Clinical Impact of a Modified Lung Allocation Score that Mitigates Selection Bias

Abstract

Purpose.

The Lung Allocation Score (LAS) is used in the U.S. to prioritize lung transplant candidates. Selection bias, induced by dependent censoring of waitlisted candidates and prediction of post-transplant survival among surviving, transplanted patients only, is only partially addressed by the LAS. Recently, a modified LAS (mLAS) was designed to mitigate such bias. Here, we estimate the clinical impact of replacing the LAS with the mLAS.

Methods.

We considered lung transplant candidates waitlisted during 2016–2017. LAS and mLAS scores were computed for each registrant at each observed organ offer date; individuals were ranked accordingly. Patient characteristics associated with better priority under the mLAS were investigated via logistic regression and generalized linear mixed models. We also determined whether differences in rank were explained more by changes in predicted pre- or post-transplant survival. Simulations examined how one-year waitlist, post-transplant, and overall survival might change under the mLAS.

Results.

Diagnosis group, six-minute walk distance, continuous mechanical ventilation, functional status, and age demonstrated the highest impact on differential allocation. Differences in rank were explained more by changes in predicted pre-transplant survival than changes in predicted post-transplant survival, suggesting that selection bias has more impact on estimates of waitlist urgency. Simulations suggest that for every 1000 waitlisted individuals, 12.8 (interquartile range: 5.2–24.3) fewer waitlist deaths per year would occur under the mLAS, without compromising post-transplant and overall survival.

Conclusions.

Implementing a modified LAS that mitigates selection bias into clinical practice can lead to important differences in allocation and possibly modest improvement in waitlist survival.

INTRODUCTION

The U.S. lung allocation system prioritizes lung transplant candidates based on the Lung Allocation Score (LAS).¹ The LAS aims to predict how long a patient would survive with versus without transplant, and is composed of two prediction models: one to predict pre-transplant survival and one to predict post-transplant survival.² Patients’ transplant benefit is estimated as the difference between predicted post- and pre-transplant survival, while their waitlist urgency is taken to be predicted pre-transplant survival.^2,3 The LAS is computed as the difference between transplant benefit and waitlist urgency (equivalently, post-transplant survival minus two times pre-transplant survival), and is normalized so that it ranges between 0 and 100, with higher scores indicating greater priority for transplant.³

Although LAS scores are calculated using each patient’s most recent demographic and clinical variables, the models used to predict pre- and post-transplant survival underlying the LAS do not fully account for selection bias. Such bias arises due to dependent censoring (individuals are removed from the waitlist once they receive transplant) and survivor bias (individuals must survive long enough for a suitable donor organ to become available).⁴ We previously developed a modified LAS (mLAS) using inverse probability of treatment and censoring weighting (IPTW and IPCW) in order to mitigate selection bias.⁴ We then demonstrated improved discrimination and calibration for the mLAS compared to the LAS. We also showed that the mLAS would affect patient rankings considerably.

In this paper, we evaluate the impact of implementing this mLAS in clinical practice. More specifically, we use observed data to investigate the demographic and clinical characteristics of individuals who would have received better priority under the mLAS compared to the LAS. We also conduct simulations to estimate how waitlist, post-transplant, and overall survival might change under the mLAS. Understanding the clinical impact of the mLAS is especially relevant now, as the transplant community is currently developing a new organ allocation framework, the continuous distribution model, which aims to increase the flexibility of the scoring algorithm so that organs are allocated to patients more equitably. The sources of bias outlined above would still be in play under this continuous distribution model unless they are recognized and addressed.^5–7

METHODS

This study utilizes pre- and post-lung transplant data from the United Network for Organ Sharing (UNOS). Our cohort consisted of all patients 18 years or older who were listed for single or bi-lateral lung transplantation in the United States between January 1, 2016 and December 31, 2017. This cohort is consistent with the testing cohort used in Schnellinger et al. (2021),⁴ and ensures that enough follow-up time accrued among transplanted patients to evaluate one-year post-transplant survival.

We applied the modified and existing LAS models to our cohort to estimate both mLAS and LAS scores for each patient at each possible offer date, as in our previous paper.⁴ This approach circumvents the issue of exception requests, whereby some patients’ LAS scores may be higher than that estimated by the LAS model due to ad hoc adjustments made by UNOS at the request of transplant centers. At each offer date, eligible patients were ranked twice: first using their mLAS scores, and second using their LAS scores (not considering exception requests). Patients were then grouped into two categories (better versus same or worse priority) based on how their rank would change under the mLAS compared to the LAS. We combined individuals who received the same rank together with those who received worse priority because the number of individuals who received the same rank was too small, and dropping these individuals from the analysis entirely would force the resulting probabilities to be interpreted as conditional rather than marginal probabilities. Although we could have instead grouped individuals who received the same rank with those who received better priority, we felt that keeping the better priority individuals separate would be more meaningful to patients and clinicians, as this category then represents individuals whose chances of receiving transplant would increase under the mLAS.

To examine the demographic and clinical characteristics of patients who receive better priority under the mLAS relative to the LAS, univariable and multivariable logistic regression models were fit. The outcome variable for these models was categorical change in rank (better priority versus same or worse priority), and predictors included patients’ diagnosis group, age, gender, race/ethnicity, primary payment source, education level, employment status, UNOS geographic region, body mass index (BMI), blood type, human leukocyte antigens (HLA) mismatch, prior transplant, prior cardiac surgery, smoking status, diabetes, functional status, cardiac index, mechanical ventilation, six-minute walk distance, creatinine, and oxygen need at rest. Covariates were only included in the multivariable model if they were statistically significant at the $\alpha =0.05$ level in the univariable models.

To evaluate the extent to which changes in prioritization are driven by changes in predicted pre- or post-transplant survival between the mLAS and LAS, we split the data into worse priority and better priority subsets. Generalized linear mixed models (GLMM) were fit to each subset using the continuous differences in ranks for each patient under the mLAS and LAS as outcomes, and the difference in predicted pre-transplant survival and difference in predicted post-transplant survival as predictors. GLMMs were used to account for the fact that patients can appear on multiple organ offer dates and receive different rankings on each date. Generalized r² values were obtained for each GLMM model via the r2glmm package.⁸ We repeated these analyses stratified by the demographic and clinical characteristics that were deemed to have a significant impact on prioritization changes based on the logistic regression models.

Finally, we undertook a statistical simulation – adapted from Vock et al.⁹ – to investigate how the mLAS would impact observed waitlist and post-transplant survival if it were implemented in clinical practice. In brief, we selected a random set of organ offer dates from those observed in our testing cohort, simulated characteristics of hypothetical donor organs, and allocated these donor organs based on the mLAS and LAS to patients in our testing cohort who were alive and eligible for transplant at each offer date. The entire simulation was repeated 100 times (due to computational constraints) to obtain distributions of Kaplan-Meier estimates and demographic/clinical characteristics. We also conducted sensitivity analyses in which we varied the transplant offer rate to explore how lower or higher offer rates might impact results. Additional simulation details are provided in the Appendix. Analyses were conducted in R (R Foundation for Statistical Computing, Vienna, Austria) and Stata (StataCorp LLC, College Station, TX).

RESULTS

Observed Analyses

Table 1 summarizes the demographic and clinical characteristics of the complete waiting list population as well as the subset of individuals who received transplant. In the full waitlist population, covariates were measured at the time of waitlist registration; among the subset of transplanted individuals, covariates are shown both at the time of waitlist registration and at the time of transplantation. In the full waitlist population, the median waiting time was 57 days (interquartile range, IQR: 16–154 days), 5.7% of these patients died on the waitlist during the two-year follow-up time, 0.5% died within one year of waitlist registration, and 77.6% received transplant. Among those who received transplant, the median waiting time was 39 days (IQR: 13–102), the median follow-up time after transplant was 199 days (IQR: 68–365), 10.9% died after transplantation during the two-year follow-up time, and 8.3% died within one year of transplantation. The distributions of some clinical characteristics differed between the transplanted group and the full waitlist population. For example, the proportion of patients with restrictive lung disease was higher among transplanted individuals (60.1%) compared to the full waitlist population (57.4%). Conversely, the proportion of patients with obstructive lung disease was lower among transplanted individuals (25.0%) compared to the full waitlist population (27.0%). At waitlist registration, the distributions of continuous mechanical ventilation, functional status, and six-minute walk distance were comparable among the full waitlist population and among the subset of individuals who would eventually go on to receive transplant. Conversely, at transplantation, a larger proportion of individuals in the post-transplant group were on continuous mechanical ventilation (7.7%) compared to the full waitlist population (4.1%); a smaller proportion of individuals in the post-transplant group required no assistance with daily living tasks (5.0%) compared to the full waitlist population (11.3%); and the median (IQR) six-minute walk distance was somewhat lower among transplanted individuals (800.0 [445.0, 1059.0] feet) compared to the full waitlist population (880.5 [580.0, 1142.0] feet).

Table 1.

Demographic and clinical characteristics of the complete waiting list population and the subset of this population who received transplant. In the full waitlist population, covariates were measured at the time of waitlist registration; among the subset of transplanted individuals, we display covariates measured at the time of waitlist registration and at the time of transplant.

	Waiting List	Post-transplant (at waitlist registration)	Post-transplant (at transplant)
Total number of patients (N)	5354	4154	4154
Waiting time (days), median (IQR)	57.0 (16.0, 154.0)	39.0 (13.0, 102.0)	---
Death on waitlist within 1 year of waitlist registration	25 (0.5%)	---	---
All deaths on waitlist	288 (5.7%)	---	---
Removal from waitlist due to transplant	4154 (77.6%)	4154 (100.0%)	---
Follow-up time post-transplant (days), median (IQR)	---	---	199.0 (68.0, 365.0)
Death within 1 year of transplant	---	---	346 (8.3%)
All deaths post-transplant	---	---	420 (10.9%)
REGION
1	185 (3.5%)	160 (3.9%)	160 (3.9%)
2	953 (17.8%)	680 (16.4%)	680 (16.4%)
3	522 (9.7%)	405 (9.7%)	405 (9.7%)
4	636 (11.9%)	534 (12.9%)	534 (12.9%)
5	878 (16.4%)	675 (16.2%)	675 (16.2%)
6	110 (2.1%)	67 (1.6%)	67 (1.6%)
7	438 (8.2%)	334 (8.0%)	334 (8.0%)
8	312 (5.8%)	251 (6.0%)	251 (6.0%)
9	180 (3.4%)	126 (3.0%)	126 (3.0%)
10	684 (12.8%)	528 (12.7%)	528 (12.7%)
11	456 (8.5%)	394 (9.5%)	394 (9.5%)
GENDER
F	2263 (42.3%)	1594 (38.4%)	1594 (38.4%)
M	3091 (57.7%)	2560 (61.6%)	2560 (61.6%)
RACE/ETHNICITY
White	4224 (78.9%)	3339 (80.4%)	3339 (80.4%)
Black	552 (10.3%)	397 (9.6%)	397 (9.6%)
Hispanic	411 (7.7%)	299 (7.2%)	299 (7.2%)
Asian	124 (2.3%)	93 (2.2%)	93 (2.2%)
Other	43 (0.8%)	26 (0.6%)	26 (0.6%)
DIAGNOSIS
A (Obstructive Disease)	1444 (27.0%)	1038 (25.0%)	1038 (25.0%)
B (Pulmonary Hypertension)	299 (5.6%)	182 (4.4%)	182 (4.4%)
C (Cystic Fibrosis)	538 (10.0%)	436 (10.5%)	436 (10.5%)
D (Pulmonary Fibrosis)	3073 (57.4%)	2498 (60.1%)	2498 (60.1%)
BLOOD TYPE
A	2100 (39.2%)	1702 (41.0%)	1702 (41.0%)
AB	195 (3.6%)	157 (3.8%)	157 (3.8%)
B	607 (11.3%)	474 (11.4%)	474 (11.4%)
O	2452 (45.8%)	1821 (43.8%)	1821 (43.8%)
Age (years), median (IQR)	60.0 (52.0, 66.0)	61.0 (52.0, 66.0)	61.0 (52.0, 66.0)
Bilirubin (mg/dL), median (IQR)	0.7 (0.7, 0.7)	0.7 (0.7, 0.7)	0.7 (0.7, 0.7)
BMI (kg/m3), median (IQR)	26.0 (22.0, 29.2)	26.0 (22.1, 29.1)	25.9 (22.1, 29.0)
Height (feet), median (IQR)	5.6 (5.3, 5.8)	5.6 (5.3, 5.8)	5.6 (5.3, 5.8)
Cardiac index <2 L/min/m2	896 (16.7%)	717 (17.3%)	596 (14.3%)
Central venous pressure (mmHg), median (IQR)	5.0 (5.0, 8.0)	5.0 (5.0, 8.0)	5.0 (5.0, 8.0)
Continuous mechanical ventilation	217 (4.1%)	160 (3.9%)	320 (7.7%)
Creatinine (serum) (mg/dL), median (IQR)	0.8 (0.7, 1.0)	0.8 (0.7, 1.0)	0.8 (0.7, 1.0)
Diabetes	1074 (20.1%)	895 (21.5%)	971 (23.4%)
Forced vital capacity % predicted, median (IQR)	48.0 (38.0, 62.0)	48.0 (37.0, 61.0)	45.0 (36.0, 58.0)
Functional status (none)	604 (11.3%)	472 (11.4%)	209 (5.0%)
Oxygen need at rest (L/min), median (IQR)	4.0 (2.0, 6.0)	4.0 (2.5, 6.0)	4.0 (2.5, 8.0)
pCO2, median (IQR)	43.0 (40.0, 50.0)	43.0 (40.0, 50.0)	45.0 (40.0, 53.0)
Pulmonary artery systolic pressure (mmHg), median (IQR)	38.0 (31.0, 48.0)	38.0 (30.0, 47.0)	38.0 (31.0, 49.0)
Six-minute walk distance (feet), median (IQR)	880.5 (580.0, 1142.0)	880.0 (562.0, 1146.0)	800.0 (445.0, 1059.0)

To illustrate how patients’ scores and ranks might change under the mLAS, we highlight differences in scores and ranks for three individuals from one offer date (April 25, 2016), one who received better priority under the mLAS, one who received worse priority under the mLAS, and one who experienced no change in priority under the mLAS (Table 2). We emphasize that an individual’s rank depends not only on their own score, but also on the scores of all other patients eligible for transplant on each particular offer date. Thus, a given change in score does not always result in the same change in rank. Schnellinger et al. (2021) includes scatterplots summarizing differences in scores and ranks for all eligible patients across all offer dates in our testing cohort.⁴ Similarly, Table 3 (Figure 1) displays the odds ratio estimates (predicted probabilities) for better versus same or worse priority under the mLAS by demographic and clinical characteristics for all eligible patients across all possible offer dates. Odds ratios greater than 1 for a given category indicate that a person in that category is more likely to receive better priority under the mLAS relative to a person in the reference category. Figure 1 shows that diagnosis group, six-minute walk distance, continuous mechanical ventilation, functional status, and age exhibit the largest impact on prioritization changes (predicted probability plots for additional covariates appear in Appendix Figure 1). Individuals with restrictive lung disease are 13.6 (95% confidence interval, CI: 13.3–13.8) times more likely to receive better priority under the mLAS relative to individuals with obstructive lung disease; individuals whose six-minute walk distance falls between 928–1160 feet are 28.6 (95% CI: 27.6–29.6) times more likely to receive better priority under the mLAS relative to individuals whose six-minute walk distance falls between 0–656 feet; individuals receiving continuous mechanical ventilation are 18.7 (95% CI: 16.5–21.1) times more likely to receive better priority under the mLAS relative to individuals who do not require continuous mechanical ventilation; individuals who require no assistance in daily living tasks are 21.3 (95% CI: 20.0–22.7) times more likely to receive better priority under the mLAS relative to individuals who require at least some assistance with these tasks; and the odds of receiving better priority under the mLAS decrease as age increases.

Table 2.

Illustrative cases of how patients’ scores and ranks might change under the mLAS. Individuals were chosen to highlight better, no change, and worse priority based on a single offer date in our testing cohort (April 25, 2016), and were ranked relative to all 437 patients eligible for transplant on that day (i.e., ranks ranged from 1 to 437).

Patient Description	LAS	mLAS	Difference in predicted Waitlist Urgency between mLAS and LAS (in days)	Difference in predicted post-transplant survival between mLAS and LAS (in days)	Rank under LAS	Rank under mLAS	Change in Priority
64 year old female with restrictive lung disease, overweight (BMI=28.0), at least some assistance needed with daily living tasks, six-minute walk distance: 945 feet	33.64	37.45	-11.87	17.96	324	190	Better
58 year old male with obstructive lung disease, normal weight (BMI=22.7), at least some assistance needed with daily living tasks, six-minute walk distance: 804 feet	32.27	32.62	2.779	9.337	388	388	No Change
35 year old female with infective lung disease, normal weight (BMI=20.2), at least some assistance needed with daily living tasks, six-minute walk distance: 1001 feet	37.15	35.30	15.50	10.76	218	278	Worse

Table 3.

Estimated odds ratios for better versus worse priority under the modified LAS by demographic and clinical characteristics at each possible offer date.

	Univariable (Unadjusted) Model		Multivariable (Adjusted) Model
Covariate	Odds Ratio	95% Confidence Interval	Odds Ratio	95% Confidence Interval
Obstructive Lung Disease	REF		REF
Pulmonary Vascular Disease	1.17*	(1.15, 1.20)	0.78*	(0.75, 0.81)
Infective Lung Disease	0.14*	(0.13, 0.14)	0.01*	(0.01, 0.01)
Restrictive Lung Disease	7.24*	(7.17, 7.32)	13.6*	(13.3, 13.8)
Age (years) [18,50)	REF	N/A N/A	REF	N/A N/A
Age (years) [50,59)	2.16*	(2.13, 2.19)	0.59*	(0.58, 0.61)
Age (years) [59,65)	1.83*	(1.81, 1.85)	0.38*	(0.37, 0.38)
Age (years) [65,80]	1.39*	(1.38, 1.41)	0.15*	(0.14, 0.15)
Male	REF	N/A N/A	REF	N/A N/A
Female	0.81*	(0.81, 0.82)	0.83*	(0.82, 0.84)
BMI Underweight	0.05*	(0.05, 0.05)	0.01*	(0.01, 0.01)
BMI Normal	REF	N/A N/A	REF	N/A N/A
BMI Overweight	2.60*	(2.58, 2.63)	1.98*	(1.94, 2.01)
BMI Obese	3.71*	(3.64, 3.77)	2.07*	(2.02, 2.12)
Height (feet) [4.33,5.25)	REF	N/A N/A	Excluded due to collinearity with BMI
Height (feet) [5.25,5.50)	1.17*	(1.16, 1.19)
Height (feet) [5.50,5.75)	1.27*	(1.26, 1.29)
Height (feet) [5.75,6.92]	1.37*	(1.36, 1.38)
Blood Type A	REF	N/A N/A	REF	N/A N/A
Blood Type AB	1.31*	(1.28, 1.33)	2.02*	(1.94, 2.11)
Blood Type B	1.07*	(1.05, 1.08)	0.98	(0.96, 1.00)
Blood Type O	1.11*	(1.10, 1.11)	1.07*	(1.06, 1.09)
No Previous Transplant	REF	N/A N/A	REF	N/A N/A
Previous Transplant	1.46*	(1.40, 1.53)	0.64*	(0.61, 0.67)
UNOS Region 1	REF	N/A N/A	REF	N/A N/A
UNOS Region 2	0.34*	(0.32, 0.35)	0.49*	(0.46, 0.51)
UNOS Region 3	0.45*	(0.44, 0.47)	0.56*	(0.53, 0.58)
UNOS Region 4	0.41*	(0.39, 0.42)	0.52*	(0.49, 0.55)
UNOS Region 5	0.43*	(0.41, 0.44)	0.51*	(0.48 0.54)
UNOS Region 6	0.42*	(0.40, 0.44)	0.38*	(0.35, 0.42)
UNOS Region 7	0.35*	(0.34, 0.36)	0.88*	(0.84, 0.93)
UNOS Region 8	0.21*	(0.20, 0.22)	0.40*	(0.37, 0.42)
UNOS Region 9	0.38*	(0.37, 0.40)	0.39*	(0.36, 0.42)
UNOS Region 10	0.53*	(0.51, 0.55)	0.74*	(0.70, 0.79)
UNOS Region 11	0.40*	(0.38, 0.41)	0.72*	(0.68, 0.77)
No Cigarette Use	REF	N/A N/A	REF	N/A N/A
Cigarette Use	1.00	(0.99, 1.01)	0.91*	(0.90, 0.93)
HLA Mismatch (55% missing)			Excluded due to missingness
0	REF	N/A N/A
1	0.24*	(0.16, 0.34)
2	0.40*	(0.28, 0.55)
3	0.45*	(0.32, 0.63)
4	0.44*	(0.32, 0.62)
5	0.54*	(0.39, 0.76)
6	0.46*	(0.33, 0.64)
Primary Payment Source/Insurance			Excluded due to ambiguity in how to combine groups to ensure sufficient sample sizes for stable parameter estimates
Private Insurance	REF	N/A N/A
Medicaid	0.69*	(0.68, 0.66)
Medicare Fee for Service	0.88*	(0.86, 1.01)
Medicare & Choice	0.67*	(0.66, 0.79)
Children’s Health Insurance Program	0.01*	(0.00, 0.03)
Department of VA	0.58*	(0.56, 0.60)
Other government insurance	0.97*	(0.94, 1.00)
Self	3.30*	(2.81, 3.87)
Donation	drop	(perfect prediction)
Free Care	0.66*	(0.50, 0.87)
Pending	19.9*	(10.8, 36.8)
Foreign Government	0.84*	(0.80, 0.88)
Education Level (3% missing)
None	REF	N/A N/A	REF	N/A N/A
Grade School	1.01	(0.65, 1.59)	0.69*	(0.48, 0.99)
High School or GED	0.96	(0.61, 1.51)	0.43*	(0.30, 0.61)
Some College	1.09	(0.69, 1.71)	0.49*	(0.35, 0.71)
Associate or Bachelor’s Degree	1.14	(0.73, 1.79)	0.43*	(0.30, 0.61)
Post-college or Graduate Degree	1.67*	(1.07, 2.63)	0.55*	(0.39, 0.78)
Employment Status (53% missing)			Excluded due to missingness and because variable is not clinically important
Not Employed	REF	N/A N/A
Employed	1.47*	(1.44, 1.50)
Prior Cardiac Surgery (2% missing)
No	REF	N/A N/A	REF	N/A N/A
Yes	1.54*	(1.51, 1.57)	1.26*	(1.20, 1.32)
Prior lung surgery (52% missing)			Excluded due to missingness; use prior cardiac surgery instead
No	REF	N/A N/A
Yes	1.86*	(1.81, 1.92)
Diabetes
No	REF	N/A N/A	REF	N/A N/A
Yes	0.85*	(0.84, 0.86)	2.00*	(1.97, 2.04)
Functional Status
At least some assistance needed	REF	N/A N/A	REF	N/A N/A
No assistance needed	3.44*	(3.37, 3.52)	21.3*	(20.0, 22.7)
Cardiac index
≥2 L/min/m2	REF	N/A N/A	REF	N/A N/A
<2 L/min/m2	1.50*	(1.49, 1.52)	3.31*	(3.24, 3.38)
Mechanical ventilation
Not continuous	REF	N/A N/A	REF	N/A N/A
Continuous	1.61*	(1.55, 1.67)	18.7*	(16.5, 21.1)
Six-minute walk distance
Q1: [0, 656) feet	REF	N/A N/A	REF	N/A N/A
Q2: [656, 928) feet	2.12*	(2.10, 2.15)	5.10*	(5.01, 5.18)
Q3: [928, 1160) feet	5.98*	(5.91, 6.05)	28.6*	(27.6, 29.6)
Q4: [1160, 4000) feet	3.00*	(2.97, 3.04)	7.44*	(7.28, 7.61)
Creatinine (serum)
Q1: [0.20,0.67) mg/dL	REF	N/A N/A	REF	N/A N/A
Q2: [0.67,0.80) mg/dL	1.32*	(1.31, 1.34)	0.47*	(0.46, 0.48)
Q3: [0.80,0.93) mg/dL	1.58*	(1.56, 1.60)	0.40*	(0.39, 0.41)
Q4: [0.93,6.83] mg/dL	1.29*	(1.27, 1.31)	0.19*	(0.19, 0.20)
Oxygen need at rest
Q1: [0, 2) L/min	REF	N/A N/A	REF	N/A N/A
Q2: [2, 3) L/min	0.88*	(0.86, 0.89)	0.98*	(0.96, 1.00)
Q3: [3, 4) L/min	0.91*	(0.90, 0.91)	1.15*	(1.14, 1.17)
Q4: [4,35] L/min	1.19*	(1.18, 1.21)	1.17*	(1.15, 1.20)
Race/Ethnic: White	REF	N/A N/A	REF	N/A N/A
Race/Ethnic: Black	1.84*	(1.82, 1.87)	1.34*	(1.30, 1.37)
Race/Ethnic: Hispanic	2.73*	(2.67, 2.79)	1.17*	(0.13, 1.20)
Race/Ethnic: Asian	1.67*	(1.62, 1.72)	1.25*	(1.19, 1.32)
Race/Ethnic: Other	1.05*	(1.02, 1.08)	0.66*	(0.60, 0.71)
Baseline Odds (exp(Intercept))	N/A (varies by model)		4.87*	(1.74, 13.6)

^*Statistically significant at the $\alpha =0.05$ level

Figure 1.

Bar charts of the predicted probability of receiving higher priority under the modified LAS compared to the existing LAS for each covariate individually, after adjusting for all other covariates. Covariates exhibiting the largest impact on prioritization changes appear here; additional covariates appear in Appendix Figure 1.

In probability terms, individuals with restrictive lung disease had an 81.1% probability of receiving better priority under the mLAS. Conversely, individuals with obstructive lung disease were almost equally likely to receive better priority (47.2%) versus same or worse priority (52.8%) under the mLAS (Figure 2). Individuals whose six-minute walk distance fell between 928–1160 feet had the highest probability of receiving better priority under the mLAS (76.1%) compared to individuals whose walk distance fell below or above that range. Individuals receiving continuous mechanical ventilation or who required no assistance with daily living tasks also had higher probabilities of receiving better priority under the mLAS. Finally, the probability of receiving better priority under the mLAS decreased as age increased.

Figure 2.

Kapan-Meier estimates of one-year pre-transplant (waitlist) survival, one-year post-transplant survival, and one-year overall survival from the reference simulation (i.e., 6 offers per day) for the overall simulated population (A) and the discordant set (B).

To quantify the extent to which changes in prioritization are driven by changes in predicted pre- or post-transplant survival between the mLAS and LAS, separate generalized r² statistics were obtained for each panel in these plots, as well as overall (Table 4). In both the worse and better priority subsets, changes in predicted pre-transplant survival explained a greater proportion of the variability in differences in rank than changes in predicted post-transplant survival. Among individuals who received worse priority under the mLAS, changes in predicted pre-transplant survival accounted for 14.4% of the variability in differences in rank, while changes in predicted post-transplant survival accounted for 2.8% of this variability. Similarly, among individuals who received better priority under the mLAS, changes in predicted pre-transplant survival accounted for 21.5% of the variability in differences in rank, while changes in predicted post-transplant survival accounted for 10.0% of this variability. This pattern was mostly maintained after stratifying by diagnosis group and six-minute walk distance. However, for individuals with obstructive lung disease who received better priority, changes in predicted post-transplant survival accounted for nearly the same proportion of variability in differences in rank (i.e., 24.8%) compared to changes in predicted pre-transplant survival (i.e., 24.9%).

Table 4.

Generalized r² values obtained from generalized linear mixed models with continuous differences in ranks for each patient under the modified and existing LAS as the outcome and differences in predicted pre-and post-transplant survival as predictors.

Model	Covariate	Difference in Predicted Survival	Lower Priority	Higher Priority
Overall	---	Pre-transplant	0.144 (0.142, 0.147)	0.215 (0.212, 0.217)
		Post-transplant	0.028 (0.027 0.030)	0.100 (0.098 0.101)
Stratified	Obstructive Lung Disease	Pre-transplant	0.498 (0.494 0.501)	0.249 (0.245 0.254)
		Post-transplant	0.067 (0.064 0.069)	0.248 (0.244 0.253)
	Pulmonary Vascular Disease	Pre-transplant	0.049 (0.043 0.055)	0.268 (0.257 0.279)
		Post-transplant	0.033 (0.028 0.038)	0.020 (0.016 0.024)
	Infective Lung Disease	Pre-transplant	0.239 (0.233 0.245)	0.184 (0.166 0.201)
		Post-transplant	0.064 (0.060 0.068)	0.088 (0.075 0.103)
	Restrictive Lung Disease	Pre-transplant	0.018 (0.016 0.021)	0.294 (0.291 0.297)
		Post-transplant	0.006 (0.005 0.008)	0.085 (0.083 0.087)
Stratified	Six-minute walk Q1: [0, 656) feet	Pre-transplant	0.039 (0.037 0.042)	0.244 (0.238 0.250)
		Post-transplant	0.024 (0.022 0.026)	0.025 (0.022 0.028)
	Six-minute walk Q2: [656, 928) feet	Pre-transplant	0.227 (0.222 0.232)	0.198 (0.193 0.202)
		Post-transplant	0.045 (0.049 0.042)	0.127 (0.123 0.131)
	Six-minute walk Q3: [928, 1160) feet	Pre-transplant	0.091 (0.086 0.097)	0.280 (0.276 0.285)
		Post-transplant	0.073 (0.068 0.079)	0.203 (0.199 0.207)
	Six-minute walk Q4: [1160, 4000) feet	Pre-transplant	0.349 (0.343 0.355)	0.207 (0.202 0.211)
		Post-transplant	0.029 (0.026 0.032)	0.159 (0.154 0.163)

Simulation

Our reference simulation involved 364 offer dates and a transplant rate of approximately 6 offers per day, as this rate mimics current donor capacity. Kaplan-Meier estimates of one-year pre-transplant (waitlist) survival, one-year post-transplant survival, and one-year overall survival among all individuals appear in Figure 2A. Waitlist survival improved under the mLAS compared to the LAS, with a median difference of 1.28% (IQR: 0.52%−2.43%). In a waitlist population of 1000 individuals, this result translates into 12.8 (IQR: 5.2–24.3) fewer waitlist deaths per year under the mLAS. Post-transplant and overall survival remained comparable across models. The majority (84.4% [IQR: 83.9%−84.9%]) of individuals received hypothetical transplant under both LAS models. Among the subset of individuals (15.6% [IQR: 15.1%−16.1%]) to whom organs were differentially allocated under the mLAS (discordant set), the median difference in waitlist survival was 6.89% (IQR: 2.46%−11.5%) (Figure 2B). Overall survival in this discordant set appears slightly more favorable under the mLAS as well, with a median difference of 2.52% (IQR: 0.90%−4.16%). In a population of 1000 transplanted individuals, these results imply that 844 (IQR: 839–849) of these individuals would be the same under the two LAS models, but the remaining 156 (IQR: 151–161) individuals would differ. That is, in 156 (IQR: 151–161) instances, the mLAS selects a different person for transplant than the LAS. Among these differentially transplanted individuals, 68.9 (IQR: 24.6–115.0) fewer waitlist deaths and 25.2 (IQR: 9.0–41.6) fewer overall deaths occur per year under the mLAS. Demographic and clinical characteristics of individuals in the discordant set appear in Appendix Figure 2. Increasing or decreasing the transplant rate (to 9 or 3 offers per day, respectively) did not substantially change our results (Appendix Figures 3 and 4).

DISCUSSION

In this study, we used observed and simulated data to examine the clinical impact of a modified LAS score designed to mitigate selection bias. We found that changes in prioritization were more pronounced for patients with certain demographic and clinical characteristics, such as diagnosis group (individuals with restrictive lung disease were more likely to receive better priority), six-minute walk distance (individuals in the third quartile of walk distance had the highest probability of receiving better priority), continuous mechanical ventilation (individuals receiving continuous mechanical ventilation were more likely to receive better priority), and functional status (individuals who required no assistance in daily living tasks had a higher probability of receiving better priority). Changes in predicted pre-transplant survival tended to explain a greater proportion of the variability in differences in rank than changes in predicted post-transplant survival. Simulations suggest that one-year waitlist survival may improve slightly under the mLAS relative to the LAS, whereas one-year post-transplant and overall survival remain comparable under the two models. Among individuals who received hypothetical transplant under one LAS but not the other, waitlist and overall survival appears more favorable under the mLAS; post-transplant survival remains similar to that under the LAS.

The fact that changes in prioritization under the mLAS may be more pronounced for some patients but not others is clinically relevant, as it implies that implementation of the mLAS could lead to important differences in allocation. For example, individuals with restrictive lung disease – who tend to be sicker and unable to wait long for transplant – had an 81.1% probability of receiving better priority under the mLAS (Figure 1). Conversely, individuals with obstructive lung disease – who tend to survive longer without transplant, albeit with lower quality of life – were almost equally likely to receive better priority (47.2%) versus same or worse priority (52.8%) under the mLAS. Moreover, for individuals with obstructive lung disease who received better priority, changes in predicted post-transplant survival accounted for nearly the same proportion of variability in differences in rank (i.e., 24.8%) compared to changes in predicted pre-transplant survival (i.e., 24.9%). Such observations suggest that while improvements in the prediction of waitlist urgency tend to have the largest impact on patient prioritization, changes in the prediction of post-transplant survival can impact prioritization for some subgroups of patients. This result is important to consider, especially as the transplant community continues to debate the role that post-transplant survival should play in organ allocation.^6,10

With regards to six-minute walk distance, continuous mechanical ventilation, functional status, and age, our analyses indicate that after adjusting for other covariates, younger, healthier individuals may have a higher probability of receiving better priority under the mLAS compared to older, frailer individuals. These results are consistent with recent research advocating for more transparency around the impact of age and frailty on pre- and post-transplant survival.^11,12 Such findings could also help inform discussions on what role these factors should play in organ allocation.^13,14

Our simulation demonstrated that the mLAS may yield modest improvements in waitlist survival. The extent of improvement in waitlist survival was larger among the subset of individuals to whom organs were differentially allocated under the mLAS. These findings suggest that alternative organ allocation schemes can confer as much or more survival benefit to patients as the LAS. However, they also imply that evaluating the performance of allocation systems solely based on survival might not capture the full extent of transplant benefit. This observation is consistent with literature calling for greater emphasis on quality of life when evaluating the risks and benefits of transplantation.^15–17

Our study has some limitations. First, while we used observed data to compare the order in which patients were prioritized under the two LAS models and examined the demographic and clinical characteristics of patients who received better priority under the mLAS, we cannot know whether patients who died on the waitlist under the LAS would, in fact, have received transplant had the mLAS been used instead. This limitation motivated us to conduct simulations where we examined how patients’ waitlist and post-transplant survival might change if the mLAS were implemented in clinical practice. Limitations of these simulations include a simplified allocation policy based on blood type and region only (i.e., ignoring other salient, but difficult to measure, factors to organ matching, such as donor/recipient size and sensitization, donor organ quality and acceptance criteria, travel constraints that arise when delivering donor organs to transplant candidates, and recent allocation policy changes surrounding geography such as acuity circles and continuous distribution¹⁸). Future work should incorporate these additional factors into simulations to evaluate how the mLAS might perform in more realistic settings.

Overall, this study demonstrates that implementing a modified LAS that mitigates selection bias into clinical practice can lead to important differences in allocation and possibly modest improvement in one-year waitlist survival, without adversely affecting one-year post-transplant or overall survival. These findings can inform ongoing efforts to modify lung allocation policy, such as the continuous distribution model.

LIST OF ABBREVIATIONS

BMI

Body Mass Index

CI

Confidence Interval

GLMM

Generalized Linear Mixed Models

HLA

Human Leukocyte Antigens

IPCW

Inverse Probability of Censoring Weighting

IPTW

Inverse Probability of Treatment Weighting

IQR

Interquartile Range

LAS

Lung Allocation Score

mLAS

Modified Lung Allocation Score

UNOS

United Network for Organ Sharing

US

United States