  The Scientific Registry of Transplant Recipients (SRTR) system has become a
rich resource for understanding the complex mechanisms of graft failure after
kidney transplant, a crucial step for allocating organs effectively and
implementing appropriate care. As transplant centers that treated patients
might strongly confound graft failures, Cox models stratified by centers can
eliminate their confounding effects. Also, since recipient age is a proven
non-modifiable risk factor, a common practice is to fit models separately by
recipient age groups. The moderate sample sizes, relative to the number of
covariates, in some age groups may lead to biased maximum stratified partial
likelihood estimates and unreliable confidence intervals even when samples
still outnumber covariates. To draw reliable inference on a comprehensive list
of risk factors measured from both donors and recipients in SRTR, we propose a
de-biased lasso approach via quadratic programming for fitting stratified Cox
models. We establish asymptotic properties and verify via simulations that our
method produces consistent estimates and confidence intervals with nominal
coverage probabilities. Accounting for nearly 100 confounders in SRTR, the
de-biased method detects that the graft failure hazard nonlinearly increases
with donor's age among all recipient age groups, and that organs from older
donors more adversely impact the younger recipients. Our method also delineates
the associations between graft failure and many risk factors such as
recipients' primary diagnoses (e.g. polycystic disease, glomerular disease, and
diabetes) and donor-recipient mismatches for human leukocyte antigen loci
across recipient age groups. These results may inform the refinement of
donor-recipient matching criteria for stakeholders.
