Biometrics 62, 910–917 September 2006 DOI: 10.1111/j.1541-0420.2006.00527.x A Sequential Stratification Method for Estimating the Effect of a Time-Dependent Experimental Treatment in Observational Studies Douglas E. Schaubel, 1, ∗ Robert A. Wolfe, 1 and Friedrich K. Port 2 1 Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109-2029, U.S.A. 2 University Renal Research and Education Association, Ann Arbor, Michigan 48103, U.S.A. ∗ email: deschau@umich.edu Summary. Survival analysis is often used to compare experimental and conventional treatments. In ob- servational studies, the therapy may change during follow-up and such crossovers can be summarized by time-dependent covariates. Given the ever-increasing donor organ shortage, higher-risk kidneys from ex- panded criterion donors (ECD) are being transplanted. Transplant candidates can choose whether to accept an ECD organ (experimental therapy), or to remain on dialysis and wait for a possible non-ECD transplant later (conventional therapy). A three-group time-dependent analysis of such data involves estimating param- eters corresponding to two time-dependent indicator covariates representing ECD transplant and non-ECD transplant, each compared to remaining on dialysis on the waitlist. However, the ECD hazard ratio estimated by this time-dependent analysis fails to account for the fact that patients who forego an ECD transplant are not destined to remain on dialysis forever, but could subsequently receive a non-ECD transplant. We propose a novel method of estimating the survival benefit of ECD transplantation relative to conventional therapy (waitlist with possible subsequent non-ECD transplant). Compared to the time-dependent analysis, the proposed method more accurately characterizes the data structure and yields a more direct estimate of the relative outcome with an ECD transplant. Key words: Cohort study; Failure time data; Matching; Proportional hazards model; Risk set; Survival analysis. 1. Introduction End-stage renal disease (ESRD; also known as chronic kid- ney failure) is increasing in many countries worldwide and has become a major public health issue due to its associated mortality and health care cost. Patients with renal failure must receive either dialysis or a kidney transplant in order to remain alive. Medically suitable patients are placed on a wait- ing list in order to receive a cadaveric renal transplant. Gen- erally, mortality rates are significantly lower post-transplant compared to those on the waitlist (WL) (Wolfe et al., 1999; Rabbat et al., 2000). Due to the ever-increasing shortfall in availability of donor organs, patients are electing to receive a cadaveric organ from an expanded criterion donor (ECD) with increasing frequency. Port et al. (2002) formally quantified the term “ECD” to apply to deceased donors in whom trans- planted kidneys are associated with more than a 70% increase in transplant failure, compared to a non-ECD kidney. Com- parisons between ECD and non-ECD transplant outcomes are useful, but a more relevant comparison is between accepting an ECD transplant and “conventional therapy,” which is to remain on the WL with the potential to subsequently receive a non-ECD transplant. The Cox (1972) proportional hazards model provides an extremely flexible way to make covariate-adjusted mortal- ity comparisons among therapies when a patient’s mode of therapy may change over time. The model is widely used for survival analysis and is readily accepted by clinicians. As ap- plied to the current setting, where there are three mutually exclusive “states” (WL dialysis, ECD transplant, and non- ECD transplant), time-dependent indicator covariates could be set up for the two transplant states and a proportional haz- ards analysis could be carried out in a straightforward man- ner. The estimated hazard ratio (HR) for ECD would reflect the mortality contrast between an ECD transplant and dial- ysis on the WL. In interpreting the ECD/WL hazard ratio, patients currently on the WL could determine the reduction in mortality hazard which would apply at that point in time if they received an ECD transplant compared to remaining on the waitlist. Although informative, this “three-group time-dependent” (T3) analysis does not address the choice faced by the candi- date. The question for the patient is not “Would I be better off with an ECD transplant than being on dialysis?” but, rather, “Would I be better off accepting an ECD organ, given that, if I do not accept it, I could subsequently be offered a non- ECD organ?” The “experimental” group is ECD transplant. However, the “conventional therapy” group is not “waitlist,” but, rather, “refusing the ECD organ and possibly receiving 910 C  2006, The International Biometric Society