Statistical models were estimated using rank ordered logistic regression , a conventional discrete choice modeling technique. Discrete choice techniques assume that when people choose between different options, they will select the one that yields the highest level of desirability. The purpose of discrete choice modeling is to use data collected from choices made by individuals to estimate statistical models that capture these desirability assessments. For the present study, a “match run”, the ordered list of candidates for which an organ is sequentially allocated, determined the rank ordering of candidates.
To estimate statistical models that capture current lung allocation policies for adult and pediatric donors, we used data for all non-import match runs from 2018. The year 2018 was chosen to reflect the current, non-Donor Service Area (DSA)-based geographic distribution of lungs, since DSA priority was removed from lung allocation policy in November 2017 .
On an adult (≥ 18 years old) donor match run, candidates are prioritized based on their proximity to the donor hospital, so that candidates in Zone A receive universal priority over candidates located farther away. On match runs from donors younger than 18 years of age, the match system first offers lungs to pediatric candidates (first to those < 12, followed by 12–17 year olds). As in adult allocation, candidates are prioritized based on their proximity to the donor hospital; however, unlike in adult allocation, for pediatric (< 18 years old) donors zones A, B, and C are treated as one large (up to 1000 NM) zone, without boundaries at 250 NM and 500 NM. Due to these differences in sorting and classification, we developed separate adult and pediatric models.
Adult Donor Match Run Data
This study used data from the Organ Procurement and Transplantation Network (OPTN). The OPTN data system includes data on all donors, wait-listed candidates, and transplant recipients in the US, submitted by the members of the Organ Procurement and Transplantation Network (OPTN), and has been described elsewhere. The Health Resources and Services Administration (HRSA), US Department of Health and Human Services provides oversight to the activities of the OPTN contractor. IRB exemption was obtained from the US Department of Health and Human Services Health Resources and Services Administration (HRSA).
Data produced by 6,466 match runs for 5,913 adult donors were obtained. An average of 402 candidates were ranked in each match run. As a result, we had data for 2,602,794 ranked candidates, with some candidates appearing on multiple match runs. Candidates screened off of match runs, for example if the donor’s age exceeded the transplant center’s maximum acceptance age, were excluded. Four major attributes are used to rank candidates in each match run: (1) medical priority (LAS), (2) candidate age, (3) candidate’s transplant center proximity to the donor hospital, and (4) blood type identical, compatible, or intended incompatible with the donor.
Pediatric Donor Match Run Data
Rankings produced from 534 match runs for 488 pediatric donors were used for the pediatric model. An average of 274 candidates were ranked in each match run. As a result, 175,342 observations for estimating the pediatric donor lung allocation model were made. The same major attributes were used to rank pediatric donors as adult candidates. To see how current lung allocation policy sorts these candidates, we calculated the number of candidates who fall into the different classifications. Figure 2 shows the sequence of classifications under the current lung allocation policy .
Analogous to how consumers determine desirability of products based on their attributes, the matching algorithm can be imagined as assigning an unobserved priority score to each candidate during every match run based on that candidate’s characteristics. More formally, the priority score assigned to each candidate j can be represented by the following function:
uj = vj + εj, j = 1,…, J,
where vj is the observable component of the function that depends on the attributes of the candidate (e.g., location, blood type).
Adult Donor Model Estimation
For the adult donor model, we specified the observable component of the priority function using the specification in the following equation:
V = βLAS × LAS + βCHILD × CHILD + βDISTANCE × DISTANCE + βABO_IDENTICAL × ABO_IDENTICAL
where LAS is a continuous, linear variable that captures the lung allocation score (in our sample, this variable ranges from 0.07 to 96.23); CHILD is a dummy-coded variable that equals 1 for pediatric candidates below the age of 12, and 0 for all other candidates; DISTANCE is a continuous, linear variable that captures the distance from a candidate to the donor hospital in NM (in our sample this variable ranges from 0 to 4,415.25 NM); ABO_IDENTICAL is an effects-coded variable that is equal to 1 for candidates with identical blood type as the organ donor and is equal to − 1 for candidates with a compatible (or intended incompatible) blood type to the organ donor.
Pediatric Donor Model Estimation
For the pediatric donor model, we specified the observable component of the priority function using the specification in the following equation:
V = βLAS × LAS + βCHILD × CHILD + βADOLESCENT × ADOLESCENT + βDISTANCE × DISTANCE + βABO_IDENTICAL × ABO_IDENTICAL
where LAS is a continuous, linear variable that captures the lung allocation score for patients older than 12 years (in our sample, this variable ranges from 0 to 96.23); CHILD is a dummy-coded variable that equals 1 for pediatric candidates below the age of 12, and 0 for all other candidates; ADOLESCENT is a dummy-coded variable that equals 1 for candidates between the ages of 12 and 17 years old and 0 for all other candidates; DISTANCE is a continuous, linear variable that captures the distance from a candidate to the donor hospital in NM (in our sample, this variable ranges from 0 to 4,040.68 NM); ABO_IDENTICAL is an effects-coded variable that is equal to 1 for candidates with the same blood type as the donor and is equal to − 1 for candidates with a compatible blood type or incompatible blood type to the donor.
Model estimation was performed using Stata statistical software, Release 16, StatCorp LLC, College Station, TX.
Determining the Relative Importance of Factors
We used the model coefficients to rank candidate attributes in terms of their relative importance to the ordering of candidates in lung allocation, separately for the adult donor and pediatric donor models. This was done by taking the difference between the score for the most preferred level of an attribute and the score for the least preferred level of the same attribute.
We quantified “exchange rates” to express the relative importance of each factor compared to distance. These rates convey the number of NM required to have the same effect on a candidate’s total score as a change in LAS; blood type identical vs. compatible; or pediatric vs. adult candidate.
Evaluating Model Performance
After estimating the adult and pediatric donor models, we used the resulting parameters to calculate a points-based composite allocation score for each candidate. We used these scores to predict the rank that each of the candidates would have received if the points-based system had been used. The closer these predicted rankings are to the actual rankings, the more the points-based scores reflect the current lung allocation policy. Spearman’s rank correlation coefficient and Kendall’s Tau were used for comparing predicted and actual rankings.