Adult Donor Model Results
Table 1 contains the coefficients from the rank-ordered logit model estimated for adult donors. The direction of these coefficients tells us how changing one attribute would change a candidate’s ranking in a given match run. Specifically, we see that candidates are ranked higher if they are adults, have higher LAS scores, are registered at a transplant center closer to the donor hospital, or have an identical blood type to the donor.
Table 1.Rank-ordered logit estimates.
Adult Donor
Mean Coefficient (Standard Error)
|
Pediatric Donor
Mean Coefficient (Standard Error)
|
Medical Priority
|
Lung allocation score
|
0.040*** (<0.001)
|
0.038*** (<0.001)
|
Candidate Age
|
Less than 12 years old
|
−1.601*** (0.026)
|
1.946*** (0.056)
|
Between 12 and 17 years old
|
1.928*** (0.033)
|
Proximity
|
Distance (NM)
|
-0.007*** (<0.001)
|
-0.007*** (<0.001)
|
Candidate Blood Type Relative to Donor Blood Type
|
Identical
|
1.008*** (<0.001)
|
0.978*** (0.004)
|
Compatible
|
-1.008*** (<0.001)
|
-0.978*** (0.004)
|
Notes: (1) Blood type variables are effects coded, candidate age variables are dummy coded, LAS and distance are coded as continuous variables. (2) *** denotes p < .01 for statistical significance relative to adjacent categories.
Distance in our sample ranges from 0 to 4,415.25 NM. This implies that the maximum difference in distance score is 30.907 (30.907 = 0 – (–0.007 * 4,415.25)). By making this calculation for each attribute, we ranked candidate attributes in order of importance, where larger maximum differences imply greater importance. These calculations are presented in Table 2. Based on these calculations, proximity was found to be the most important attribute in lung allocation.
Table 2. Ranking candidate attributes by importance in lung allocation.
Candidate Attribute
|
Score for Most Preferred Value
|
Score for Least Preferred Value
|
Difference
|
Importance Rank
|
Adult Donor Model
|
Medical Priority
|
3.849
|
0.000
|
3.849
|
2
|
Candidate Age
|
0.000
|
-1.601
|
1.601
|
4
|
Proximity
|
0.000
|
-30.907
|
30.907
|
1
|
Candidate Blood Type Relative to Donor Blood Type
|
1.008
|
-1.008
|
2.016
|
3
|
Pediatric Donor Model
|
Medical Priority
|
3.657
|
0.000
|
3.657
|
2
|
Candidate Age
|
1.946
|
0.000
|
1.946
|
4
|
Proximity
|
0.000
|
-28.285
|
28.285
|
1
|
Candidate Blood Type Relative to Donor Blood Type
|
0.978
|
-0.978
|
1.956
|
3
|
Note: Calculations performed using coefficients reported in Table 1, which were rounded to third decimal place.
The coefficients were also used to quantify the relative importance of candidate attributes by expressing changes in one attribute in terms of another. For example, as seen in Table 3, reducing a patient’s LAS by 25 points lowers their composite allocation score by exactly 1 point (–1 = 0.040 * 25). By comparison, increasing the patient’s distance from the donor hospital by 142.857 NM reduces their composite allocation score by exactly 1 point (–1 = –0.007 * 142.857). Thus, in terms of the composite score, being 142.857 NM closer to the donor hospital is equivalent to having a 25-point higher LAS. In Table 3, we compared the impact on the composite score of changes in each attribute in terms of changes in a candidate’s proximity to the donor hospital.
Table 3. Converting changes in each attribute into changes in NM (“exchange rates”).
Change in Attribute
|
Change in Composite Allocation Score
|
Equivalent Change in NM
|
Adult Donor Model
|
Medical Priority: reduce LAS by 25 points
|
-1.000
|
142.857
|
Candidate Age: reduce candidate age from at least 12 years old to below 12 years old
|
-1.601
|
228.714
|
Candidate Blood Type: change candidate blood type from identical to donor to compatible with donor
|
-2.016
|
288.000
|
Pediatric Donor Model
|
Medical Priority: reduce LAS by 25 points
|
-0.950
|
135.714
|
Candidate Age: reduce candidate age from at least 18 years old to below 12 years old
|
1.946
|
-278.000
|
Candidate Blood Type: change candidate blood type from identical to donor to compatible with donor
|
-1.956
|
279.429
|
Note: Calculations performed using coefficients reported in Table 1, which were rounded to the third decimal place.
In addition to providing information on the relative importance of individual attributes, we can use the coefficients reported in Table 1 to calculate composite allocation scores for actual or hypothetical candidates. For example, suppose a set of lungs from an adult donor has become available and there are two adult candidates on the match. The first candidate (“A”) is an adult, located 200 NM away from the donor hospital, has a LAS score of 50, and an identical blood type to the donor. The second candidate (“B”) is an adult, located 251 NM away from the donor hospital, has a LAS score of 90, and also an identical blood type to the donor. Based on current policy, the LAS 50 patient would be offered the donor lungs before the much more medically urgent patient with a LAS of 90. However, based on the coefficients in Table 1, the composite score associated with candidate A would be 1.608, and the score associated with candidate B would be 2.851. Therefore, under the composite score approach, the candidate order would be reversed compared to the current, classification-based policy. Despite being outside of the 250 nautical mile boundary, the composite scoring approach would allow the severity of medical need reflected in an LAS of 90 to more than compensate for the relatively minimal additional distance required to ship the organ to this candidate (see Table 4).
Table 4. Example of composite score ranking vs. current policy ranking for two candidates.
Candidate
|
LAS
|
Proximity (NM)
|
Blood type vs. donor
|
Current policy ranking
|
Composite score
|
Composite score rank
|
A
|
50
|
200
|
Identical
|
1
|
1.608
|
2
|
B
|
90
|
251
|
Identical
|
2
|
2.851
|
1
|
To assess the degree to which candidate rankings from the composite score reflect rankings under the current policy, we calculated candidates’ scores for 2,359 match runs that included at least 10 candidates and quantified the correlation between score-based ranks and current policy ranks. (This comparison is illustrated in the Supplementary Table by showing rankings under the current vs. a score-based policy for the first 25 candidates for a sample match run.) We chose to only calculate new rankings for a sample of match runs, because calculating predictive performance metrics is computationally time-consuming when dealing with a large number of observations. Table 5 reports Spearman correlation coefficients and Kendall’s Tau comparing points-based rankings with the actual rankings produced by the matching algorithm for the 2,359 match runs. As shown in the table, the mean for both of these coefficients is at least 0.80, suggesting that points-based rankings are (on average) very similar to the actual rankings.
Table 5. Predictive performance metrics.
Mean
|
Minimum
|
25th Percentile
|
50th Percentile
|
75th Percentile
|
Maximum
|
Adult Donor Model (N=2,359)
|
Spearman correlation
|
0.933
|
0.318
|
0.916
|
0.941
|
0.958
|
1.000
|
Kendall’s Tau
|
0.803
|
0.273
|
0.765
|
0.808
|
0.843
|
1.000
|
Pediatric Donor Model (N=453)
|
Spearman correlation
|
0.911
|
0.451
|
0.897
|
0.930
|
0.949
|
1.000
|
Kendall’s Tau
|
0.792
|
0.551
|
0.754
|
0.797
|
0.833
|
1.000
|
Note: We chose only to calculate new rankings for 2,359 out of the total 6,466 adult donor match runs due to the computationally expensive nature of calculating predictive performance metrics on very large datasets. We only calculated new rankings for 453 of the total 534 pediatric donor match runs because the 81 remaining match runs each included fewer than 10 candidates.
Figure 3 illustrates a scatter plot of the current policy rankings and points-based rankings for an adult donor match run with 873 candidates and having the median Kendall’s Tau of 0.808. If the current policy rankings and points-based rankings were identical, all points on this scatter plot would lie on the 45-degree line extending from the origin (illustrated in red). In reality, we see that though the rank correlation is high, there are still notable differences between the two sets of rankings. Specifically, some candidates in zones B and C—for example, candidates Y and Z as annotated on the figure—have higher priority (numerically lower ranking) under the points-based system than under current policy. This is because the current system grants absolute priority to candidates in more proximal zones. By contrast, under a points-based system, candidates farther away from a donor hospital may have other attributes (e.g. higher LAS scores) that overcome their lack of proximity.
Pediatric Donor Model Results
Table 1 contains the coefficients from the rank-ordered logit model estimated from pediatric donor match runs. As in the adult model, these coefficients were used to make inferences about how candidate attributes influence donor lung allocation. Specifically, the score-based system ranks candidates higher if they are younger than 12 years old, have a higher LAS, are registered at a transplant center closer to the donor hospital, or have identical blood type to donors. Based on calculations shown in Table 2, proximity was found to be the most important attribute in allocating pediatric donor lungs.
Table 3 shows that for the pediatric donor model, an increase in 25 LAS points is equivalent to being 135.714 NM closer in terms of the composite score. Table 5 reports Spearman correlation coefficients (mean of 0.911) and Kendall’s Tau (0.792) for comparing points-based rankings with the actual rankings produced by the matching algorithm for all 453 pediatric donor match runs having at least 10 candidates.
Figure 4 illustrates a scatter plot of the current policy rankings and points-based rankings for a 138-candidate, pediatric donor match run having the median Kendall’s Tau of 0.797. As in the adult donor model, we see that there are some differences between the two sets of rankings. Specifically, as seen with the adult donor model, candidates in further away zones are sometimes ranked higher than more proximal candidates under the points-based system compared to current policy. For example, though all zone A candidates would rank ahead of Candidate I under the classification-based system, Candidate I would rank near the very top under a points-based system due to having an extremely high LAS of 92.
Discussion and conclusions
Although the computerized match system plays a critical role in matching donor organs and candidates, the value judgments inherent in the current classification-based system can be opaque. An alternative way to make organ allocation decisions is to leverage a points-based framework that transparently expresses the relative importance of proximity, medical priority, and other factors to form a mathematically-derived, composite score.
Our analysis sought to determine if preferences and priorities within current lung allocation policy could be captured, at least approximately, by composite scores. First, we used rank ordered logistic regression, a conventional discrete choice modeling technique, to estimate two statistical models based on match runs from 2018 – one for adult donor lungs and one for pediatric donor lungs. These statistical models estimated scores that quantified how important the following candidate attributes are in lung allocation rankings: (1) medical priority (i.e., LAS), (2) candidate age, (3) candidate proximity to donor hospital, and (4) blood type. Second, we confirmed that the estimated scores approximately reflect the current lung allocation policy by comparing score-based candidate rankings with rankings from the current system. Overall, we demonstrate that these rankings are highly correlated with the original ranks produced by the matching algorithm.
The proximity of the candidate’s transplant hospital to the donor hospital was found to be the most important factor in a composite score that reflects the current policy. In terms of attribute “exchange rates,” 25 LAS points equates to just 143 NM, implying that a nearby candidate with LAS of 45 would be prioritized ahead of a LAS 70 candidate just 150 NM further away. The rationale for prioritizing patients based on proximity reflects both system efficiency and organ viability considerations, as transporting lungs over long distances incurs transportation costs, travel time by the surgical recovery team, and potentially detrimental effects of organ ischemia time [15–19]. The manner and degree to which proximity should influence candidate rankings is a matter of ongoing debate [20–22].
Although the results we present are insightful, it is important to note that they are subject to limitations. First, due to the opacity of the current, classification-based system, the precise value judgments that manifested from the revealed preference analysis do not necessarily reflect policymakers’ intended value judgments. Second, the model specification we used for several key attributes oversimplified the way these attributes entered the lung allocation rankings. For example, in both the adult donor and pediatric donor models, we only estimated a single coefficient for candidates younger than 12 years old. As a result, we did not differentiate between candidates with “Priority 1” from candidates with “Priority 2” [1] status, which may slightly reduce the accuracy of both models’ predictions. We also simplified the composite score by omitting the waiting time attribute, which plays a subordinate role in lung allocation (essentially serving merely as a tiebreaker between two candidates with identical LAS or medical priority).
In the current policy, distance is either infinitely important (across zones) or of zero importance (within zones). This composite scoring approach yields an average estimate of the impact of distance as a continuous linear function (Figures 5 and 6). Though specification of distance as a continuous, linear term instead of a zone-based categorical variable departs from the structure of current policy, this linear parameterization is more consistent with the spirit and intent of composite-score based allocation.
Revealed preference analysis of match runs produced a composite score that captures the essence of current policy while removing hard boundaries. As highlighted in Table 4, this approach avoids artificial boundaries that currently preclude a candidate with a greater medical priority (LAS) from being ranked higher than a lower-LAS patient solely because the higher-LAS candidate’s transplant hospital is on the other side of a geographic zone. The linear parameterization also permits highly interpretable value judgment expressions (i.e., “exchange rates”), as shown in Table 3.
So, could developing composite scores through revealed preference analysis be the solution to migrating lung allocation policy to the continuous allocation framework? This is a possibility, although recent policy deliberations of the OPTN Lung Transplantation Committee (Lung Committee) have suggested the need for the new system to include several new attributes—for example, candidate height and degree of Human Leukocyte Antigen (HLA) allo-antibody sensitization—that are not included in current policy. These factors would somehow need to be appended to the composite scores shown here. An alternative approach would be to develop an entirely new composite scoring system based on a reevaluation of the degree to which proximity and other factors should be valued relative to medical need, as opposed to deriving the composite score from the current policy, which some have criticized [23].
The primary value in these revealed preference-derived scores, we believe, is in highlighting the degree to which each of the four key attributes influences candidate rank-ordering under the current policy for comparison to an idealized policy (i.e., the relative importance the OPTN and broader transplant community believe these factors should have in a new allocation system).
The Lung Committee is exploring the use of analytic hierarchy process (AHP), a structured approach to eliciting value judgments and preferences from stakeholders, to establish this idealized policy [24–28]. The AHP results will be compared with the revealed preference analysis presented herein to stimulate discussion on the appropriate level of importance to be placed on each attribute, in accordance with federal regulation governing organ allocation policies [4].
In theory, a carefully crafted, continuous version of lung allocation policy has the potential to make greater use of the limited supply of donor lungs by transplanting more patients with the highest predicted benefit of transplant while also ensuring that access to lungs is equitable and accounting for inefficiencies related to transportation logistics over long distances and under tight time restrictions. Simulation modeling will be used to forecast the impact of composite scoring options compared to current policy, and as with all OPTN policy changes, the effects of the new policy on patients and the transplant network as a whole will be closely monitored to determine if adjustments are necessary. Policy changes will entail fine-tuning the score (e.g., increasing the coefficient of some variables and decreasing others) as opposed to shuffling classifications. The composite scoring approach should allow lung allocation to readily adapt to future innovations; for example, if technologies such as ex-vivo lung perfusion [29] become widely used and can reduce the deleterious effect of organ ischemia time associated with travel, the score can be tuned by reducing the relative importance of proximity compared to other factors. And as evidence supporting an association between other factors (e.g., donor/candidate size-matching; use of extra-corporeal membrane oxygenation) and recipient outcomes is generated, the score can be augmented to account for such discoveries. This continuous composite score approach to lung allocation policy has the potential to more effectively utilize the limited supply of donor lungs in a manner consistent with the priorities and preferences of the transplant community.