# A SIMPLE MODEL TO ESTIMATE SURVIVAL AFTER RETRANSPLANTATION OF THE LIVER1

To formulate a model predicting survival after liver retransplantation, we analyzed in detail the last 150 cases of hepatic retransplantation at UCLA. Cox proportional hazards regression analysis identified five variables that demonstrated independent simultaneous prognostic value in estimating patient survival after retransplantation: (1) age group (pediatric or adult), (2) recipient requiring preoperative mechanical ventilation, (3) donor organ cold ischemia ≥12 hr, (4) preoperative serum creatinine, and (5) preoperative serum total bilirubin. The Cox regression equation that predicts survival based on these covariates was simplified by assigning individual patients a risk classification based on a 5-point scoring system. We demonstrate that this system can be employed to identify a subgroup of patients in which the expected outcome is too poor to justify retransplantation. These findings may assist in the rational selection of patients suitable for retransplantation.

Dumont-UCLA Center for Liver Transplantation and Surgery, Department of Surgery and Department of Biomathematics, UCLA Medical Center, Los Angeles, California and Transplantation Services, Baylor University Medical Center, Dallas, Texas

^{1}Presented in abstract form at the 17th Annual Meeting of the American Society of Transplant Physicians, May 9-13, 1998, Chicago, IL.

^{2}Dumont-UCLA Center for Liver Transplantation and Surgery, Department of Surgery.

^{3}Address correspondence to: J.F. Markmann, Dumont-UCLA Center for Liver Transplantation and Surgery, Department of Surgery, UCLA Medical Center, 77-120 CHS, Los Angeles, CA 90095-7054.

^{4}Department of Biomathematics, UCLA Medical Center.

^{5}Transplantation Services, Baylor University Medical Center.

^{6}Department of Surgery Hospital of the University of Pennsylvania.

Received 26 May 1998.

Accepted 27 October 1998.

*Abbreviations: BUMC, Baylor University College of Medicine; ICU, intensive care unit; PNF, primary nonfunction; UNOS, United Network for Organ Sharing.

The demand for liver allografts far exceeds the currently available supply. As a result, a growing number of patients die while awaiting liver transplantation. For this reason, the optimal use of each donor organ is paramount ^{(1)}. Consequently, recent efforts in the field have focused on maximizing organ utilization by promoting expanded use of living donation and split liver transplantation, and reducing demand by proscribing transplantation in patients whose predicted outcome after transplantation is too poor to justify use of an organ ^{(2)}. Nowhere has the appropriateness of transplantation been questioned more than in the care of patients with a failed initial graft ^{(3)}. The controversy over the obligation of the transplant team to a patient who has already received a transplant versus a patient awaiting a primary transplant is further fueled by the finding that patients undergoing retransplantation have significantly inferior outcome compared to patients receiving a first graft ^{(4-6)}. Moreover, retransplantation dramatically increases health care resource consumption and cost ^{(7)}.

We recently examined the survival of all 299 patients retransplanted (with 356 livers) at UCLA over a 13-year period ^{(8)}. We found that the 1-year patient survival after retransplantation was 62% compared to an 83% survival for patients undergoing primary transplantation during the same time period. In addition, the intensive care unit (ICU*) and hospital length of stay and total charges accrued were markedly greater for retransplanted patients. However, for moral and ethical reasons, along with the near 50% long-term survival in those receiving multiple grafts, retransplantation should still be considered an appropriate clinical option. However, it should only be offered to patients with a reasonable likelihood of achieving an outcome justifying the use of valuable organs.

To this end, this work defines a mathematical model capable of predicting survival after hepatic retransplantation. It was our goal that the model has both theoretical and practical clinical applicability. For this reason, we required that it be based on a small number of variables easily accessible before transplant that were simple (noninvasive) and inexpensive. The model we describe fulfills these criteria and was validated using independent retransplant patient data sets from another institution (Baylor University Medical Center [BUMC]) and the United Network for Organ Sharing (UNOS) registry.

## PATIENTS AND METHODS

*UCLA retransplanted patients.* From June 1, 1992 to October 31, 1996, the Dumont-UCLA liver transplant center performed 1097 consecutive liver transplants. During that period, 150 patients were retransplanted with 170 liver allografts (18 patients required a total of three grafts each and 2 patients a total of four grafts each). Pediatric patients (<18 years of age) comprised 25 of the 150 patients retransplanted (17%). At the time of retransplantation, 115 patients (77%) were UNOS status 1 (ICU care), 18 (12%) were UNOS status 2 (hospitalized but not in the ICU), and 17 (11%) were UNOS status 3 (admitted from home for transplantation).

*Study design and end-points.* We performed a retrospective analysis of the medical record of the 150 retransplanted patients. Follow-up was confirmed for all patients by documentation of either recent clinic visit or laboratory testing, or by telephone verification of the patient's status (alive or deceased). Graft survival, defined as time from transplant to patient death or retransplant, and patient survival served as study end-points. Patient survival was calculated from the date of the first retransplant.

*Variables studied.* Donor and preoperative recipient variables were studied for their impact on survival. The four donor variables examined were: age, days of hospitalization before procurement, maximum dosage of dopamine, and cold ischemia time (defined as the time from arterial cross-clamping in the donor to portal reperfusion in the recipient). The seven recipient variables examined were: UNOS status, the need for pretransplant ICU care, pretransplant hospital care, pretransplant mechanical ventilation, renal failure requiring pretransplant dialysis (dialysis), primary diagnosis, the cause of primary graft failure, interval from primary to subsequent transplants, and primary immunosuppressant (FK vs. cyclosporine). The following four pretransplant laboratory values were also analyzed: total bilirubin, prothrombin time, blood urea nitrogen, and creatinine. For the multivariate analysis, the continuous variables creatinine and total bilirubin were tested untransformed and after logarithmic transformation.

*Statistical analyses.* Survival was estimated using the Kaplan-Meier method. For univariate survival analysis, continuous variables were dichotomized at their median. Variables found to have univariate significance were then analyzed for independent significance using Cox multivariate regression using JMP (SAS Institute Inc, Cary, NC) or the SAS statistical software package (SAS Institute Inc., Cary NC) ^{(9,10)}. In selecting variables for the regression model, both forward and backward stepwise procedures and best subset procedures were used. Unless otherwise specified, a probability value of <0.01 was required for variable inclusion in the model. No first-order interactions between variables were identified. To evaluate the fit between the regression model and the actual patient data, the survival curve predicted by the model was compared with observed patient survival calculated by the Kaplan-Meier method. Probability values for survival differences were assessed by a rank-sum test.

*Data sets used for validation of the Cox model.* For cross-validation of the Cox regression model derived from patients retransplanted at UCLA, we utilized two independent data sets. The first data set we tested was from the BUMC liver transplant program. It included data on 149 consecutive liver retransplants in 135 patients during the period from May 1985 through March 1998. Thirteen patients received a third graft and 2 patients a fourth graft. Patient survival and the five variables (pretransplant mechanical ventilation, ischemia, creatinine, total bilirubin, and age group) were included in the data base. Data were complete for 128 of the 149 transplants (86%). For statistical analysis, only those patients retransplanted after January 1, 1992 with complete data were included (n=58) so that the date of transplant was comparable to that of the UCLA cohort.

Second, we obtained a data base including all retransplanted patients in the UNOS data registry during the period from 1988 through 1996 (n=3347). This included the following variables: graft and patient survival, donor age, donor treatment with dopamine (yes or no), duration of donor organ cold ischemia, recipient UNOS status, ICU versus hospital versus non-hospital care at the time of transplant, pretransplant mechanical ventilation, dialysis (reported only since 1994), creatinine, total bilirubin, prothrombin time, recipient age, recipient sex, primary diagnosis, and retransplant diagnosis (primary nonfunction [PNF] or other). Because of the high level in incomplete data reporting before 1994 and to make the date of transplant more comparable to the other data sets, we performed survival analysis only on UNOS patients retransplanted after April 1, 1994. This includes a subset of 1117 retransplanted UNOS patients, for which 861 patients had complete data for the five variables of interest: pretransplant mechanical ventilation, ischemia, creatinine, total bilirubin, and age group.

## RESULTS

*Univariate and multivariate regression analysis.* By univariate comparison, nine variables were found to be significantly associated with UCLA patient survival (Table 1) ^{(8)}. Of these, five preoperative conditions were identified as independent predictors of survival by Cox proportional hazards regression analysis: (1) use of a donor organ with >12 hr of cold ischemia time (ischemia), (2) recipient requirement for preoperative mechanical ventilation, (3) preoperative serum creatinine level, (4) preoperative serum total bilirubin, and (5) whether the recipient was a child or an adult (age group). Each of these covariates demonstrated statistical significance (*P*<0.05) except age group. Age group did not reach statistical significance (*P*=0.20), but was included for both biological and practical considerations. The resulting Cox equation that estimates 1-year survival in retransplanted patients is shown: *estimated survival*=0.611^{exp (R-1.6856)}, where 0.611 is the mean 1-year survival for the patient group and *R* is the patient risk score calculated by: *R*=(0.726× *cold ischemia*+0.561×*ventilator status*+0.0292×*serum bilirubin*+0.202×*serum creatinine*+0.526× *age group*). In this equation, the three categorical variables are defined as follows: *cold ischemia*=1 if ≥12 hr and 0 if <12 hr, *ventilator status*=1 if preoperative ventilation is required and 0 if not, *age group*=1 if adult and 0 if child. The two continuous variables *serum bilirubin* and *serum creatinine* are represented as preoperative serum values in mg/dl. The mean overall risk score for the group is 1.6856.

This equation can be used to predict individual patient survival after retransplantation. In fact, one can select what might be considered an acceptable outcome and identify patients with risk scores predicting survival either above or below that level. (The relationship between Cox risk score and predicted survival at 1 year is shown in Fig. 1.) For example, we have previously suggested that an expected 1-year survival of <40%, (which is less than half of that anticipated with a primary transplant at most centers) represents an unacceptable use of a valuable organ. Thus, from the above equation (and Fig. 1), we determined that a risk score of >2.3 corresponds to an expected 1-year survival of <40%. The observed survival of UCLA patients stratified for risk score above or below 2.3 is shown in Figure 2. The survival of the low-risk group (Cox risk score <2.3) was significantly less than those with a the high-risk score (*P*<0.0001).

To determine how well the predicted survival fit with observed survival, the survival curve predicted by the Cox model was compared for patients with risk score of greater or less than 2.3 with the actual Kaplan-Meier survival curve of patients with the same scores. Good fit between Cox predicted and Kaplan-Meier observed survival is seen for UCLA patients who are grouped above (Fig. 3, top) and below (Fig. 3, bottom) the 2.3 Cox risk score threshold.

*Simplified model to predict survival after liver retransplantation.* Although the formula above is the most precise representation of the data we presented, it proves somewhat cumbersome for routine clinical application. For this reason, we employed a simplified schema in which all five variables were binary in nature (i.e., either 0 or 1). This was accomplished by dichotomizing the two continuous variables creatinine and total bilirubin at their median value (1.6 and 13 mg/dl, respectively), thereby rendering them categorical. Each covariate was then assigned an equal weight of 1 point (i.e., 1 point was awarded for adults, organ ischemia <12 h, preoperative ventilator requirement, total bilirubin ≥13, and creatinine ≥1.6). Patients were then grouped into one of six risk classes, based on the sum total of points obtained.

Using the Cox equation, we calculated the predicted survival for UCLA patients for each of the 32 possible combinations of the five binary covariates. These classes were segregated by age group and are shown in Table 2. For each age group, there were six risk classes with nonoverlapping survival estimates based on whether none, one, two, three, four, or all five of the conditions were satisfied. This is represented as risk classes 0-5. For example, for adults in whom only one of the four (non-age-related) conditions was present (risk class=2), Cox predicted survival ranged from 67% to 72% at 1 year. If risk class=3, survival ranged from 43% to 53%. If risk class=4, the Cox risk score was ≤2.4 and predicted survival ranged from 20% to 27%. If all five conditions were present, estimated survival was 6.0% at 1 year. A similar pattern was evident for pediatric patients, and survival for a given risk class was similar between pediatric and adult patients. Note that, inasmuch as 1 point is added for being an adult, the maximum pediatric class is 4. Similarly, the lowest possible risk class for an adult is 1 compared with a possible 0 class for pediatric patients. This is reflected in the better overall survival seen for pediatric patients compared with adults, and is a direct consequence of older recipient age conferring a negative impact on survival (Table 2).

*Actual survival based on UCLA risk class.* In an attempt to confirm the discriminatory value of risk class in predicting survival, we calculated Kaplan-Meier curves for retransplanted adult patients segregated by UCLA risk class calculated retrospectively. As can be seen in Figure 4, survival at 1 year decreases incrementally with increasing class and demonstrates approximate, qualitative, and quantitative fit with estimated 1-year survival predicted by the Cox regression equation detailed in Table 2. Because of small sample size, patients having 4 or 5 total risk points were grouped together. This high-risk group (class 4 or 5) was comparable to patients selected based on Cox risk score >2.3, and who have expected survival <40% at 1 year.

*Validation of risk score and UCLA risk class in predicting retransplanted patient outcome.* To evaluate the applicability of retransplant patient Cox equation determined risk score and the simplified UCLA risk class model to other patient populations, we applied both models to two independent sets of retransplanted patient data. First, we analyzed the survival of patients retransplanted at the BUMC. A risk score calculated using UCLA patient-derived Cox equation was used to stratify Baylor patient survival by risk score above or below the threshold value of 2.3. Data are presented in Figure 5 showing actual Kaplan-Meier survival and Cox predicted survival for patients scoring <2.3 (Fig. 5A) or ≥2.3 (Fig. 5B). Although only a small number of patients were in the high-risk group, good fit between predicted and observed survival is seen.

Similar to the calculation used for UCLA patients, we also examined Baylor patient survival based on segregation by UCLA risk class criteria. Baylor patients were assigned a risk class of 0-5, based on the cumulative points obtained for presence (1 point) or absence (0 points) of each of the five parameters: (1) donor organ ischemia >12 hr, (2) recipient age >18 years, (3) requirement for preoperative mechanical ventilation, (4) preoperative serum total bilirubin ≥13 mg/dl, and (5) preoperative serum creatinine level. ≥1.6. Figure 6 shows the observed survival of 58 patients stratified for risk class. No patients in the BUMC data base scored 0 of 5 possible points, reflecting in part the fact that they were predominantly adults (98%). Class 4 and 5 were combined because of the small number of patients in these groups. The results for retransplanted Baylor patients were qualitatively similar to that seen for UCLA patients. Patient survival correlated with risk class, and a statistically significant difference (*P*=0.007) in Kaplan-Meier survival is evident comparing BUMC patients scoring 0-3 (1 year, 67%) versus those scoring 4-5 (1 year, 40%).

A similar approach was used to analyze retransplanted patients reported to the UNOS data registry. Survival of 861 UNOS patients stratified by risk score is shown in Figure 5 (C and D). Comparison of Cox predicted survival versus Kaplan-Meier actual survival shows good fit for low-risk patients. For high-risk patients, i.e. those with risk score ≥2.3, the Cox model slightly overestimates mortality for the group. We believe this is attributable to the fact that documentation of complete follow-up was not possible for the UNOS patients, as it was for both UCLA and Baylor patient groups.

We also examined UNOS patient survival based on UCLA risk class (Fig. 7). As with UCLA and BUMC patients, outcome is highly correlated with risk class. Patients in class 4 or 5 had a 1-year survival rate of 43.7%. This was significantly less than the 67% 1-year survival seen in patients within risk class 3 or less (*P*<0.0001). Again, the slightly higher overall survival in the high-risk group is likely attributable to incomplete follow-up for the UNOS cohort.

*Comparison of patient populations.* The data base from UCLA, BUMC, and UNOS were compared for patient characteristics (Table 3). Patient populations were similar with respect to 1-year patient survival, average cold ischemia time, and the preoperative laboratory values for total bilirubin and creatinine. The cohorts differed considerably, however, with respect to the percentage of adult patients and the requirement for the mechanical ventilation preoperatively. These differences are evident in the relative percentage of patients listed as UNOS status 1, and also in the proportion of patients within the various risk classes.

*Relationship of resource utilization to risk class.* We sought to determine whether retransplanted patients in high-risk versus low-risk classes would differ in their health care resource utilization. We analyzed a subset of retransplanted patients (n=81, of whom n=76 had relevant data) in which both transplants were performed during the same admission (Table 4). We examined mean total length of hospital stay, mean length of ICU stay, and median total charges accrued during the admission. Charges are expressed a relative charges comparing low- and high-risk groups. Data for length of stay were compared to a group of 862 unselected transplants performed during the same time period. Length of stay, especially ICU length of stay, as well as total charges accrued were greater in the group of patients with risk score 4-5 compared with those scoring only 0-3. Statistical significance was not achieved (*P*=0.2), however, which is likely a result of the wide range in both groups.

## DISCUSSION AND CONCLUSIONS

We investigated the preoperative factors predictive of poor outcome after hepatic retransplantation. In so doing, we defined a mathematical model that adequately predicts survival after retransplantation. It is based on five noninvasive and readily available clinical parameters. Application of this model to a liver retransplant candidate can provide a reliable estimate of expected survival. For example, we have suggested that an expected 1-year patient survival of less than 40% is an unreasonable use of an organ that would be anticipated to result in a near 80% 1-year survival in a recipient of a primary transplant. Thus, we suggest that patients with a Cox risk score of 2.3 or above, which predicts 1-year survival of <40%, should not be considered suitable candidates for retransplantation.

Because the Cox regression equation is somewhat complex, we have also derived a simplified approach, which we have termed the UCLA risk classification; this groups patients into five risk classes based on 5-point scoring system. A single point is received for each of the following parameters: adult (>18 years old), organ cold ischemia >12 hr, preoperative mechanical ventilator requirement, total bilirubin >13 mg/dl, and creatinine >1.6. Patients having 4 or 5 out of a possible 5 total points had 1-year survival of approximately 27% in UCLA patients (and an average Cox risk score of 2.6) and approximately 40% in both BUMC and UNOS registry patients. The survival of patients scoring 4 or 5 was significantly less than the survival of patients with score of 3 or less. This risk classification system adequately discriminated high-risk/low-survival patients in all three data bases to which it was applied.

The results derived from the UNOS data are statistically the most convincing validation of our risk class model, because the data represent the participation of a large number of transplant centers and permit analysis of a vast number of patients. Because of the high frequency of missing data, however, we were concerned about possible selection bias resulting from incomplete data reporting and follow-up. For this reason, we cross-validated our model on the data from another institution. In this case, although the data set contained a smaller number of patients, we feel the follow-up and data reporting are more reliable. In both cases, however, the risk class system adequately discriminated high- and low-risk patients. For the UNOS cohort, the actual survival was slightly higher than that estimated by the model. This could be easily explained if follow-up or reporting of mortality data were incomplete. For obvious practical reasons, we were unable to confirm directly the current status of UNOS patients as we were able to do for UCLA and BUMC patients. Thus, although the absolute survival of the UNOS patients may be less meaningful, the model clearly discriminated high- and low-risk patients.

The UNOS data base was also studied as an independent data set to determine which variables proved significant using Cox proportional hazard methodology (data not shown). The model we derived from this analysis was similar to the UCLA model, and four of the five same covariates were independently identified as significant using the UNOS data. The only covariate not included was age group, and this was statistically marginal in the UCLA analysis but forced into the UCLA equation for the reasons already mentioned. The four covariates common to both Cox models had approximately equal regression coefficients, except that the strength of cold ischemia time was half as large in the UNOS model. In addition to the four variables present in the UCLA Cox equation, the UNOS Cox analysis also identified UNOS status as an independent predictor of survival. Whether this represents an additional relevant variable overlooked in the UCLA analysis is unclear. In our prior analysis, ICU status proved significant in univariate comparison. It may be however, that the preponderance of UNOS status 1 patients in the UCLA cohort (77%) did not allow enough statistical power in the Cox analysis to accurately assess the importance of differences in the UNOS status 2 and 3 patients. In fact, analysis of our data suggested only 22% power (using a *P*-value of <0.05 and a relative risk of 0.512 for the effect of UNOS status) to confirm the effect of UNOS status on survival. Thus, our data are not negative regarding UNOS status but are inconclusive. In any case, we do not favor inclusion of this parameter in the model. All patients selected as unsuitable by both the Cox risk score and the UCLA risk class approaches were UNOS status 1. We do not feel that it is appropriate nor do we think it likely to occur that a status 2 or 3 patient be denied retransplantation. Furthermore, we favor the UCLA-derived Cox equation as the data are based on more reliable reporting and follow-up.

A number of other investigators have examined the factors associated with outcome after retransplantation ^{(11-13)}. In 1995, Doyle et al. ^{(14)} reported a large series of retransplanted patients in which factors influencing survival were analyzed by logistic regression. The variables found by these authors to be significant in determining patient survival were quite similar to those identified in our Cox risk score and UCLA risk class models. Specifically, recipient age, creatinine, bilirubin, and ventilator status were all found to be relevant. Three additional variables, donor age and gender and choice of recipient immunosuppression, also proved important in their study but not in ours.

In a more recent work, Rosen et al. ^{(15)} performed a Cox regression analysis on a set of retransplanted patients from the UNOS data registry. In their analysis, recipient age, bilirubin and creatinine were again identified as independently associated with survival. In their work, UNOS status and cause for retransplant (PNF or non-PNF) were also significant variables. An important difference between this UNOS study and our analysis of UCLA patients is that the two variables, duration of donor organ ischemia and preoperative ventilator requirement, that have the largest regression coefficients in our UCLA model were not considered in that analysis. Whether either PNF or UNOS status would remain as significant covariates had pretransplant mechanical ventilation status and cold ischemia been included in their work is unknown; however, in our own Cox analysis of the UNOS data, PNF was not significant when entered with pretransplant mechanical ventilation status, and UNOS status was only statistically significant comparing patients in the ICU versus those awaiting transplant at home.

The similarity between the variables identified by three large and independent investigations provides strong support for the accuracy of the methodology and the validity of our conclusions. The appropriate application of this information can be reasonably debated, however. The <40% survival level we selected as unreasonable is somewhat arbitrary and may require modification depending on the patient population, and may change with relative improvements in survival that come with advances in the field of hepatic transplantation. For example, we would not routinely apply this approach to pediatric patients despite the fact that, for the same Cox risk score or UCLA risk class, the survival of adult and pediatric patients is comparable. In addition, in cases of rapid graft failure as a result of PNF or hepatic artery thrombosis, a transplant team might be more compelled to retransplant even if there is a high risk of poor outcome. Thus, such a model as we have presented, although providing valuable information for clinical decision making, does not supplant seasoned clinical experience.

It is noteworthy that, of the parameters discussed, the surgeon can control only the duration of organ ischemia. This suggests that, in transplanting patients with a number of the other negative prognostic indicators, minimizing the period of cold ischemia and the avoidance of a marginal graft are critical to optimizing success. This finding may be relevant to suggested changes in organ distribution, which by necessity incur an increase in organ cold ischemia times to allow shipping of grafts between distant regions. Ironically, this is likely to occur most frequently for the sickest, highest status recipients, which are also precisely the patients in which outcome will be impacted most negatively.

Application of the model we have described will theoretically result in improved overall survival after retransplantation and an increase in efficiency of organ utilization. In our own institution, we would anticipate that recipient selection using this system would result in an increase in 1-year survival of retransplanted patients from the current baseline of 61% to 67%, the survival rate seen in low-risk retransplanted patients. This would entail excluding from retransplantation approximately 20% of the patients that would have otherwise been transplanted (i.e., those with Cox risk score >2.3 or risk class 4 and 5).

The trend toward increased length of stay and total charges for high-risk patients is somewhat surprising, given their greater likelihood of early death after transplant. It suggests, however, that the cost to benefit ratio for this group is even higher than expected based only on examination of their survival curves. Exclusion of these high-risk individuals should also lead to increased financial efficiency by a reduction in the average cost of hepatic retransplantation and liver transplantation in general.

In summary, we believe that the model we have presented can be employed to identify patients at high risk for poor outcome after retransplantation of the liver. This should provide valuable information on which to base sound clinical judgement for the selection of candidates suitable and appropriate for retransplantation.