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Potential conflict of interest: Nothing to report.
The usual method of estimating survival probabilities, namely the Kaplan-Meier method, is suboptimal in the analysis of deaths on the transplant waiting list. Death, transplantation, and withdrawal from list must all be considered. In this analysis, we applied the competing risk analysis method, which allows evaluating these end points individually and simultaneously, to compare the risk of waiting list death across era, blood types, liver disease diagnosis, and severity (Model for End-stage Liver Disease; MELD). Of 861 patients registered on the waiting list at Mayo Clinic Rochester between 1990 and 1999, 657 (76%) patients underwent transplantation, 82 (10%) died while waiting, 41 (5%) withdrew from the list, and 81 (9%) patients were still waiting as of February 2002. The risk of death at 3 years was 10% by the competing risk analysis. During the study period, the median time to transplantation increased from 45 to 517 days. In univariate analyses, there was no significant difference in the risk of death by era of listing (P = .25) or blood type (P = .31), whereas the risk of death was significantly higher in patients with alcohol-induced liver disease and those with higher MELD score (P < .01). A multivariable analysis showed that after adjusting for MELD, blood type, and diagnosis, patients listed in the latter era had higher mortality. In conclusion, the competing risk analysis method is useful in estimating the risk of death among patients awaiting liver transplantation. (HEPATOLOGY 2006;43:345–351.)
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Orthotopic liver transplantation (OLT) has been recognized as an effective means of restoring health in patients who have sustained irreversible liver injury.1 Successful outcome of OLT has led to a steady increase in its application, whereas the number of available deceased donor organs has remained essentially stationary, creating a shortage of organs for transplantation. This, in turn, has led to a dramatic increase in the number of patients on the waiting list and in their waiting time.2 Likewise, the number of deaths on waiting list has also increased.3, 4 For example, between 1990 and 1999, the number of liver transplant candidates waiting at year end increased 12-fold (from 1,237 to 14,709), and the number of deaths on the waiting list increased 6-fold (from 317 to 1,753). These figures have been widely publicized as a gauge of the efficiency of the organ allocation system. As a response to these issues, transplantation policy makers have introduced a number of changes in the liver prioritization scheme, even before the Model for End-stage Liver Disease (MELD) was implemented in 2002. In parallel, the increasing shortage of organs throughout the 1990s resulted in an adaptation in many transplantation programs: to accrue waiting time and to maximize the chance to receive an organ in a timely fashion, liver transplant candidates were placed on the waiting list at the earliest possible time. Despite all these endeavors in the liver transplant community, the fundamental issue in liver allocation remains the mismatch between the supply and need for donor livers for transplantation
Although the phenomenon of donor shortage and waiting list death is easily understandable, statistical methods for its analysis are not so straightforward. A patient registered for liver transplantation experiences one of three possible outcomes while on the waiting list: transplantation, death, or withdrawal from the list. These outcomes are competing risks, because the occurrence of one outcome either precludes or alters the probability of the occurrence of the others. The usual method to describe survival of a population is the Kaplan-Meier analysis.5 This analysis only allows for one event type and thus describes what the death rate would be if no alternative outcome existed. For multiple outcome data such as wait list outcome, one of wo approaches is often taken to “adapt” the Kaplan-Meier to the task: either all outcomes are consolidated, giving an estimated curve of the time to first event (e.g., death or transplantation), or the individual curve for a given event type (e.g., death) is created by treating all other events (e.g., transplantation) as though the patient were lost to follow-up at that point. Thus, if the latter approach is used to estimate the risk of death, patients are censored at the time of transplantation or withdrawal.
In this study, we demonstrate the competing risk analysis, an alternative approach to Kaplan-Meier, in which the competing risks in liver transplant candidates are addressed forthright. The aims of the project were (1) to compare death rate among liver transplant wait list registrants estimated by the Kaplan-Meier and competing risk analyses, (2) to examine the longitudinal trend in the waiting list mortality utilizing the competing risk method, and (3) to identify factors that determine the risk of death on waiting list among OLT candidates. These are relevant issues today, because current epidemiologic data, such as those regarding hepatitis C and obesity-related fatty liver disease, point to a continued increase in the demand for OLT in the foreseeable future.6–8
OLT, orthotopic liver transplantation; MELD, Model for End-stage Liver Disease; UNOS, United Network for Organ Sharing.
Materials and Methods
Waiting List Registrants.
This work represents an analysis of the survival experience in patients who were registered on the liver transplant waiting list at Mayo Clinic, Rochester, MN, over a 10-year span, between February 1990 and August 1999. Because the purpose of this study related to adult patients with end-stage chronic liver disease, pediatric liver transplant candidates (age <17 years) and patients with acute liver disease were excluded. Likewise, patients with hepatic malignancies were not considered to be representative of end-stage chronic disease and were excluded. The study time frame was chosen to avoid any potential effect of the change in the organ allocation that occurred with the introduction of MELD (February 2002), while ensuring reasonable duration of follow-up.9 Only initial listings were included.
Liver transplant candidates who met the inclusion criteria were identified by review of United Network for Organ Sharing (UNOS) registration records. Of these candidates, most of those who underwent liver transplantation had been prospectively enrolled in an institutional database, which was originally established for a federally supported multicenter study.10 Data elements in the database were broad and included demographic, clinical, and biochemical data at the time of UNOS registration, immediately before transplantation, and at subsequent post-OLT follow-up. In patients who were not represented in the database, complete inpatient and outpatient medical records were used to verify liver disease diagnosis and to extract information at the time of registration, including demographic information, blood group, and laboratory data. The outcome—transplantation, death on the list, or withdrawal from the list—was also obtained from the medical record and patient registration data. These results of follow-up were assessed as of the end of February 2002. Data beyond March 2002, were excluded because of the significant changes in organ allocation at that time. Patients whose last recorded evaluation was before February 2002 were treated as “still waiting” as of their last visit date.
Competing Risk Analysis.
The three competing outcomes while on the waiting list for liver transplantation include transplantation, death, or withdrawal from the list. A key element in survival analyses in general is the hazard of failure, which represents the probability of failure conditional on patients being at risk at a given time. The term failure is used in survival analysis to mean any resolution, whether negative (i.e., death) or positive (i.e, transplantation). In the absence of competing risks, that is, when there is only one type of failure, the parameter of interest is the estimate of the probability of failure in all patients under study. In contrast, if competing risks exist, hazards for each type of failure need be considered. The number of failures from the competing risk (e.g., liver transplantation) will influence the number of failures from the cause of interest (e.g., death before receiving a liver transplant) and consequently the estimate of the probability of failure from the latter. Furthermore, failures from the competing risk (liver transplantation) reduce the number of patients at risk of failure from the cause of interest (death without transplantation). Just as in Kaplan-Meier analysis, incomplete follow-up affects our knowledge of a patient's outcome, but not the outcome itself. No matter the number of competing events, patients who have not achieved an outcome of interest during the time they are being observed are censored, acknowledging that any of the outcomes are still possible.
Statistical calculations were conducted using the SAS11 (SAS, Cary, NC) and S-Plus (Insightful Corp., Seattle, WA)12 packages. Briefly, in the competing risk model, estimates of cumulative incidence for each event type are obtained using the survival functions from all event types. For each event type and each time t, the cumulative incidence is obtained by summing the product of the overall survival and the hazard for the respective event type over all time points t and less. In turn, the overall survival is 1 minus the sum of the cumulative incidences for the different event types. If a patient experiences a competing event, the potential contribution for that patient thereafter is zero, because failure from the event of interest is no longer possible. Cumulative incidence estimates are available in S-plus from version 7.0 onward. SAS macros for both simple competing risk estimates and the estimates after adjustment for covariates are also available from the authors. For the exact formulae, see Kalbfleisch and Prentice.5
Factors Associated With Death on Waiting List.
Using the competing risk analysis, we examined several factors that may affect the waiting list mortality. These included the calendar year, blood group, liver disease diagnosis, and liver disease severity. As to the calendar year, the study period was divided into four eras, namely 1990 to 1992, 1993 to 1995, 1996 to 1997, and 1998 to 1999. These were simply selected to include roughly equal number of registrants per era. Blood groups included types O, A, B, and AB. Liver disease diagnosis was grouped into alcohol-induced, cholestatic, viral, and other disease categories. Liver disease severity was measured using MELD.13 MELD was adopted as the criteria by which donor organs are distributed by UNOS in February 200214–16; patient accrual in this study preceded the implementation of MELD. The formula for MELD used in this study is MELD = 9.57*loge(serum creatinine) + 3.78* loge(serum total bilirubin) + 11.20* loge(INR) + 6.4, according to its original description.13
In computing the effect of these potential prognostic factors, cumulative incidence curves were drawn for each category (for example, ABO blood groups). The statistical significance between these categories was assessed by using the test described by Gray.17 To consider these factors simultaneously, competing risks models were constructed based on the Cox proportional-hazards model.5 This was undertaken by treating the main factor (e.g., era) as a stratum and other variables (blood group, diagnosis, MELD) as covariates. For the competing risk Cox model, cumulative incidence standard deviations were estimated using bootstrapping, allowing testing between categories.18
During the study period, between February 1990 and August 1999, 861 patients were registered onto the UNOS waiting list at Mayo Clinic, Rochester, and met the inclusion criteria. As of the closure of the study in February 2002, 657 (76%) patients had undergone liver transplantation. Of the remaining 204 patients, 82 (40%) died while waiting, 41 (20%) withdrew from the list, and 81 (40%) patients were still waiting. Of the 81 patients classified as still waiting, there were 49 (60%) whose last recorded evaluation was less than 2 years after their registration date. Twelve patients were first withdrawn from the list and subsequently died within the 3 months after withdrawal. These were considered to represent patients “too sick to transplant” and were classified as deaths.
Table 1 summarizes patient characteristics of waiting list registrants. Comparing across the 4 eras, a noticeable shift occurred in the type and severity of liver disease over time. A decrease occurred in the proportion of liver transplant candidates with cholestatic liver disease, accompanied by increases in the proportion with viral hepatitis and other types of liver disease (P < .01). The MELD score at the time of registration decreased from a median of 18 in the earliest era to a median of 13 in the most recent, indicating a decrease in the severity of liver disease (P < .01). This decrease occurred across all disease types.
Table 1. Characteristics of Patients Who Were Registered for a Liver Transplantation at Mayo Clinic, Rochester, MN
NOTE. Values reported are summaries of patients at their activation date. P values are calculated using Wilcoxon rank sum test for continuous variables and chi-square test for categorical variables.
Abbreviation: IQR, interquartile range (25th to 75th percentiles).
Age, mean ± SD
50.2 ± 10.4
49.3 ± 10.5
50.5 ± 11.0
49.3 ± 11.0
51.5 ± 8.6
Male sex, n (%)
Diagnosis, n (%)
Blood type, n (%)
Bilirubin, mg/dL Median (IQR)
3.4 (2.0 to 7.6)
5.6 (2.7 to 13.4)
4.0 (2.0 to 8.3)
2.9 (1.7 to 5.4)
2.8 (2.0 to 5.1)
Creatine, mg/dL Median (IQR)
0.9 (0.8 to 1.2)
0.9 (0.8 to 1.1)
0.9 (0.8 to 1.2)
1.0 (0.8 to 1.2)
1.0 (0.8 to 1.2)
INR Median (IQR)
1.4 (1.2 to 1.6)
1.5 (1.3 to 2.0)
1.4 (1.2 to 1.6)
1.3 (1.1 to 1.5)
1.3 (1.1 to 1.5)
MELD Median (IQR)
14.5 (11 to 19)
18 (13 to 23)
15 (11 to 19)
13 (10 to 17)
13 (11 to 17)
Figure 1 compares two methods of assessing overall survival of waiting list patients. The Kaplan-Meier method estimates the risk of death among waiting list patients to be 15% at 1 year and 26% at 3 years. Estimates taking into account competing risks are much lower at 8% at 1 year and 10% at 3 years.
Figures 2 through 5 illustrate cumulative incidence curves for transplantation, death, and withdrawal from the list without adjusting for other factors. Figure 2 compares the occurrence of competing events for the 4 eras. An obvious increase occurs in the median time to transplantation from 45 days for patients registering in the first era to 141 days for the second, 199 days for the third, and 502 days for the last. Mortality during the first 2 years was 7% in the first era, 8% in the second, 9% in the third, and 14% in the last. Virtually all patients in the first era had achieved an outcome by 1 year. In the other 3 eras, very few additional deaths were observed beyond the first 2 years (mortality at 5 years was 9%, 9%, and 16% for the second, third, and fourth eras, respectively). As expected, follow-up was less complete in the later eras: One person was censored in the first era, compared with 56 censored patients in the most recent era, 39 of whom were followed less than 2 years. The change in transplantation rate was statistically significant (P < .01), whereas the change in death rate was not (P = .12).
Figure 3 compares blood types. Waiting list registrants with blood type O experienced a significantly longer waiting time than others (P < .01). The median waiting time for blood type O was 281 days, followed by 205 days for blood type B, 105 days for blood type A, and 99 days for blood type AB. Similarly, liver transplant candidates with blood group O had the highest risk of death (10% risk of death during the first year, compared with 9% for blood type B, 9% for blood type AB, and 7% for blood type A), although the differences did not reach statistical significance (P = .30).
Figure 4 compares the 4 diagnosis groups, namely alcoholic, cholestatic, viral, and other categories. Listing diagnosis had a significant impact on the waiting time (P < .001) and risk of death (P = .008). The waiting time was the longest (median 220 days) in hepatitis C virus and the risk of death the highest (17.3% at 2 years) in alcohol-induced liver disease. Cholestatic disease had the shortest waiting time (136 days) and lowest death rate (6.6%). There was no statistically significant difference in the probability of withdrawal among the diagnostic categories.
Figure 5 illustrates the relationship between MELD at the time of listing and the subsequent events. The probability of death increased progressively with increasing MELD score (P < .001). For example, risk of death at 3 months was 0% for MELD < 10, 3.1% for MELD 10 to 20, 11.7% for MELD 21 to 30, and 22.2% for MELD > 30. Moreover, in the highest MELD group (MELD > 30), nearly all patients reached an end point (transplantation or death) shortly after their registration, with virtually no one withdrawing from the list. In the lowest MELD group (MELD < 10), by contrast, more patients were withdrawn than died.
Figure 6 represents a multivariate analysis that compares the 4 eras' cumulative incidence of death on the waiting list, while adjusting for MELD, blood group, and diagnosis. This analysis showed an increase in mortality across the 4 eras, with 2-year mortality rate of 6% in the first era, 9% in the second, 10% in the third, and 18% for the most recent era (P < .01). This increase is greater than that shown in Fig. 2, mostly because patients had lower MELD at the time of registration in more recent eras; therefore, the cumulative incidence of death did not show a marked increase in the univariate analysis. However, once the data were adjusted for MELD (and blood group and diagnosis), more recent eras were indeed associated with higher mortality.
Deaths on transplant waiting lists have been one of the most visible parameters of organ allocation and distribution in deceased donor liver transplantation.3 An exponential growth has occurred in the number of transplant candidates in the recent decade.16, 19 Because the supply of deceased donor organs is limited, the competition for the limited resources has grown, according to the number of waiting list registrants. The process in which potential liver transplant candidates are evaluated and registered on the waiting list entails complex decision making based on a multitude of physical and psychosocial factors. Among those who get registered, analysis for the subsequent outcome needs to take into account the competing nature between transplantation and death.
We present a statistical method to calculate unbiased estimates for mortality risk among transplant candidates on the waiting list. We demonstrate that the Kaplan-Meier method overestimates the risk of death on waiting list, which is in agreement with similar observations that have been made for heart and renal transplantation candidates.20, 21 Second, when the competing risk analysis is applied to data obtained from an unselected population of waiting list registrants, liver disease severity as measured by MELD had the most significant association with the risk of death on waiting list. In addition, patients in more recent eras had longer waiting time and higher mortality, as shown in our multivariable analysis. Although the generalizability of these findings at other centers and in other regions needs to be examined, our work supports the use of MELD as an indicator of the risk of waiting list mortality.
In the comparison between the Kaplan-Meier and competing risk analyses, it is important to recognize that one method is not always superior to the other. Rather, the two analyses address different questions. The Kaplan-Meier result for death is an estimate of what the death rate would be, if all other endpoints were removed, for example, the transplant programs discontinued. The competing risk analysis produces an estimate of death rates in the presence of a transplant program. The Kaplan-Meier estimate may be the most appropriate to answer certain “what if” questions, for example, when counseling a patient about their future course without transplantation, or when deciding which of two candidates should receive a given liver. For evaluating the result of a transplant program, however, the competing risk estimate is a more appropriate metric.
Both Kaplan-Meier and competing risk estimates require that censoring be independent of outcome, in other words, that patients are not lost to follow-up just before major events, as when patients who are too ill stop showing up for appointments. The Kaplan-Meier estimate has the further assumption that each endpoint is independent of the others, for example, that transplant is not a marker of imminent death or withdrawal, an assumption that may not hold in the waiting list environment. The Kaplan-Meier estimate of death rate will always be higher than the competing risk estimate, because it assumes that these recipients and ex-candidates are removed from the observation without achieving an endpoint. Analysis of risk of wait list death while accounting for non-death events allows representation of the experience pertinent to patients on the waiting list, for whom both transplantation and death are real possibilities.
In part because of the paucity of software for the competing risks problem in standard statistical packages, analyzing competing risk data as a series of single endpoint problems by use of the Kaplan-Meier estimator has been common. However, in assessing the effect of blood type, disease, and time trends on waiting list mortality, we believe the competing risk estimate is more apropos to the question at hand by addressing what the effect of blood group is on waiting list deaths in the presence of OLT, rather than what it would be if OLT ceased. The disadvantage of the competing risk estimate is that the results may not be as generalizable to other transplant programs: a program with less severe organ restrictions may not have had the same increase in death rate, for instance.
When other covariates were not accounted for, the dramatic increase in the median waiting time during the study period did not appear to be associated with appreciable increase in the risk of death. This dissociation between the waiting time and the risk of death may be explained at least in part by the practice of listing patients early, rather than improved care over time leading to prolonged survival in patients with end-stage liver disease. During the 1990s, as the perceived chance of receiving OLT decreased, patients were put on the waiting list earlier in the disease progression to accrue waiting time. The influence of the changing case-mix is visible in the apparent contradiction between the univariate analysis (Fig. 2), showing a steady death rate across the 4 eras, and the multivariable analysis (Fig. 6), showing an increase in death rate across eras. A widespread adaptation of this practice further increased the number of registrants and the time on the waiting list but effectively decreased the death rate, by saturating the list with low-risk patients. In a sense, this represents a case of lead time bias artificially introduced by the physicians and, thus, if patients had been listed at a fixed MELD score over time, we would likely have seen a significant rise in the wait list mortality. The adoption of the minimal listing criteria in the latter part of 1998 had a stabilizing influence on the addition of new registrants.22 Our data show a decrease in degree of illness over the first 3 eras, leveling off in 1998 to 1999 (Table 1). Furthermore, the follow-up is much more complete in the early eras. Of the patients listed in 1990 to 1992, only 1 person (<1%) had not reached an endpoint during our study period. Of those listed in 1998 to 1999, 25% were still on the wait list at the end of the study.
Disease severity at the time of listing has been recognized as an important predictor of waiting list death. The MELD scale has been validated as an objective measure of liver disease severity based on a number of patient groups, ranging from patients with compensated liver cirrhosis from cholestatic and non-cholestatic liver disease to those requiring inpatient care for decompensated liver disease.13 The current data demonstrate that MELD correlated with short-term mortality risk in the population in which the application of MELD is relevant, namely, liver transplant candidates. The fact that virtually all patients with MELD greater than 30 were transplanted or died within 6 months of listing indicates that these patients were at very high risk of death, unless they underwent transplantation soon after registration. The previous organ allocation system partly recognized patients at risk of imminent death, because approximately 80% of patients with high MELD (>30) underwent transplantation. The current MELD-based system explicitly considers short-term risk of death as the most important criterion for organ allocation, purporting to minimize the overall risk of death on the list.23
In conclusion, we demonstrate that the most appropriate method of assessing the risk of death in a population awaiting liver transplantation is the competing risk analysis, taking into account simultaneously death and liver transplantation. The usual method for survival analysis, namely the Kaplan-Meier method, estimates survival in the absence of transplantation. Thus, for patients on a liver transplant waiting list, the Kaplan-Meier estimates risk of death to be higher than what patients actually experience. Our data showed that there was a dramatic increase throughout the 1990s in the competition for organs, leading to longer waiting time and higher risk of death. Our data again demonstrate that the MELD scale is a useful measure of risk of death among patients on a waiting list and lend further support to the adoption of MELD.