Can liver transplantation provide the statistical cure?

Authors


  • The authors of this article have no conflicts of interest to disclose.

Abstract

Liver transplantation (LT) represents the only chance of long-term survival for patients with end-stage liver disease. When the mortality rate for transplant patients returns to the same level as that for the general population, they can be considered statistically cured. However, cure models in the setting of LT have never been applied. Data from 1371 adult patients undergoing LT for the first time between January 1999 and December 2012 at 2 Italian centers were reviewed in order to establish probabilities of being cured by LT. A parametric Weibull model was applied to compare the mortality rate after LT to the rate expected for the general population (matched by sex and age). The observed 3-, 5-, and 10-year overall survival rates after LT were 77.8%, 73.3%, and 65.6%, respectively, and they did not differ between the 2 centers (P = 0.37). The cure fraction for the entire study population was 63.4% (95% confidence interval = 52.6%-72.0%), and the time to cure was 10 years with a 90% confidence level. The best cure fraction was observed for younger recipients without hepatitis C virus (HCV) who had favorable donor-recipient matches, that is, low Donor Model for End-Stage Liver Disease (D-MELD) scores (90.1%); conversely, the lowest probability was observed for elderly HCV recipients with high D-MELD scores (34.6%). The time to cure was 6.22 years for non-HCV patients and 14.78 years for HCV patients. The median survival time for uncured patients was 2.29 years. Among uncured recipients, the longest survival time was observed for younger patients (7.31 years). In conclusion, we provide here a new clinical measure for LT suggesting that survival after transplantation can approximate that of the general population and provide a statistical cure. Liver Transpl 20:210-217, 2014. © 2013 AASLD.

Abbreviations
γ

location parameter

λ

scale parameter

λ(t)

excess hazard rate

π

cure fraction

D-MELD

Donor Model for End-Stage Liver Disease

HBsAg

hepatitis B surface antigen

HBV

hepatitis B virus

HCC

hepatocellular carcinoma

HCV

hepatitis C virus

h(t)

overall hazard

h*(t)

expected hazard for the general population

LT

liver transplantation

MELD

Model for End-Stage Liver Disease

R(t)

relative survival

S(t)

observed overall (all-cause) survival

S*(t)

expected survival of general population

Su(t)

specific survival function for uncured patients

tMedian

median survival

Liver transplantation (LT) has emerged over the past 3 decades as the only effective therapy for patients with end-stage liver disease. Advances in surgical techniques, immunosuppression, and perioperative care have greatly improved both the outcomes and the utilization of LT, with which a 5-year survival rate as high as 80% can currently be achieved.[1] Some reports have shown that transplant patients can even achieve a 10-year survival rate as high as 60% and a 20-year survival rate close to 50%.[2, 3] Recent evidence also suggests that a satisfactory quality of life can be achieved by long-term survivors, and this suggests that LT can restore not only physiological abilities but also psychological well-being.[3, 4] Thus, long-term survival is possible after LT, but whether transplant patients can be considered cured is currently unknown. In epidemiology, cure is said to occur when the mortality rate of patients diagnosed and treated for a specific disease returns to the same level expected for the general population. Cure models are a special type of survival analysis and assume that a proportion of the subjects will never die as a consequence of the specific disease that has been treated; that, in turn, determines a plateau for the survival curve of all patients who have been treated.[5] Survival after LT can be viewed in terms of the proportion of patients who have a mortality rate similar to that expected for the general population and can consequently be considered cured of their liver disease and the proportion of patients who are bound to die after transplantation. The cure fraction is particularly interesting for patients as well as clinicians because it provides a useful measure of the probability of success of transplantation. To date, this aspect has never been investigated in the setting of LT, and the aim of the present study was thus to assess the probabilities of being cured by LT.

PATIENTS AND METHODS

Patient Population

Between January 1999 and December 2012, LT was performed 1708 times at 2 Italian surgical departments. The inclusion criteria for eligibility in the present study were as follows: (1) an adult LT procedure (age >18 years), (2) transplantation for the first time (retransplants were excluded), and (3) no combined transplants (eg, kidney-liver transplants, heart-liver transplants, or multivisceral-liver transplants). In addition, patients with human immunodeficiency virus and recipients of anti–hepatitis C virus (HCV) donor grafts were excluded because they represented particular situations in which transplantation was performed within specific experimental studies. After the application of the inclusion criteria, 1371 patients were eligible for the present study (883 in Bologna and 488 in Padua). The policies of the 2 centers have been previously published. In particular, for patients with hepatocellular carcinoma (HCC), the criteria for transplantation were extended beyond the Milan criteria[6] to cover patients successfully undergoing a down-staging procedure (Bologna) and patients with favorable tumor characteristics at biopsy (Padua).[7, 8] Among the variables stored in each center's database, the following were selected: recipient age and sex; etiology of liver disease; viral hepatitis status [hepatitis B virus (HBV) and HCV]; presence and stage of HCC; biochemical Model for End-Stage Liver Disease (MELD) score recorded on the day of the transplant; donor age and sex; and dates of transplantation, death, and last follow-up visit. The Donor Model for End-Stage Liver Disease (D-MELD) score was also properly calculated and categorized according to accepted thresholds.[9]

The standard immunosuppressive regimens included cyclosporine and tacrolimus; both were associated with tapered doses of steroids, which were usually withdrawn 6 to 12 months after the operation. Since May 2004, mammalian target of rapamycin inhibitors (sirolimus and everolimus) were administrated either as primary immunosuppressive agents or in combination with reduced doses of calcineurin inhibitors in patients with impaired renal function or calcineurin inhibitor neurotoxicity and in patients with a high risk for tumor occurrence or de novo malignancies after LT. Anti-CD25 antibodies or anti-thymocyte globulins were used at the time of transplantation as induction therapy for a minority of the patients.

In hepatitis B surface antigen (HBsAg)–positive recipients, antivirals used before transplantation continued to be used after transplantation in association with anti-HBV–specific immunoglobulins; in recipients who were HBsAg-negative and received organs from anti-core–positive donors, the combined prophylaxis consisted of lamivudine and anti-HBV–specific immunoglobulins in all cases. None of the HCV-positive patients received preemptive antiviral therapy, which was conversely started when HCV recurrence was suspected after the exclusion of vascular, biliary, drug, and infectious causes of serum liver test abnormalities and was confirmed by either a liver biopsy sample confirming HCV recurrence and/or detectable quantitative HCV RNA in serum. Antiviral therapy was avoided or discontinued in patients who developed severe rejection, systemic bacterial infections, or severe depression despite antidepressants or who showed a lack of a biochemical and/or viral response after at least 3 months of therapy. Granulocyte colony-stimulating factor and erythropoietin were used to check for adverse effects of antiviral therapy.

Description of the Cure Model

In the present study, a mixture cure model was chosen for the analysis of the cure fraction (π) after LT. The mixture cure fraction model assumes that 2 groups exist: those who are cured of their disease and thus have a mortality rate similar to that expected for the general population and those who are uncured (or bound to die) after therapy. The estimation of π relies on the computation of the relative survival [R(t)], which is the observed overall (all-cause) survival [S(t)] divided by the expected survival [S*(t)] of the general population. In this model, the overall survival of transplant patients can be written as follows:

display math(1)

The hazard analogue of R(t) is the excess hazard rate [λ(t)]. The overall hazard [h(t)] is the sum of the expected hazard for the general population [h*(t)] and the λ(t) value associated with transplantation:

display math(2)

Both S*(t) and h*(t) are assumed to be known and are usually obtained from general population data sources. The estimation of π is based on the assumption that R(t) has an asymptote at π. Similarly, h(t) for transplant patients will, some years after the procedure, return to the same level as that for the general population, and this means that λ(t) is nearly zero after a certain temporal endpoint. The model can be expressed as follows:

display math(3)

A proportion of the transplant patients (π) will be cured and will not experience mortality excess, whereas the remaining patients (1 − π) will be uncured. Su(t) is the specific survival function for uncured patients, and it is estimated by the model along with the cure proportion. Cure models rely on a parametric assumption of survival distribution, and a Weibull distribution for Su(t) is often used in mixture cure models.[10, 11] Thus, the λ and γ coefficients of the Weibull model, where λ is the scale parameter and γ is the location parameter, are appropriately fitted. The median survival (tMedian) of uncured patients can be obtained from the cure model with the following equation:

display math(4)

Finally, the time to cure is assessed. Because cure models define cure as occurring when time tends to infinity, the time to cure is calculated with 3 different levels of confidence: 80% (α = 0.2), 90% (α = 0.1), and 95% (α = 0.05).

Statistical Analysis

Clinical category characteristics for patients are reported as numbers of cases and percentages, and differences between subgroups were compared with Fisher's exact test. Distributions of continuous variables were first checked for normality with the Kolmogorov-Smirnov test. Because a normal distribution could not be confirmed for any continuous variables, these are reported as medians and interquartile ranges (25th to 75th percentiles), and differences between subgroups were compared with a nonparametric test (the Mann-Whitney test). Overall survival was computed from the day of LT until death or the most recent follow-up visit. Survival rates at different temporal endpoints were obtained with the Kaplan-Meier method. The estimations of expected survival and expected hazard for the general population at the time of a patient event (death) were derived from population survival tables obtained from the Italian National Institute of Statistics,[12] and they were matched by patient age and sex. Statistical analyses were computed with SPSS for Windows 13.0 (SPSS, Inc., Chicago, IL). The cure model was computed with the strsmix package developed for Stata software (StataCorp LP, College Station, TX).[13] A P value < 0.05 was considered statistically significant in all the analyses. The study was approved by the institutional review boards of both centers.

RESULTS

The baseline characteristics of the study population, which consisted of 1371 patients, are detailed in Table 1 together with overall survival rates. The median age of the whole study group was 55 years (range = 18-72 years), and the patients were predominantly male (72.1%) without a difference between the 2 transplant centers (P > 0.10 in both cases). Conversely, the 2 centers differed significantly with respect to the prevalence of HBsAg-positive patients (P = 0.002) and alcoholic patients (P = 0.02) and with respect to the severity of liver dysfunction (P < 0.05) as confirmed by a significant difference in the MELD scores (P < 0.001). The D-MELD scores also significantly differed between the 2 centers (P < 0.001). Three hundred eighty-one patients (27.8%) in the entire study population died after a median follow-up of 4.7 years (range = 1 day to 14.4 years) with 1-, 3-, 5-, and 10-year survival rates of 87.0%, 77.8%, 73.3%, and 65.6%, respectively (Fig. 1). Despite the different clinical features, the overall survival rates were comparable between the 2 centers (P = 0.37), although marginally lower survival in the first year after transplantation was observed at the Bologna center.

Table 1. Baseline Characteristics of the Study Population Used for the Cure Fraction Estimation
VariableAll Patients (n = 1371)Bologna Patients (n = 883)Padua Patients (n = 488)P Value
  1. a

    Continuous variables are reported as medians and interquartile ranges (25th to 75th percentiles).

  2. b

    The recipient age ranged from a minimum of 18 years to a maximum of 72 years.

  3. c

    The MELD score ranged from a minimum of 6 to a maximum of 46.

  4. d

    The donor age ranged from a minimum of 8 years to a maximum of 95 years.

  5. e

    The values within parentheses are 95% confidence intervals.

Recipient age (years)ab55 (48-60)55 (47-61)55 (48-60)0.75
Recipient sex: male [n (%)]989 (72.1)646 (73.2)343 (70.3)0.26
Etiology [n (%)]    
HBsAg-positive cirrhosis350 (25.5)249 (28.2)101 (20.7)0.002
HCV cirrhosis685 (50.0)428 (48.5)257 (52.7)0.14
Alcoholic cirrhosis202 (14.7)115 (13.0)87 (17.8)0.02
Cholestatic disease106 (7.7)75 (8.5)31 (6.4)0.17
Other123 (9.0)84 (9.5)39 (8.0)0.38
HCC [n (%)]528 (38.5)356 (40.3)172 (35.2)0.07
Within Milan criteria [n (%)]423 (30.9)298 (33.7)125 (25.6) 
Total bilirubin (mg/dL)a3.13 (1.5-7.91)3.61 (1.62-10.05)2.53 (1.33-5.15)<0.001
Serum creatinine (mg/dL)a0.92 (0.79-1.20)0.95 (0.80-1.20)0.89 (0.78-1.13)0.004
International normalized ratioa1.53 (1.28-1.88)1.61 (1.34-2.00)1.37 (1.22-1.63)<0.001
MELD scoreac17 (12-23)18 (13-24)14 (11-19)<0.001
6-14 [n (%)]543 (39.6)285 (32.3)258 (52.9) 
15-20 [n (%)]375 (27.4)241 (27.3)134 (27.5) 
21-30 [n (%)]365 (26.6)287 (32.5)78 (16.0) 
>30 [n (%)]88 (6.4)70 (7.9)18 (3.7) 
Donor sex: male [n (%)]746 (54.4)478 (54.1)268 (54.9)0.82
Donor age (years)d58 (43-70)61 (45-72)54 (39-66)<0.001
D-MELD scorea876 (570-1302)1001 (651-1450)722 (480-1026)<0.001
<338 [n (%)]113 (8.2)59 (6.7)54 (11.1) 
338-1628 [n (%)]1078 (78.6)667 (75.5)411 (84.2) 
>1628 [n (%)]180 (13.1)157 (17.8)23 (4.7) 
Overall survival (%)e   0.37
1 year87.0 (85.1-88.7)86.3 (83.8-88.3)88.3 (85.6-90.2) 
3 years77.8 (75.4-80.0)77.8 (74.8-80.5)77.8 (73.7-81.3) 
5 years73.3 (70.7-75.7)72.8 (69.5-75.8)74.2 (69.8-78.1) 
10 years65.6 (62.3-68.6)64.8 (60.8-68.5)66.7 (60.5-72.2) 
Figure 1.

Overall relative survival from the cure model fit. Notably, the relative survival plot for all patients falls within the 95% confidence interval of the Kaplan-Meier estimate, and this indicates that the model is well calibrated. Uncured patients experienced 50% survival 2.29 years after transplantation. There were 990 censored patients (72.2%).

Cure Model Results

The cure model showed that in the entire study population, the overall probability of being cured by LT was 63.4% (95% confidence interval = 52.6%-72.0%), and the overall median survival time for uncured patients was 2.29 years (Fig. 1). The excess of hazard after transplantation is plotted in Fig. 2: it started at a 100-fold risk with respect to the general population soon after transplantation and decreased progressively during follow-up. However, although the hazard excess of all patients tended to approximate zero with the passage of time, that of the uncured patients remained approximately 10%.

Figure 2.

Excess hazard rates from the cure model fit. This measure represents the excess hazard related to LT. The sum of the excess hazard and the expected hazard for the general population represents the overall hazard for transplant patients.

Cure fractions and median survival times for uncured transplant patients stratified by clinical features are detailed in Table 2. The best cure fraction was observed for patients undergoing transplantation for alcoholic liver disease (76.4%), whereas the worst cure fraction was observed for patients undergoing transplantation for HCV cirrhosis (54.2%). Among the uncured recipients, the longest survival time was observed for younger recipients (7.31 years). Clinical variables were further stratified, and the cure fraction results are presented in Table 3. The probability of being cured by LT decreased as the recipient age increased. Younger transplant patients without HCV who had favorable donor-recipient matches (ie, low D-MELD scores) experienced the highest probability of being cured by LT (90.1%); conversely, the lowest probability was observed for elderly HCV patients with high D-MELD scores (34.6%).

Table 2. Estimation of Cure Fractions and Survival for Uncured Transplant Patients Stratified by Clinical Features
 Patients (n)Cure Fraction (%)aMedian Survival of Uncured Patients (Years)
  1. NOTE: Continuous variables have been categorized on the basis of their median values (see Table 1).

  2. a

    The values within parentheses are 95% confidence intervals.

All patients137163.4 (52.6-72.0)2.29
Bologna patients88360.1 (43.3-76.2)2.72
Padua patients48863.8 (54.8-72.8)2.09
Recipient age < 55 years67667.4 (58.7-76.0)7.31
Recipient age ≥ 55 years69558.7 (48.1-69.3)1.41
Male patients98965.4 (55.7-75.2)2.14
Female patients38258.9 (40.9-76.9)2.55
HCV-positive68554.2 (45.3-63.1)2.43
HCV-negative68675.0 (66.1-83.9)1.51
Alcoholic disease20276.4 (66.5-86.1)2.20
Cholestatic disease10668.1 (54.3-81.9)2.30
Other etiologies12364.1 (50.0-78.3)2.29
Presence of HCC52860.0 (48.9-71.0)3.22
Absence of HCC83864.8 (55.9-73.8)1.68
MELD score < 1767868.8 (60.4-77.2)2.43
MELD score ≥ 1769358.6 (48.4-68.8)2.03
Donor age ≤ 58 years69267.4 (58.6-76.2)2.27
Donor age > 58 years67958.2 (47.2-69.3)2.28
Table 3. Quantification of the Cure Fraction With Respect to Age and Covariates
 Cure Fraction (%)a
Age: 18-48 YearsAge: 49-55 YearsAge: 56-60 YearsAge: >60 Years
  1. a

    The values within parentheses are 95% confidence intervals.

Baseline cure fraction67.4 (57.7-77.1)64.6 (55.8-73.5)60.5 (50.4-70.5)56.3 (44.2-68.4)
Male recipients69.7 (60.8-78.7)65.7 (56.8-74.6)61.7 (51.6-71.8)57.7 (45.5-69.8)
Female recipients66.1 (54.9-77.3)62.1 (51.1-73.3)58.0 (46.3-69.8)54.0 (40.6-67.4)
All HCV patients57.8 (45.9-69.6)54.9 (43.4-66.5)52.1 (40.0-64.3)49.3 (35.8-62.8)
Absence of HCC58.3 (46.2-70.3)55.6 (43.8-67.3)52.9 (40.4-65.3)50.1 (36.3-64.0)
Presence of HCC56.2 (42.7-69.7)53.5 (40.4-66.7)50.8 (37.3-64.3)48.1 (33.5-62.7)
D-MELD score < 33872.5 (60.8-84.2)70.1 (58.6-81.6)67.7 (55.5-80.0)65.3 (51.7-79.0)
D-MELD score = 338-162857.1 (44.6-69.7)54.7 (42.5-67.0)52.4 (39.6-65.1)49.9 (35.9-64.0)
D-MELD score > 162841.8 (24.1-59.4)39.4 (22.0-56.7)37.0 (19.4-54.6)34.6 (16.1-53.1)
Non-HCV patients75.6 (67.7-83.6)72.8 (65.1-80.5)70.0 (61.2-78.8)67.2 (56.5-77.9)
Absence of HCC76.0 (68.0-84.1)73.3 (65.4-81.2)70.6 (61.6-79.6)67.9 (56.9-78.9)
Presence of HCC74.0 (63.7-84.3)71.3 (61.4-81.2)68.6 (58.1-79.1)65.9 (53.9-77.9)
D-MELD score < 33890.1 (81.8-98.4)87.7 (79.4-96.0)85.3 (55.5-75.8)82.9 (71.4-94.4)
D-MELD score = 338-162874.7 (66.4-83.0)72.3 (64.2-80.4)69.9 (60.8-79.1)67.5 (56.4-78.6)
D-MELD score > 162859.3 (45.1-73.6)56.9 (42.9-71.0)54.5 (40.0-69.1)52.2 (36.4-67.9)

In Fig. 3, the time elapsing since transplantation is plotted against the level of confidence in order to produce an estimation of the time to cure. The entire study group exceeded the 90% confidence level 10 years after transplantation (overall time to cure), and this meant that survivors 10 years after LT could be considered cured with 90% certainty. Various times to cure with respect to clinical features and levels of confidence are reported in Table 4. For non-HCV patients, the estimated time to cure, when the confidence level was set at 90%, was 6.22 years. At the same confidence level, the time to cure for HCV patients was estimated to be 14.78 years. The time necessary to obtain a 95% confidence level ranged from 10.76 to 25.04 years after transplantation.

Figure 3.

Overall time to cure and time to cure stratified by HCV positivity. The time to cure was estimated as a function of time and the level of confidence. When a 90% level of confidence was chosen, the time to cure occurred 10 years after transplantation.

Table 4. Estimation of the Time to Cure for Transplant Patients at Different Levels of Confidence
 Patients (n)Time to Cure (Years)
80% (α = 0.2)90% (α = 0.1)95% (α = 0.05)
  1. NOTE: Continuous variables were categorized on the basis of their median values (see Table 1). Because cure models define cure as occurring when time tends to infinity, the time to cure was estimated on the basis of different levels of confidence. For example, in the entire study group, cure was achieved with a 90% level of confidence 10 years after LT.

All patients13713.1610.0118.86
Recipient age < 55 years6762.148.3416.74
Recipient age ≥ 55 years6954.5812.2421.80
Male patients9892.769.3017.92
Female patients3824.0411.3320.54
HCV-positive6856.2914.7825.04
HCV-negative6861.016.2213.90
Alcoholic disease2020.944.2610.76
Cholestatic disease1061.947.9416.16
Other etiologies1232.959.6518.42
Presence of HCC5284.2611.8621.46
Absence of HCC8382.849.6118.55
MELD score < 176781.757.5215.49
MELD score ≥ 176934.5011.9721.30
Donor age ≤ 58 years6922.208.5817.27
Donor age > 58 years6794.8512.8422.80

DISCUSSION

In the 1990s, cure rate models, which are survival models incorporating a cure fraction, emerged as powerful analytic tools in statistical literature, but unfortunately, they have remained underused in clinical settings. These models are mainly applied in oncology,[14-17] and their importance is supported by the US National Cancer Institute, which has developed freely accessible statistical software that can fit cure models.[18] In oncology, cure models can be interesting because they make it possible to know if and when a survivor can be considered cured of his or her cancer. Likewise, patients undergoing LT can experience very long-term survival.[3, 4] To the best of our knowledge, this is the very first report to estimate the cure fraction for transplant patients. This measure represents an interesting way of characterizing and studying patients' outcomes after transplantation (a clinical scenario in which some patients can achieve very long survival times). The clinical utility of the cure fraction lies mainly in the possibility of correctly informing transplant candidates and recipients about the probability of success for their transplant and providing a single and understandable measure rather than survival rates. In fact, some major concerns of transplant candidates are related to the uncertainty of being able to return to a normal life, and the present results can help clinicians to give more precise answers to candidates.

Data sets in which there might be a subset of long-term survivors among patients can be easily identified by an examination of the survival curve. If the survival curve tends to a plateau at the end of the study, a cure model can be an appropriate and useful way of analyzing data.[5] As can be noted from the present analysis (see Fig. 1), this is a feature that can be found after LT.[19] In the present study, we observed that the proportion of patients who would be cured with transplantation was approximately 63%: for a candidate or a transplant recipient who would like to know what his or her probability of being cured by LT is, this could well represent the desired information. This measure represents the fraction of patients who will face the same mortality risk after transplantation that the general population faces, although it depends on clinical circumstances.

Medical circumstances able to modify the cure fraction are those well known to be able to affect survival after transplantation. Consequently, the best cure fractions (Table 3) were observed for non-HCV recipients (ranging from 52.2% to 90.1%), and the worst cure fractions were observed for HCV recipients (ranging from 34.6% to 72.5%). However, it is interesting to observe how the survival of uncured patients changed between these 2 groups. In fact, the median survival of uncured patients, who could be considered fatal cases bound to die, was higher for HCV patients (2.43 years) versus non-HCV patients (1.51 years). A possible explanation relies on the clinical observation that the cause of death for HCV patients is often a chronic disease (ie, HCV recurrence) that will slowly lead to death; conversely, most non-HCV patients are cured, but those who are uncured experience a disease with a rapid and unchangeable clinical course as the cause of death. Nevertheless, the longer median survival of uncured HCV patients agrees with the capabilities of medical care, which can guarantee survival for these patients even if a cure can be hard to achieve. It is also interesting to observe that the cure fraction was higher for younger recipients and that this was accompanied by the longest survival estimated for uncured patients. This finding is consistent with the higher life expectancy foreseen for younger people. From the opposite point of view, this finding is in keeping with the fact that, even if older recipients are generally carefully screened before surgery, their long-term survival is significantly less than that of other age groups. The literature reports that after the first year, the major causes of death are age-related problems, including cardiovascular, cerebrovascular, and respiratory events and de novo cancers.[19, 20] It should be noted that most such cured patients become new patients with cardiovascular, metabolic, renal, and sometimes even oncological diseases, which reduce their life expectancy. This aspect is likely already captured by the cure model because it can be speculated that the cure fraction would be higher than 63.4% if recipients were not dying from such long-term complications.

In addition to the question whether a recipient can be cured, the second question is when a patient can be considered cured. As already outlined in the Patients and Methods section, cure models define cure as occurring when time tends to infinity, so it is impossible to obtain a precise time to cure. However, in the present study, we attempted to assess when survivors could be considered cured with a reasonably low level of uncertainty by setting the levels of significance at 0.05, 0.1, and 0.2; this means that the findings have 95%, 90%, and 80% levels of confidence, respectively (Table 4). At the 90% level of confidence, survivor patients could be considered statistically cured from the tenth year after transplantation onward. The shortest time to cure was observed for alcoholic recipients, but unfortunately for HCV recipients, the time to cure was approximately 15 years after transplantation. At a higher level of confidence, the time after transplantation always exceeded 10 years, but the latter result has to be considered with caution because in the present study, the longest follow-up did not exceed 14.4 years.

Two particular aspects of the present analysis deserve dedicated discussions. First, even though the present work was conducted with a relatively large number of patients, the results came from just 2 centers. Thus, probably not all recipient features and outcomes were captured as a result of transplant and allocation policies. In addition, even if stratification had been applied, the size of certain subgroups would have become too small to allow a reliable fit of the cure model. For example, for recipients with HCV, the cure fraction was relatively low, but it is known that other factors such as the HCV genotype and the possibility of achieving a sustained virological response before and/or after transplantation can have an impact on patient survival and, ultimately, the cure fraction. The present article shows that a cure model can be successfully applied to the LT setting, but these aspects probably require further, larger (eg, through an analysis of European Liver Transplant Registry or United Network for Organ Sharing databases), and dedicated studies. Second, how this measure can be used to set allocation policies is intriguing. In particular, there is presently no standard for designating LT as futile, even if it has been suggested that a 5-year patient survival rate less than 50% could define an unsustainable donor-recipient match.[9] It seems rational to use the cure fraction, a measure that is not time-dependent, to derive suggestions for defining futile transplantation, but before any conclusions can be drawn, a benchmark for assessing the sustainability of LT is needed,[21] eventually through cost-effectiveness analyses.[22] However, whether a cure fraction less than 50%, such as that found for older HCV recipients with or even without an unfavorable donor-recipient match, can be considered an acceptable outcome after LT is debatable.

In conclusion, we have presented a new statistical measure for assessing survival after LT. The cure fraction can be of interest not only to clinicians but also to candidates who would like to be fully informed about what awaits them after LT. Saying that LT is the only chance to cure end-stage liver disease is not merely an optimistic view of the treatment's effectiveness because transplantation can really achieve a statistical cure.

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