Outcomes matter: estimating pre-transplant survival rates of kidney-transplant patients using simulator-based propensity scores

The current kidney allocation system in the United States fails to match donors and recipients well. In an effort to improve the allocation system, the United Network of Organ Sharing (UNOS) defined factors that should determine a new allocation policy, and particularly patients’ potential remaining lifetime without a transplant (pre-transplant survival rates). Estimating pre-transplant survival rates is challenging because the data available on candidates and organ recipients is already “contaminated” by the current allocation policy. In particular, the selection of patients who are offered (and decide to accept) a kidney is not random. We therefore expect differences in mortality-related characteristics of organ recipients and of candidates who have not received transplant. Such differences introduce bias into survival models.

Existing approaches for tackling this selection bias either ignore the difference between candidates and recipients or assume that selection to transplant is based solely on patients’ pre-transplant information, irrespective of the potential allocation outcome. We argue that in practice the allocation is dependent on the anticipated allocation outcome, which is a major factor in selection to transplant. Moreover, we show that ignoring the anticipated outcome increases model bias rather than decreases it. In this paper, we propose a novel simulator-based approach (SimBa) that adjusts for the selection bias by taking into account both pre-transplant and anticipated outcome information using simulation. We then fit survival models to kidney transplant waitlist data and compare the different adjustment methods. We find that SimBa not only fits the data best, but also captures a key aspect of the current allocation policy, namely, that the probability of kidney allocation increases in the expected pre-transplant life years.

1. Health condition in KPSAM is modeled through (1) medical updates recorded during major status changes (given to the simulator as an input), and (2) time-dependent variables, such as age, dialysis time, etc. that the simulator automatically keeps updated over time. The simulation also incorporates health updates in a more realistic way compared to any static model (such as the logistic regression): updated information is introduced into the model only when it becomes available (i.e., when the change occurs), and only if it occurs before the event of transplant or death. In contrast, static models include status update information in a static fashion, as if it is available upon patient arrival, and irrespective of the outcome.

2. Simultaneous transplantation of a kidney and pancreas is performed for those who have kidney failure as a complication of insulin-dependent diabetes mellitus (also called Type I diabetes).

3. The data reported here have been supplied by the United Network for Organ Sharing as the contractor for the Organ Procurement and Transplantation Network. The interpretation and reporting of these data are the responsibility of the author(s) and in no way should be seen as an official policy of or interpretation by the OPTN or the U.S. Government.

4. Under the assumption of Poisson arrival times, as evidenced from the data.

5. We examined predictive accuracy for the deceased group based on separate training and holdout samples. While all three survival models generated mostly near-zero prediction errors, SimBa was much better at predicting PTLY values of deceased candidates who joined the waitlist late in the study and died early. This result emphasizes the importance of including the arrival time (rather than only the PTLY) in the model.

Authors and Affiliations

1. Graduate School of Business, Bar Ilan University, Ramat Gan, Israel

   Inbal Yahav

2. Indian School of Business, Hyderabad, India

   Galit Shmueli

Corresponding author

Correspondence to Inbal Yahav.

This work was supported in part by Health Resources and Services Administration contract HHS/HRSA SRTR. The content is the responsibility of the authors alone and does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S. Government.

Appendix A: Description of variables in U.S. kidney waitlist dataset

Below is a list of variables used throughout the paper. We list their abbreviation and description.

ABO type AB (ABO_AB):

Patient’s blood group is AB

ABO type B (ABO_B):

Patient’s blood group is B

ABO type O (ABO_O):

Patient’s blood group is O

Age (AGE):

Patient’s age upon arrival

African American (AFRICAN):

Patient’s race is African American

Albumin (ALBUMIN):

Patient albumin level. Low albumin levels reflect possibility of diseases in which the kidneys cannot prevent albumin from leaking from the blood into the urine and being lost

Body Mass Index (BMI):

Patient’s Body Mass Index (ratio of weight to square root of the hight). BMI provided a measure of a patient’s overweight (BMI > 25) or underweight (BMI < 18.5)

Diabetes (DIAB):

Indicates whether a patient is diabetic

Diagnosis unknown (NotSPECIFIED):

Indicates whether a patient has no diagnosis

Dialysis (DIAL):

Indicates whether a patient needs dialysis

Functional status: minor disability (MINOR_DIS):

Patient can function with no assistance

Functional status: some disability (SOME_DIS):

Patient can function with little assistance

Hospitalization History (HOSPITALIZATION):

Number of previous hospitalizations

Hypertension (HYPERTENSION):

Indicates whether a patient was diagnosed with malignant hypertension (a complication of hypertension characterized by very elevated blood pressure)

Human Leukocyte Antigen (HLA):

Mean patient’s antigen match with donors pool (ranges between [0,6])

Male (MALE):

Patient’s gender is male

No Antigens (ABDR):

Indicates weather the patients has no antigens

Number of A antigens (A):

Number of a patient’s A antigens

Number of B antigens (B):

Number of a patient’s B antigens

Number of DR antigens (DR):

Number of a patient’s DR antigens

Panel Reactive Body (PRA):

Patient’s Panel Reactive Antibody (PRA) level (measure for sensitization level)

Polycystic kidneys (POLYCYSTIC):

Indicates weather a patient was diagnosed with polycystic kidney syndrome (a genetic disorder that results in massive enlargement of the kidneys)

Previous transplant (PrevTRANS):

Indicates whether a patient had previous transplants

Simultaneous kidney-pancreas (KP):

Indicates whether a patient is waiting for simultaneous pancreas-kidney transplant

Time on dialysis (DT):

Dialysis time in years upon arrival

Appendix B: Graphical comparison between the AFT models

Comparison of CCA, logistic, and SimBa AFT model coefficients. Each line corresponds to the parameter’s 95 % confidence interval

Full size image

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