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.
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© 1999 Lippincott Williams & Wilkins, Inc.
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