, and serum albumin) (Table 2).

TABLE 1. Donor and Recipient Characteristics of the Liver Transplants Presented According to Whether the

Patients Were Included or Excluded From Analysis Due to Missing Data

Liver Transplants

Included in the Analysis

(n � 20,301)

Liver Transplants Excluded

From Analysis Because of

Missing Data in at Least

One Predictor

(n � 9,703)

Donor CharacteristicsAge, years, mean (SD) 38 (17) 38 (17)Cold ischemia time, hours, mean (SD) 8.6 (4.1) 9.2 (4.5)Race/ethnicity (%)

White 77% 75%Black and African American 11% 12%Hispanic 10% 10%Other (mostly Asian) 2% 3%

Male (%) 60% 61%

Recipient CharacteristicsBMI at transplant, kg/m2, mean (SD) 28 (5.6) 28 (5.8)Age, years, mean (SD) 50 (10) 50 (11)UNOS urgency status 1 (%) 7.5% 10%Male (%) 64% 62%Race/ethnicity (%)

White 76% 76%Black and African American 7% 8%Hispanic 11% 10%Other (mostly Asian) 5% 6%

Recipient diabetes (%) 17% 17%MELD* score, mean (SD] 16.5 (7.8) 17.1 (8.1)Albumin, g/dL, mean (SD) 2.9 (0.7) 2.9 (0.8)Recipient liver disease (%)

Hepatitis C (or hepatitis C and B) 32% 30%Hepatitis B 5% 5%Alcoholic cirrhosis 22% 20%Primary biliary cirrhosis 6% 6%Cryptogenic cirrhosis 9% 11%Hepatocellular carcinoma or

cholangiocarcinoma4% 3%

Other 22% 25%Region of transplantation† A � 14.5%, B � 8.6%,

C � 3.6%, D � 14.4%,E � 10.5%, F � 11.8%,G � 8.8%, H � 3.8%,I � 5.6%, J � 8.5%,K � 10.0%

A � 16.0%, B � 10.0%,C � 3.5%, D � 14.9%,E � 6.9%, F � 15.3%,G � 5.0%, H � 3.1%,I � 10.0%, J � 7.7%,K � 7.7%

*MELD score values range 6-40.†The 11 UNOS transplant regions were randomly assigned the letters A-K.



TABLE 2. Adjusted Hazard Ratios and Regression Coefficients for the Predictors Included in the Multivariate Model

for Patients Without HCV

Patients

(n)

Person

Years

(n)

Graft

Failure*

(n)

Incidence

of Graft

Failure

Per

Hundred

Person

years

Hazard

Ratio

Adjusted

Hazard

Ratio†

Adjusted

Regression

Coefficient†

P Value for

Multivariate

Analysis

Total 13,824 41,764 3,449 8.3 N/A N/A N/A N/ADonor CharacteristicsAge (years)Age2 � 1,444‡ N/A N/A N/A N/A 1.000151 1.000147 0.000147 �0.001

Cold ischemia time(hours)

0 to �6.4 3,912 10,609 818 7.7 1 1 0 N/A6.4 to �8.8 4,079 12,084 987 8.2 1.11 1.10 0.09 0.058.8 to �11.3 3,447 11,195 903 8.1 1.13 1.11 0.10 0.0311.3 to �14.3 1,677 5,605 502 9.0 1.28 1.24 0.22 �0.00114.3 to �60 709 2,271 239 10.5 1.47 1.51 0.41 �0.001

Race/ethnicityWhite 10,764 33,103 2,636 8.0 1 1 0 N/ABlack and African

American1,449 4,158 406 9.8 1.20 1.26 0.23 �0.001

Hispanic 1,299 3,727 318 8.5 1.05 1.19 0.17 0.03Other (mostly Asian) 312 776 89 11.5 1.33 1.45 0.37 0.001

GenderMale 8,229 25,471 1,962 7.7 1 1 0 N/AFemale 5,595 16,293 1,487 9.1 1.16 1.12 0.11 0.002

Recipientcharacteristics

BMI category (kg/m2)at transplant

15 to �25 5,244 16,474 1,363 8.3 1 1 0 N/A25 to �30 4,632 14,185 1,126 7.9 0.95 0.91 �0.10 0.0230 to �35 2,524 7,058 596 8.4 0.97 0.89 �0.12 0.0335 to �40 1,016 2,953 234 7.9 0.93 0.84 �0.17 0.0240 to �55 408 1,093 130 11.9 1.37 1.30 0.26 0.005

Age category (years)18 to �43 2,956 9,907 748 7.5 1 1 0 N/A43 to �50 3,149 9,972 750 7.5 0.97 0.98 �0.02 0.850 to �57 3,449 9,929 824 8.3 1.03 1.03 0.03 0.657 to �63 2,495 7,116 632 8.9 1.10 1.11 0.10 0.08�63 1,775 4,840 495 10.2 1.24 1.24 0.21 0.001

UNOS urgency statusNot 1 12,495 37,204 2,989 8.0 1 1 0 N/A1 1,329 4,560 460 10.1 1.36 1.18 0.17 0.008

GenderMale 8,548 24,721 2,198 8.9 1 1 0 N/AFemale 5,276 17,043 1,251 7.3 0.87 0.95 �0.06 0.09


American931 2,652 265 10.0 1.18 1.13 0.12 0.03

Hispanic 1,472 4,353 331 7.6 0.91 0.89 �0.12 0.007Other (mostly Asian) 734 2,046 146 7.1 0.83 0.78 �0.25 0.002

Recipient diabetesNo 11,537 35,819 2,809 7.8 1 1 0 N/AYes 2,287 5,945 640 10.8 1.27 1.27 0.24 �0.001

MELD score N/AMELD score � 14§ N/A N/A N/A N/A 1.0191 1.0178 0.0176 �0.001

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Predictors of Survival After LiverTransplantation in HCV-infected Patients

A similar sequential process to that described aboveresulted in a final multivariate model for patientswith HCV that included 4 donor characteristics (age, coldischemia time, gender, and race/ethnicity) and 7 reci-pient characteristics (age, BMI, MELD score, status attime of transplantation, gender, race/ethnicity, and dia-betes mellitus) (Table 3). This model was different fromthe model in patients without HCV in that albumin andcause of liver disease were not included and MELD scorewas coded as a categorical rather than continuous vari-able.

Model Validation

Figures 1 and 2 compare predicted survival to the sur-vival observed in groups not used in the derivation ofthe prediction models. There is good agreement be-tween predicted and observed survival in both HCV andnon-HCV patients. Almost identical variables were se-lected in each of these prediction models that used 90%of the dataset, as for the models shown in Tables 1 and2 that used 100% of the dataset.

The Impact of Donor and RecipientCharacteristics on Predicted PosttransplantSurvival

Tables 4 and 5 show the predicted survival at varioustimes after transplantation for selected donor and re-

TABLE 2. (Continued)

Patients

(n)

Person

Years

(n)

Graft

Failure*

(n)

Incidence

of Graft

Failure

Per

Hundred

Person

years

Hazard

Ratio

Adjusted

Hazard

Ratio†

Adjusted

Regression

Coefficient†

P Value for

Multivariate

Analysis

Albumin�3.3 3,387 10,451 756 7.2 1 1 0 N/A2.8 to �3.3 3,801 11,623 914 7.9 1.08 1.02 0.02 0.62.4 to �2.8 3,894 12,014 984 8.2 1.13 1.03 0.03 0.52.1 to �2.4 1,127 3,176 322 10.1 1.34 1.21 0.19 0.003�2.1 1,615 4,500 473 10.5 1.39 1.25 0.22 �0.001

Recipient liver diseaseAlcoholic cirrhosis 4,500 13,460 1,210 9.0 1 1 0 N/AHepatitis B 988 2,996 222 7.4 0.83 0.78 �0.24 0.002Primary biliary

cirrhosis1,180 4,252 236 5.6 0.66 0.69 �0.37 �0.001

Cryptogenic cirrhosis 1,915 6,137 476 7.8 0.89 0.84 �0.17 0.005Other 4,394 13,475 1,078 8.0 0.91 0.88 �0.13 0.003Hepatocellular

carcinoma orcholangiocarcinoma

847 1,444 227 15.7 1.37 1.43 0.35 �0.001

Abbreviation: N/A, not applicable.*Graft failure was defined as liver failure (with or without retransplantation) or patient death from any cause†Adjusted using Cox proportional hazards regression for all the variables shown in the Table and stratified on the 11geographical UNOS transplantation regions.‡Donor age was squared, then 1,444 (the median square value) was subtracted.§The MELD score was calculated with values of 6 to 40, then 14 (the median MELD score) was subtracted.

Figure 1. Comparison of predicted survival (solid lines) toobserved survival (dotted lines) after liver transplantationamong patients without HCV divided into 3 nonoverlappingrisk groups, using risk score cutoffs of 0.05 (corresponding tothe 33rd centile) and 0.40 (corresponding to the 66th centile).Observed survival was calculated using the Kaplan-Meiermethod. Predicted survival was based on 10 Cox proportionalhazards models each developed using a random selection of90% of the population and used to predict the survival in theremaining 10% of the population.



cipient characteristics. Results are presented sepa-rately for persons without HCV (Table 4) and with HCV(Table 5). A risk score can be calculated for each donor/recipient by adding the adjusted regression coefficientsfor each donor and recipient characteristic shown inTables 2 and 3. The hazard ratio for a donor/recipient Xrelative to the baseline donor/recipient can then becalculated using Hazard Ratio(X) � exp(Risk Score[X]).Survival at time t after transplant for a donor/recipientX can be calculated using:

S(t,X) � S0(t)(hazard ratio[X])

where Survival0(t), the survival of the baseline group atvarious times (t), is shown in the first columns of Tables4 and 5.

Tables 4 and 5 demonstrate that both donor and recip-ient characteristics have a very large impact on predictedsurvival. For example, among patients without HCV, the5-year survival of the average recipient with the averagedonor is 76%. However, when a “high-risk” recipient(MELD � 24, albumin �2.1) receives an average donorliver, the predicted 5-year survival is only 51%; and whenthe same “high-risk” recipient receives a “high-risk” donorliver (age � 60 years, cold ischemia time � 14.3 hours)then the predicted 5-year survival is down to 28%.

Calculation of a Score for Liver Donor

The model can be used to calculate the contribution tothe risk score of the 4 donor characteristics included inthe survival models. This part of the risk score, whichmay be called a score of liver donor (SOLD), is directlyrelated to the impact of the donor on posttransplantsurvival, such that the higher the SOLD the lower thesurvival. The score of liver donor for patients withoutHCV can be calculated as:

SOLD � 0.000147 � (age2�1444)

� (coefficient for cold ischemia time)

� (coefficient for race ethnicity)

� (coefficient for gender)

where the “coefficients” are the adjusted regression co-efficients shown in Table 2 for each category of coldischemia time, race/ethnicity, and gender. For in-stance, a 45-year-old white female donor with 8 hoursof cold ischemia would have the following score:SOLD � 0.000147 � (452 � 1444) � 0.09 � 0 � 0.11 �0.29. Similarly the SOLD for patients with HCV can becalculated from the coefficients in Table 3.

Prediction Models Without Cold IschemiaTime

Measurement of cold ischemia time is not possible be-fore the transplantation operation has begun. There-fore, for the purposes of predicting survival before thedonation process is initiated, we have developed modelsthat use the same predictors as the models above ex-cept cold ischemia time. The adjusted regression coef-ficients and baseline survival for these models areshown in the Table 6. Survival predicted using thesemodels showed excellent agreement with survival ob-served in groups not used in the derivation of the mod-els when compared graphically (graphs available fromauthor upon request).

DISCUSSION

In this paper, models have been developed separatelyfor patients with and without HCV that predict survivalafter liver transplantation based on a small number ofdonor and recipient characteristics available at the timeof liver transplantation. These models can be used todetermine risk scores for a given donor, recipient, ordonor/recipient combination that are directly related tosurvival after liver transplantation.

Whereas a large number of studies have evaluatedthe effect of selected donor and recipient characteristicson posttransplant survival,8-19 relatively few studiesattempted to develop comprehensive models for pre-dicting posttransplant survival, 20-23 none of which val-idated their models. Three of these models are based onsingle-center experiences and lack the large numbersnecessary to simultaneously model a large number ofcharacteristics in sufficient detail, as well as possiblylacking applicability to the entire United States trans-plant experience.20-22 The fourth is an important studythat also used UNOS data to develop models of post-transplant survival.23 However, that study was basedon much older data (1990-1996), all of the predictorswere available for only 2 years (1994-1996), and, mostimportantly, the presented models were not validated.In addition, the MELD score, which is now known to bean important predictor of posttransplant survival,15

was not used as predictor, whereas other characteris-

Figure 2. Comparison of predicted survival (solid lines) toobserved survival (dotted lines) after liver transplantationamong patients with HCV divided into 3 nonoverlapping riskgroups, using risk score cutoffs of 0 (corresponding to the33rd centile) and 0.30 (corresponding to the 66th centile).Observed survival was calculated using the Kaplan-Meiermethod. Predicted survival was based on 10 Cox proportionalhazards models each developed using a random selection of90% of the population and used to predict the survival in theremaining 10% of the population.

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TABLE 3. The Adjusted Hazard Ratios and Regression Coefficients for the Predictors Included in the Multivariate

Model for Patients With HCV

Patients

(n)

Person

Years

(n)

Graft

Failure*

(n)

Incidence of

Graft

Failure Per

Hundred

Person

Years

Hazard

Ratio

Adjusted

Hazard

Ratio†

Adjusted

Regression

Coefficient†

P Value for

Multivariate

Analysis

Total 6,477 16,338 1,790 11.0 N/A N/A N/A N/ADonor CharacteristicsAge (years)Age2 � 1,444‡ N/A N/A N/A N/A 1.000183 1.000175 0.000175 �0.001Cold ischemia time (hours)

0 to �6.4 1,868 4,115 437 10.6 1 1 0 N/A6.4 to �8.8 1,965 4,899 500 10.2 1.01 1.01 0.01 0.88.8 to �11.3 1,590 4,193 487 11.6 1.17 1.17 0.16 0.0211.3 to �14.3 718 2,155 255 11.8 1.24 1.26 0.23 0.00614.3 to �60 336 977 111 11.4 1.18 1.19 0.17 0.1


American781 1,857 201 10.8 0.97 1.02 0.02 0.9

Hispanic 683 1,624 176 10.8 0.97 1.05 0.05 0.7Other (mostly Asian) 153 344 42 12.2 1.07 1.11 0.11 0.6

GenderMale 3,955 10,243 1,033 10.1 1 1 0 N/AFemale 2,522 6,096 757 12.4 1.21 1.09 0.08 0.1

Recipient CharacteristicsBMI category (kg/m2 ) at

transplant15 to �25 1,801 4,588 666 12.3 1 1 0 N/A25 to �30 2,559 6,492 687 10.6 0.85 0.86 �0.15 0.00830 to �35 1,322 3,287 331 10.1 0.81 0.82 �0.20 0.00435 to �40 568 1,390 143 10.3 0.82 0.82 �0.20 0.0340 to �55 227 581 63 10.8 0.89 0.89 �0.11 0.4

Age category (years)18 to �43 963 3076 310 10.1 1 1 0 N/A43 to �50 2,283 5,820 602 10.3 0.96 0.94 �0.06 0.450 to �57 1,786 3,953 411 10.4 0.92 0.88 �0.13 0.157 to �63 841 2,079 260 12.5 1.15 1.12 0.11 0.2�63 604 1,409 207 14.7 1.33 1.22 0.20 0.03

UNOS urgency statusNot 1 6,282 15,662 1,692 10.8 1 1 0 N/A1 195 677 98 14.5 1.53 1.26 0.23 0.05

GenderMale 4,439 10,833 1,169 10.8 1 1 0 N/AFemale 2,038 5,505 621 11.3 1.08 1.06 0.06 0.3


American469 957 159 16.6 1.45 1.29 0.25 0.002

Hispanic 832 2,099 235 11.2 1.05 1.00 0.00 0.9Other (mostly Asian) 334 831 80 9.6 0.90 0.78 -0.24 0.03

Recipient diabetesNo 5,370 13,690 1,448 10.6 1 1 0 N/AYes 1,107 2,648 342 12.9 1.20 1.20 0.18 0.004

MELD score6 to �10.8 (25%) 6,208 19,930 1,658 8.1 1 1 0 N/A10.8 to �14.3 (50%) 6,643 20,360 1,761 8.2 1.00 1.00 0.00 0.914.3 to �19.4 (75%) 6,606 18,687 1,812 9.3 1.10 1.08 0.08 0.319.4 to �27 (90%) 4,181 11,165 1,225 10.4 1.20 1.23 0.20 0.02�27 3,047 7,095 1,048 13.9 1.54 1.66 0.50 �0.001

Abbreviations: N/A. not applicable.*Graft failure was defined as liver failure (with or without retransplantation) or patient death from any cause.†Adjusted using Cox proportional hazards regression for all the variables shown in the Table and stratified on the 11geographical UNOS transplantation regions.‡Donor age was squared, then 1,444 (the median square value) was subtracted.

tics (such as recipient BMI and diabetes and donorischemia time) that have been identified in multiplestudies,14,17,22 including the present one, to be impor-tant and independent predictors of survival, were notretained in the final models. Thuluvath et al. usedUNOS data to develop a simple model to predict survivalthat would not require a computer or calculator butmodeled only recipient and not donor characteristics.24

Patients with a very high MELD score have a highmortality, and it is estimated that every 4 hours a pa-tient dies waiting for a liver transplant.25 Hence, it mayactually be beneficial for a patient with a high MELDscore to accept a “marginal quality” liver that is avail-

able now, rather than wait for a better liver donor withbetter posttransplant survival, while risking death onthe waiting list. This was in fact suggested by a recentdecision analysis.26 However, a limitation of this deci-sion analysis acknowledged by the authors and theaccompanying editorial25 was that survival only up to 1year was modeled, that there were no good data on theimpact of a marginal (or “expanded criteria”) donor onlong-term, post-transplant survival, and that there wasno good definition of what a marginal donor was. Byproviding accurate estimates of the expected posttrans-plant survival for specific marginal donors, our modelsallow more accurate predictions in future studies of

TABLE 4. Predicted Graft Survival for Different Donor and Recipient Characteristics in Patients Without HCV

Baseline

Donor

Baseline

Recipient*

Best Donor

Best

Recipient*

Average

Donor

Average

Recipient*

Average

Donor

High-Risk

Recipient*

High-Risk

Donor

High-Risk

Recipient*

DonorCharacteristics

Age (years) 38 15 38 38 60Cold ischemia (hours) 0 to �6.4 0 to �6.4 6.4 to �8.8 6.4 to �8.8 �14.3Race White White White White WhiteGender Male Male Male Male MaleRecipient

CharacteristicsBMI category (kg/m2 )

at listing15 to �25 35 to �40 25 to �30 40 to �55 40 to �55

Age category (years) 18 to �43 43 to �50 50 to �57 �63 �63UNOS urgency status Not 1 Not 1 Not 1 Not 1 Not 1Gender Male Female Male Male MaleRace/ethnicity White Other (mostly

Asian)White White White

Recipient diabetes No No No No NoMELD score 14 6 14 24 24Albumin level �3.3 �3.3 2.8 to �3.3 �2.1 �2.1Cause of liver disease Alcoholic

cirrhosisPrimary biliary

cirrhosisAlcoholic

cirrhosisAlcoholic

cirrhosisAlcoholic

cirrhosisRisk score† 0 �1.19 0.04 0.96 1.59Hazard ratio‡ 1 0.30 1.04 2.61 4.9Survival§ at 90 days 0.92 0.98 0.92 0.80 0.66Survival§ at 1 year 0.88 0.96 0.88 0.72 0.53Survival§ at 2 years 0.85 0.95 0.84 0.65 0.45Survival§ at 5 years 0.77 0.92 0.76 0.51 0.28

*“Baseline” survival in the model was the survival of persons with the donor and recipient characteristics shown under the“baseline” column. Since the model was stratified on UNOS geographical regions, different baseline survivals can be calculatedfor each UNOS region; however, for simplicity, the average baseline survival across the entire United States is used here. “Best”donors and recipients are those with the characteristics that give the best-predicted survival. “Average” donors and recipientsare those with average values for numerical predictors (e.g., average age, BMI, etc.) and the most common categories fornominal variables (e.g., white race). “High Risk” donors or recipients have some predictors of low posttransplant survival,which are shown in bold.†The risk score can be calculated by adding the appropriate adjusted regression coefficients for each predictor shown in Table2. For instance, the risk score for average donor and high-risk recipient � (382 � 1,444) � 0.000147 (for age of 38 years) � 0.09(for cold ischemia time of 6.4 to �8.8 hours) � 0 (for white donor) � 0 (for male donor) � 0.26 (for BMI � 40) � 0.21 (for recipientage � 63) � 0 (for UNOS status not 1) � 0 (for male recipient) � 0 (for white recipient) � 0 (for nondiabetic recipient) � (24 �14) � 0.0176 (for MELD � 24) � 0.22 (for albumin �2.1) � 0.96.‡The hazard ratio is calculated as exp(risk score), e.g. exp(0.96) � 2.61 (for average donor and high risk recipient).§Survival at time t for donor/recipient X is calculated as (baseline survival at time t)hazard ratio for X . In the example above, thesurvival of the average donor bad recipient at 5 years is 0.772.61 � 0.51.

1602 IOANNOU


when it might be beneficial for a given recipient to ac-cept a given marginal donor.

The MELD score has been adopted since 2002 as thesystem that determines priority in allocating organs forliver transplantation in the United States, based on thefact that it is an excellent predictor of mortality withouttransplantation in patients with advanced liver dis-ease.5,6,27 However, 2 patients at the top of a transplantwaiting list with the same high MELD score may havevery different expected posttransplant survival due todifferences in predictors other than the MELD score(such as recipient age, underlying liver disease, diabe-tes, gender, and race, as exemplified by the modelspresented here). For instance, a 40-year-old non-dia-betic woman with primary biliary cirrhosis and a MELDscore of 30 would be expected to have a much betterposttransplant survival than a 65-year-old diabeticman with hepatitis C and a MELD score of 30, eventhough both have a similar mortality without trans-

plant, since they have the same MELD score. If 2 donorsare expected to be available at approximately the sametime, it would be more equitable for the recipient withworse predicted posttransplant survival (as determinedby the models presented here) to receive the donor withbetter predicted survival and vice versa, since thatwould make the posttransplant survival of the 2 recip-ients more similar.

The models also show that a large proportion ofpost–liver transplant mortality is determined beforethe liver transplantation has actually occurred bypretransplant characteristics of the donor and recip-ient. The models make explicit in a multivariate anal-ysis which donor and recipient characteristics havethe greatest impact on survival. Although all the vari-ables included in the model are important, donor age,cold ischemia time, recipient MELD score, and causeof liver disease have the greatest impact on survival.Tables 4 and 5 show that both high-risk recipients

TABLE 5. Predicted Graft Survival for Different Donor and Recipient Characteristics in Patients with HCV

Baseline

Donor,

Baseline

Recipient*

Best Donor,

Best

Recipient*

Average

Donor,

Average

Recipient*

Average

Donor,

High-Risk

Recipient*

High-Risk

Donor, High-

Risk Recipient*

DonorCharacteristics

Age(years) 38 15 38 38 60Cold ischemia (hours) 0 to �6.4 0 to �6.4 6.4 to �8.8 6.4 to �8.8 11.3 to �14.3Race White White White White WhiteGender Male Male Male Male MaleRecipient

CharacteristicsBMI category (kg/m2 )

at listing15 to �25 35 to �40 30 to �35 15 to �25 15 to �25

Age category (years) 18 to �43 50 to �57 50 to �57 �63 �63Status at time of

transplantationNot 1 Not 1 Not 1 Not 1 Not 1

Gender Male Male Male Male MaleRace/ethnicity White Other (Mostly

Asian)White White White

Recipient diabetes No No No Yes YesMELD score 6 to �10.8 6 to �10.8 16 24 24Risk score† (SD) 0 �0.78 �0.24 0.59 1.19Hazard ratio‡ 1 0.46 0.79 1.80 3.3Survival at 90 days 0.93 0.97 0.94 0.88 0.78Survival at 1 year§ 0.86 0.93 0.89 0.76 0.61Survival at 2 years§ 0.81 0.91 0.85 0.68 0.50Survival at 5 years§ 0.69 0.84 0.75 0.51 0.29

*“Baseline” survival in the model was the survival of persons with the donor and recipient characteristics shown under the“baseline” column. Since the model was stratified on UNOS geographical regions, different baseline survivals can be calculatedfor each UNOS region; however, for simplicity, the average baseline survival across the entire United States is used here. “Best”donors and recipients are those with the characteristics that give the best-predicted survival. “Average” donors and recipientsare those with average values for numerical predictors (e.g., average age, BMI, etc.) and the most common categories fornominal variables (e.g., white race). “High-risk” donors or recipients have some predictors of low posttransplant survival,which are shown in bold.†The risk score can be calculated by adding the appropriate adjusted regression coefficients for each predictor shown in Table3.‡The hazard ratio is calculated as exp(risk score)§Survival at time t for donor/recipient X is calculated as (baseline survival at time t)hazard ratio for X .



and/or high-risk donors can have great impact onposttransplant survival.

The degree of donor liver steatosis has been associ-ated with delayed or primary graft nonfunction, earlygraft loss, and retransplantation in some,28,32 but notall,16,33,34 previous studies. In the current study, donorliver steatosis was not associated with graft survival,either in univariate or multivariate analyses. However,liver steatosis has been recorded by UNOS only sinceOctober 1999, and it is not uniformly reported by trans-plant centers such that in our final analysis sampleonly 1,606 recipients without HCV had available dataon donor steatosis (including only 52 with �35% ste-atosis) and only 982 recipients with HCV had availabledata on donor steatosis (including only 27 with �35%steatosis). A type II error can therefore not confidentlybe excluded. In addition, since organs that were foundto have very high degrees of steatosis were probably notused for transplantation, it is difficult to assess the realimpact of donor steatosis on graft survival. However,the fact that donor BMI, which is strongly associatedwith liver steatosis and was uniformly reported, wasalso not associated with graft survival suggests that theimpact of mild to moderate donor liver steatosis on graftsurvival is likely to be small.

Increasing BMI was not associated with increasingrisk of graft failure in a monotonic fashion. Instead,among patients without HCV there was a biphasic re-lationship whereby, relative to the baseline group withBMI 15-25, graft survival was better for groups withBMI 25-30, 30-35, and 35-40, and only decreased inthe “morbidly” obese group with BMI � 40 kg/m2. Inpatients with HCV all “high” BMI groups had better

TABLE 6. The Adjusted Regression Coefficients and

Baseline Survival for Models Predicting Survival After

Liver Transplantation Without Using Cold Ischemia

Time as a Predictor are Given Here.

Adjusted Regression

Coefficient

Patients

Without

HCV

Patients

With

HCV

Donor characteristicsAge (years)Age2 � 1,444* 0.000145 0.000175Race/ethnicityWhite 0 0Black and African American 0.23 0.009Hispanic 0.16 0.03Other (mostly Asian) 0.36 0.11GenderMale 0 0Female 0.11 0.08Recipient characteristicsBMI category (kg/m2) at

transplant15 to �25 0 025 to �30 �0.10 �0.1530 to �35 �0.11 �0.2035 to �40 �0.16 �0.1940 to �55 0.27 �0.09

Age category (years)18 to �43 0 043 to �50 �0.02 �0.0750 to �57 0.03 �0.1457 to �63 0.10 0.10� 63 0.21 0.19

UNOS Urgency StatusNot 1 0 01 0.18 0.28GenderMale 0 0Female �0.06 0.05Race/ethnicityWhite 0 0Black and African American 0.12 0.26Hispanic �0.12 �0.006Other (mostly Asian) �0.26 �0.24Recipient diabetesNo 0 0Yes 0.23 0.18MELD scoreMELD score�14† 0.017 N/A

6 to �10.8 N/A 010.8 to �14.3 N/A �0.00114.3 to �19.4 N/A 0.0719.4 to �27 N/A 0.19�27 N/A 0.51

Albumin�3.3 0 N/A2.8 to �3.3 0.02 N/A2.4 to �2.8 0.03 N/A2.1 to �2.4 0.20 N/A�2.1 0.23 N/A

TABLE 6. (Continued)

Adjusted Regression

Coefficient

Patients

Without

HCV

Patients

With

HCV

Recipient liver diseaseAlcoholic cirrhosis 0 N/AHepatitis B /0.24 N/APrimary biliary cirrhosis /0.36 N/ACryptogenic cirrhosis /0.17 N/AOther /0.13 N/AHepatocellular carcinoma or

cholangiocarcinoma0.35 N/A

Baseline Survival90 days 91.4% 92.1%1 year 86.6% 85.4%2 years 83.2% 79.5%5 years 74.9% 66.0%

Abbreviations: N/A, not applicable.*Donor age was squared, and then 1,444 (the mediansquare value) was subtracted.†The MELD score was calculated with values of 6 to 40, andthen 14 (the median MELD score) was subtracted.

1604 IOANNOU


graft survival than the baseline group with BMI 15-25.Changing the baseline BMI group from 15-25 to 18-25Kg/m2 had almost no impact on the results (data notshown). These results are perhaps not so surprising,because BMI cannot distinguish between fat and mus-cle. Thus, a patient with a “normal” BMI (15 to �25kg/m2) may have a good prognosis because of absenceof central fat or may have a poor prognosis because ofsevere muscle wasting, which is very common in ad-vanced liver disease. In addition, the patients in thevery high BMI categories were likely highly selected onthe basis of other good prognostic indicators. The cur-rent results are slightly different from an earlier studybased on UNOS data suggesting that both “severe” (BMI�35 to 40 kg/m2) and “morbid” (BMI �40 kg/m2) re-cipient obesity were associated with reduced 5-yearposttransplant survival;17 however, in that study,cause of liver disease, which is an important con-founder of the association between BMI and graft sur-vival, was not adjusted for, and BMI at the time oflisting rather than at the time of transplantation wasused as the predictor.

It is likely that within transplant centers the per-ceived “quality” of a potential donor may influencewhich recipient that organ goes to. For instance, recip-ients who are very sick may be given a higher-qualityliver (if there is choice) to improve their otherwise lowposttransplant survival. Alternatively, it is possible thatlivers from donors who are considered “high-risk” or“marginal” may be transplanted more commonly in verysick recipients who cannot wait for a “better” liver tobecome available. Or, finally, a marginal liver may, per-haps, be used only in a relatively healthy recipient.These considerations suggest that there is likely to be ahigh degree of confounding between recipient and do-nor characteristics. By simultaneously adjusting for alarge number of donor and recipient characteristics andby also including in the models variables that were notstatistically significant if they affected the coefficients ofother variables, such confounding was addressed inthis study as much as possible.

The multivariate models were stratified on UNOS re-gion of transplantation. Thus, the effects of the predic-tors presented are adjusted for any potential confound-ing effect of region of transplantation. It was notpossible to adjust for each individual center, since thereare too many centers for a meaningful analysis andsince center information is not provided in the UNOSfiles. Adjusting or stratifying by center, rather thanregion, would probably make little difference overall tothe models presented, since the centers within eachregion of transplantation would have to be associatedwith survival and with specific donor/recipient charac-teristics for the center of transplantation to be an im-portant confounder. However, our models may not ap-ply to specific centers that have particular expertise inhigh-risk transplantations, such as using extended-criteria donors.

This study is based on data submitted to UNOS byindividual transplant centers, rather than data col-lected specifically for the purposes of this study. Hence

we cannot verify the accuracy of the data. Out of 30,004eligible liver transplants, we had to exclude 9,703 frommultivariate analyses because data were missing for atleast 1 predictor. However, persons with missing datawho were excluded from the analysis had similar char-acteristics to the persons included (Table 1), and it isunlikely that their exclusion has substantially influ-enced the prediction models presented here. Further-more, our model of posttransplant survival is strength-ened by the fact that it was based on approximately33% of all eligible liver transplant recipients in theUnited States. Most models of survival in non-trans-plant-related conditions are based on very small pro-portions of the at-risk population recruited from ter-tiary referral centers. Finally, predictors of survivalmight have changed slightly during the 10-year studyperiod (1994-2003), and future studies have to be doneusing even more recent samples as more UNOS dataaccrue. In particular, the ability to successfully trans-plant “marginal” organs may substantially improve.

One of our models is based on all patients withoutHCV. This model predicts survival well in the entirepopulation without HCV, but it predicts survival lesswell in certain subpopulations based on underlyingliver disease (e.g., hepatocellular carcinoma or “other”liver disease) than in others (e.g., primary biliary cir-rhosis or alcoholic liver disease). This problem can beovercome by developing survival models specific foreach major cause of liver disease, just as has been donein this paper for HCV, although this approach wasavoided in the current paper for the sake of simplicity.

It is hoped that the analyses presented here will serveas a starting point for subsequent investigators to im-prove upon the presented models. Ultimately, riskscores and predicted survivals determined from suchmodels may be an objective way to assess the risk of agiven liver donor, recipient, or donor/recipient combi-nation.

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development and validation of a model predicting graft survival after liver transplantation

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