Key words : End-stage liver disease, Kidney transplantation, Liver transplantation, Waiting list

Introduction

Simultaneous liver-kidney transplantation (SLK) is a definitive treatment option for patients with end-stage liver disease and concomitant irreversible renal dysfunction. The number of SLKs performed has increased since the adoption of the Model for End-Stage Liver Disease (MELD) score for allocation of livers.¹ At the time of SLK offer, a potential critical organ acceptance decision is whether to accept a high-risk organ or to remain on the waitlist for better quality organs.

Two donor risk scores are involved in SLK transplant. One donor risk score is the Kidney Donor Profile Index (KDPI), a tool that helps in decision-making regarding offers of deceased donor kidneys. Specifically, the KDPI score predicts how long a deceased donor kidney is expected to function relative to all other deceased donor kidneys from the past year in the United States.² Kidneys with KDPI >85% are deemed high-risk organs. The KDPI has also been shown to be a reliable measure in quantifying liver allograft quality and estimating graft survival.³ The other donor risk score is the Donor Risk Index (DRI), a measure that is used to predict liver graft survival after transplant.⁴ The DRI is not provided with organ offers and must be calculated, unlike the KDPI, which is available at the time of the organ offer in the United States.

For patients undergoing SLK, recipients of organs with KDPI >85% have been shown to have worse patient and graft survival.³ However, in certain populations, high-KDPI kidney transplant has been associated with higher short-term risk but improved long-term mortality; this suggests that, in some cases, taking a higher-risk organ is beneficial for the patient from an overall survival perspective.⁵

The decision to accept or decline an organ is often predicated on the candidate’s expected outcome if the offer is accepted versus if it is declined and the candidate remains on the waitlist. The risk of declining an organ may outweigh the risk of accepting a higher-risk organ.⁶ Characterizing which waitlist candidate may benefit from accepting a high-risk organ for SLK transplant is an important topic and may lead to program-specific decisions regarding acceptance of high-risk organs.⁷

Our study aimed to answer the question of when a patient who requires an SLK should be counseled to accept organs from high-risk donors because it would increase overall survival versus waiting for lower-risk organs. Using the prescriptive analytics technique of Markov microsimulation allowed us to determine the critical decision factors involved in deciding when to use high-risk organs for an SLK transplant. This prescriptive modeling strategy has been utilized previously to help tailor decision making on organ acceptance in transplant populations.8 Our study examined overall mortality as an outcome for potential SLK candidates.

Materials and Methods

We wanted to determine a transplant program’s critical decision factors to answer the question, “Should I counsel my patient requiring a simultaneous liver and kidney transplant to take the currently offered high-risk donor or wait for a lower-risk donor?”^9,10 We chose the prescriptive analytic technique of Markov microsimulation to answer this specific decision.

In constructing the Markov microsimulation model, we posited that different recipient risk groups would have different survival rates and retransplant rates following SLK transplant from donors with different risks. To control for recipient risk, we developed 3 recipient risk groups using well-known recipient risk factors. We followed these 3 risk groups throughout the transplant process with 3 different microsimulation models. To best determine the donor risk groups, we compared both the KDPI and DRI as a risk score.

The only endpoint used to determine the final decision was overall patient survival. Candidates who accepted high-risk organs were followed for survival after transplant and possible retransplant of the liver. Candidates who chose to wait for lower-risk organs were followed for survival throughout waitlist stay, possible transplant, and possible retransplant of the liver.

All risk factors and probabilities, including removal from waitlists because of death or being too sick, survival, and retransplant, for each patient risk group were taken directly from the Organ Procurement and Transplantation Network (OPTN) data released on September 7, 2018, based on data collected from February 27, 2002 to June 30, 2018. The United Network for Organ Sharing, as the contractor for the OPTN, supplied the data. The University of Washington Human Subjects Division deemed the OPTN database as deidentified and publicly available. Therefore, this study was exempt from human subject review and was exempt from ethics board approval.

We conducted a retrospective analysis of all US adult candidates on waitlists for a liver and kidney and recipients undergoing SLK transplant. Exclusion criteria included either being placed on a waitlist for or transplanted with multiple organs other than a kidney. Waitlist factors recorded included weeks on the waitlist until death or removal as a result of being too sick. Recipient factors recorded included age, sex, race, presence of any type of diabetes mellitus, grade of encephalopathy, calculated MELD score, albumin level, location of recipient at time of organ assignment (in intensive care unit, in hospital, or out of hospital), on life support, on dialysis, portal vein thrombosis, days waiting for transplant, previous abdominal surgery, previous liver transplant, previous transplant of any other organ, and previous SLK.

All donors were deceased donors. Donor factors recorded included the kidney donor risk index (KDRI) developed (by Rao and colleagues), either assigned or calculated.^11,12 The “Rao_KDRI” was converted to the KDPI using the OPTN KDRI to KDPI Mapping Table of March 9, 2018.¹³ Obtained donor factors that were used to calculate the donor-only KDRI¹¹ and DRI⁴ included age, height, weight, ethnicity, history of hypertension, history of diabetes mellitus, cause of donor death, race, serum creatinine level, hepatitis C serostatus, partial or split liver, location of sharing, and donation after cardiac death (DCD).⁴ Transplant logistic factors recorded included deidentified center code of the institution performing the transplant procedure, date of retransplant of either the liver or the kidney graft, weeks until recipient death, and cold ischemia time. Of note, DCD data were not excluded, as DCD status contributed to the KDPI and DRI calculations.

Statistical analyses
Continuous variables are presented as means and standard deviations, and categorical variables are presented as counts and percentages. Kaplan-Meier survival analysis with the log-rank test was used to find probabilities per week for death or removal from waitlist for being too sick, transplant survival, and retransplant in the Markov decision models. A Cox proportional hazards model was created to determine recipient risk factors used in determining the 3 risk recipient groups. Results with P < .05 were considered significant. Statistical analyses were performed using JMP-Pro version 14.3.0 (SAS Institute). TreeAge Pro 2019 (TreeAge Software) was used for medical decision analysis.

Donor risk group development
To determine the best measures to develop the donor risk groups, both the KDPI and the DRI were calculated. The Rao_KDRI had a mean and standard deviation of 1.15 ± 0.38, and the DRI was 1.19 ± 0.33. The Rao_KDRI and DRI had a strong 82.4% correlation. When both the Rao_KDRI and the DRI were placed in a multivariable Cox model controlling for recipient factors, a multicollinearity problem arose. In separate multivariable Cox models for 10-year survival, the SLK population Rao_KDRI had a relative risk (RR) of 1.49 (range, 1.43-1.55), and the model area under the curve (AUC) was 0.62. The DRI had a RR of 1.39 (range, 1.36-1.43), and the AUC was 0.62. Statistically, there would be no difference in using either the Rao_KDRI or the DRI to determine donor risk groups. Because the Rao_KDRI and the KDPI are given for all donors at the time of organ offers in the United States, we chose to use the KDPI to determine the donor risk groups to prevent the burden of calculating the DRI for our model. The Rao_KDRI was mapped to the KDPI and grouped into 3 groups: KDPI of 0 to <20%, KDPI of 20% to 85%, and KDPI of >85%.¹³ These 3 KDPI groups showed significant differences (P < .001) between groups in predicting patient survival following liver transplant (Figure 1).

Recipient risk group development
To develop the recipient risk groups, we used well-known risk factors for survival following liver transplant. To assign a recipient to a risk group, we performed univariable and multivariable Cox proportional hazards analysis for 10-year patient survival following SLK transplants, as shown in Table 1. In multivariable analyses, 16 variables were significantly associated with patient death following transplant. We chose to develop 3 recipient risk groups using each of the 16 significant variables from the multivariable Cox hazards analyses by assigning risk points based on the rounded ratios of their beta coefficients for death. The resulting points are included in Table 1. Recipients were then divided into 3 groups by quartiles. The lowest quartile (-2 to 4 points) was labeled low risk, the middle 2 quartiles (5 to 10 points) were labeled medium risk, and the highest quartile (11 to 23 points) was labeled high risk. These 3 recipient risk groups showed significant differences (P < .001) between groups in predicting patient survival following liver transplant (Figure 2).

Determination of survival probability after simul-taneous liver-kidney transplant
Three decision models were constructed for each of the 3 recipient risk groups (low-risk, middle-risk, and high-risk). Each of these patient risk groups was combined with the 3 donor risk groups determined by KDPI to construct a total of 9 subgroups. The number of each Recipient_Risk_KDPI group is given in Figure 3. Kaplan-Meier survival curves were constructed for each combination in 1-week increments to determine the survival probabilities. The Low_Risk recipient groups combined with the 3 KDPI donor risk groups produced the transplant cumulative failure rate for the low-risk recipient model.

Determination of kidney retransplant probability
Kidney retransplant rate in the SLK recipients was very low. The cumulative retransplant rate in the 0 to <20% KDPI group would not reach 1% loss until 10 years; for the 20% to 85% and the >85% KDPI groups, it would take 3 and 2 years, respectively, to reach a cumulative loss of 1%. For these 2 groups at 10 years, the cumulative loss was approximately 3%. Therefore, we elected not to follow the kidney retransplant rate in the decision model.

Determination of liver retransplant probability
Kaplan-Meier recurrence curves by week for the liver retransplant rate were constructed for SLK recipients. The liver retransplant rate in the low-risk group was significantly lower than in the other 2 groups. There was no difference in the liver retransplant rate between the middle-risk group and the high-risk group.

Determination of survival probability after liver retransplant
Kaplan-Meier patient survival curves by week were constructed for those recipients who required a liver retransplant following any prior SLK transplant. Death rate was high after liver retransplant for SLK recipients.

Determination of probability of death on waitlist
To track candidate risk groups in the decision models for the entire transplant process, the characteristics of candidates on the waitlist were assigned the same risk scores as developed for the recipient risk groups by using the points from Table 1. There were 14921 candidates who were on waitlists for an SLK transplant. The low-risk group had 4178 candidates (28.0%), the middle-risk group had 8724 candidates (58.5%), and the high-risk group had 2019 candidates (13.5%). The probability of removal from the waitlist was obtained from the Kaplan-Meier curves by week for those candidates who died or were removed for being too sick for the 3 risk groups. All 3 risk groups had significant differences in death rates on the waitlist for the first 3 years.

Program for organ offer probability
The decision model required a program to determine average probability of being offered organs each week (Prob_Program_Offered_Organ). We averaged the number of liver transplants per week by each transplant center over the course of the study for the weekly offer rate. The weekly rate could be converted into a weekly probability with the following formula: 1 - Exp(-[weekly rate]).¹⁴ Probabilities were determined for the 4 main blood type groups. For example, the probability of a weekly offer for AB blood type organs was very low at 0.10 ± 0.08.

Program for probability of allocation of organ to patient
The decision model required a program to determine the probability that a given patient would be allocated an offered organ while competing with other candidates on the waitlist. This probability of a specific patient being allocated the next offered donor liver and kidney with their blood type (Prob_Patient_Allocated_Organ) was determined on a case-by-case basis. For the decision model, we chose Prob_Patient_Allocated_Organ to be a normal distribution with a mean and standard deviation of 0.20 ± 0.05.

Model structure
Using the donor and recipient risk groups and the many probabilities as outlined, we constructed a 10-year Markov microsimulation model with 1-week duration for stage to answer our question at the time of an organ offer. The decision model started with the decision of whether a potential SLK recipient should accept the offer of an organ with KDPI >85% (Figure 4). If the decision was “yes,” the survival rate of the recipient receiving the organ with KDPI >85%, including the liver retransplant rate and subsequent time of survival, was determined for that recipient.

If the candidate’s decision was “no,” that candidate who continued on the waitlist had a chance of dying or being too sick to transplant on the waitlist, depending on the candidate’s risk group, availability of organ offers, and patient rank at the transplant center. The candidate could be allocated organs with a KDPI of 0 to 20% or 21% to 85%. Each time the candidate was offered organs with a KDPI >85%, the model could be rerun at that time. The waitlist survival and the survival rate of the recipient receiving the organs with KDPI of 0 to 20% or 21% to 85% were determined for that candidate. Other results determined for this candidate included total survival time, death rate on the waitlist, and subsequent liver retransplant rate.

Results

Microsimulation can run many patients (trials) through models and can simulate outcomes for patient populations using probabilities created for the model. However, most importantly, microsimulation can also be used for prescriptive analysis by conducting a sensitivity analysis of a model that reveals the most important decision factors to optimize the outcome of interest. We ran 150000 trials (patients) through the models for 10 years to develop stability of the results. P values are not useful in such simulation models.

Projected deaths while on waitlists among study patients
For the high-risk SLK candidates, rate of deaths while on waitlists was projected as 15.9% (Figure 5). During the first week of waiting, 4.6% of the candidates would be projected to die, with most deaths (14.8% of the total 15.9%) occurring within 3 months of waiting. For the moderate-risk candidates who waited for better organs, during the first week on the waitlist, a projected 2.6% of the candidates would die, with total rate of death while on waitlists of 8.4% for these candidates. For the low-risk candidates who waited for better organs, a projected 2.1% would die in the first week of waiting, with total rate of death on waitlists of 6.1% for these candidates.

Projected weeks of life among study patients
For high-risk SLK candidates, if they accepted KDPI >85% organs, the projected average number of weeks of life would be 254.8 ± 225.4 weeks compared with 285.6 ± 232.4 weeks if they waited for better organs (Figure 6). For moderate-risk SLK candidates who accepted KDPI >85% organs, the projected average number of weeks of life would be 290.0 ± 207.7 weeks compared with 349.5 ± 205.7 weeks if they waited for a better organ. For the low-risk SLK candidates, if they accepted KDPI >85% organs, their projected average number of weeks of life would be 333.4 ± 206.4 weeks compared with 408.8 ± 178 weeks if they waited for better organs.

Projected liver retransplant rate among study patients
In the high-risk group, those candidates who waited for better organs would experience a 1.9% probability of undergoing liver retransplant compared with 3.5% for those who would accept KDPI >85% organs for SLK. In the moderate-risk group, those candidates who waited for better organs would experience a 2.1% probability of undergoing liver retransplant compared with 3.9% for those who would accept KDPI >85% organs. In the low-risk group, those candidates who waited for better organs would experience a 2.2% probability of undergoing liver retransplant compared with 4.1% for those who accept KDPI >85% organs.

Projected 10-year cumulative death among study patients
In the high-risk group, the average overall 10-year cumulative death would be higher for those who accept >85% KDPI organs, but the disadvantage would not occur until after 2 years or 104 weeks (Figure 7A). In the moderate-risk group, the disadvantage of accepting >85% KDPI organs would become evident after 12 weeks (Figure 7B). However, in the lower-risk group, on average, there is always a disadvantage of accepting >85% KDPI organs (Figure 7C).

Prescriptive analysis
In the sensitivity analysis from our microsimulation models, we found that death rate of a specific candidate is dominated by 2 probabilities. The decision for a specific transplant program to advise a specific candidate to accept KDPI organs >85% or wait, therefore, depends on the risk group of the candidate and the following 2 probabilities. The first probability (Prob_Program_Offered_Organ) is that of the program being offered another SLK donor combination with matching blood type to that candidate. The second probability (Prob_Patient_Allocated_Organ) is that of the candidate being allocated those organs within the program. The sensitivity analysis for high-risk candidates is shown in Figure 8A. Drawing a line across from the average probability of being offered the matching organ for that candidate and drawing a line up from the probability of that candidate being allocated the next organ, the best decision for that candidate falls in 1 of the 2 regions. Any intersection point falling near the transition results in equivalent weeks lived. The 2-way sensitivity analysis for moderate-risk candidates is shown in Figure 8B. The 2-way sensitivity analysis for low-risk candidates is shown in Figure 8C.

Web site
A Web site was developed to assist clinicians in advising a potential SLK candidate to accept the offer of organs with KDPI >85% or wait for better organs (https://cbatl.shinyapps.io/SLK_Risk/). This site helps calculate the risk group for the candidate and the 2 probabilities. The Web site places the candidate in the region of the sensitivity graphs to accept KDPI >85% organs or wait for better organs.

Discussion

Simultaneous liver-kidney transplant is an important treatment option to consider for certain patients with concomitant end-stage liver and renal disease. The goal of our study was to evaluate whether a donor liver and kidney for SLK should be accepted for a given patient if the donor was high risk or whether it was better, for patient survival, to refuse this high-risk SLK transplant.

Our Markov microsimulation model was designed to evaluate each patient based on their risk profile in conjunction with the potential quality of the donor organs being offered. Our findings showed that, for any patient risk group (low, medium, or high), depending on the probabilities of being offered other organs, accepting high-KDPI organs for SLK can lead to improved patient survival. Differences in survival rates based on donor risk by KDPI in combination with different patient risk groups were statistically significant. As mentioned in our Materials and Methods section, KDPI can be used not only to determine the quality of the transplanted kidney but also to help predict patient survival following SLK.

To use our model, it is first necessary to determine the risk group of the patient. This is done by calculating points for the patient based on the multivariable Cox analysis (Table 1) and determining whether the patient belongs to the low-risk, medium-risk, or high-risk group. Second, the analysis considers the transplant program, that is, determining the program’s probability of receiving a donated liver and kidney each week with the correct blood type. Third, the program must determine a given patient’s probability of receiving the organs in consideration of the program’s waitlist. Finally, the patient’s location can be mapped on the appropriate sensitivity chart (Figure 8) based on the patient’s risk group. Any point on the graph that falls below the curve indicates that the patient would benefit from accepting a KDPI >85% organ; any point above the curve indicates that the patient should wait for a better organ since mortality is projected to be worse with acceptance of a high-risk organ than continuing to stay on the waitlist. In addition, a Web site (https://cbatl.shinyapps.io/SLK_Risk/) was constructed to aid the clinician in using our model.

Previous studies have not utilized the Markov model for decisions on transplanting of SLK candidates. However, other Markov models have been utilized in transplant decision making.^8,14 Our Markov model is a novel tool that transplant centers can use to help with decisions on whether to accept or not accept high-risk organs based on the specific patient and the probabilities of receiving additional organs.

A limitation of our study is the retrospective nature of the OPTN donor and recipient variables that we used to build our models and resulting survival curves. This limitation could have affected the probabilities used in the Markov models. All microsimulation depends on accurate probabilities; however, a longer time frame for prediction using small increments of time and use of distribution tables overcome this limitation. Practice variations could have occurred over time in our 10-year study period, which is a limitation.

The safety net and changes to kidney and liver allocation policy may certainly impact the scenario for patients being evaluated for SLK. At this time, data were not sufficient for this to be included in our full analysis. We estimate that the impact of the safety net would trend toward not accepting high KDPI organs for patients being evaluated for SLK; future work is needed to estimate the impact of the new allocation system. In conclusion, our model can be used by providers to help guide decisions around accepting high-KDPI organs for patients awaiting liver and kidney transplant versus waiting for better quality organs. Importantly, our model can inform patient-specific graft acceptance decisions while optimizing utilization of scarce life-saving organs.

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