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Comparing Expanded Criteria Donor (ECD) transplant and waitlist survival using novel two-stage estimation methods
*Qing Pan, Stat Dept, George Washington University 
Douglas E. Schaubel, Biostat Dept, University of Michigan 

Keywords: Estimated stratification indicator, Expanded Criteria Donor, Kidney transplant waiting list, Logistic model, Stratified Cox proportional hazards model, Two-stage modeling

As the demand for donor kidneys has increased, so has the frequency of Expanded Criteria Organ (ECD) kidney transplantation. It is well-known that ECD transplants have higher risk of graft failure compared to non-ECD transplant. However patients receive ECD kidney offers with no guarantee of future availability of non-ECD kidneys. Hence, an accurate contrast between ECD transplant mortality and waiting list mortality is an essential component of clinical decision-making for wait listed patients. Since 2003, patients willing to take ECD transplant are put on a separate waiting list. Although patients placed on the ECD list can still receive non-ECD offers, patients not on the ECD list will not receive ECD offers. Patients willing to accept an ECD kidney are suspected of being less healthy than than patients who decline the ECD option, perhaps in ways that extend beyond the information contained among the adjustment covariates. Therefore, an unbiased comparison between post-ECD and wait list survival requires separating these two types of patients in modeling. However, ECD waitlist status is not recorded before 2003. In order to use information of patients waitlisted before 2003, a novel two-stage procedure is proposed. In the first stage, a logistic model is fitted on post 2003 data for the probability that a patient is willing to be put on the ECD waiting list. In the second stage, Cox proportional hazards model is fitted on pooled pre- and post-2003 data. stratifying on observed or estimated waitlist membership. For pre-2003 data, the waitlist membership is replaced by the probability of being on the ECD waitlist, Asymptotic properties of the proposed estimators are derived, with their applicability to finite samples assessed through simulation. The contrast between post-ECD transplant and waitlist survival is estimated using data obtained from the Scientific Registry for Transplant Recipients.