Competing Risks Analysis of Kidney Transplant Waitlist Outcomes: Two Important Statistical Perspectives

Abstract

Modern competing risks analysis has 2 primary goals in clinical epidemiology as follows: (i) to maximize the clinician's knowledge of etiologic associations existing between potential predictor variables and various cause-specific outcomes via cause-specific hazard models, and (ii) to maximize the clinician's knowledge of noteworthy differences existing in cause-specific patient risk via cause-specific subdistribution hazard models (cumulative incidence functions [CIFs]). A perfect application exists in analyzing the following 4 distinct outcomes after listing for a deceased donor kidney transplant (DDKT): (i) receiving a DDKT, (ii) receiving a living donor kidney transplant (LDKT), (iii) waitlist removal due to patient mortality or a deteriorating medical condition, and (iv) waitlist removal due to other reasons. It is important to realize that obtaining a complete understanding of subdistribution hazard ratios (HRs) is simply not possible without first having knowledge of the multivariable relationships existing between the potential predictor variables and the cause-specific hazards (perspective #1), because the cause-specific hazards form the "building blocks" of CIFs. In addition, though we believe that a worthy and practical alternative to estimating the median waiting-time-to DDKT is to ask, "what is the conditional probability of the patient receiving a DDKT, given that he or she would not previously experience one of the competing events (known as the cause-specific conditional failure probability)," only an appropriate estimator of this conditional type of cumulative incidence should be used (perspective #2). One suggested estimator, the well-known "one minus Kaplan-Meier" approach (censoring competing events), simply does not represent any probability in the presence of competing risks and will almost always produce biased estimates (thus, it should never be used).

Keywords: cause-specific hazard rates; cause-specific waiting time-to-event distributions following kidney transplant waitlisting; conditional cumulative incidence; cumulative incidence; modern competing risks analysis.

Figure 1

(a) Nonparametric cause-specific cumulative incidence curves for the whole cohort in Stewart et al. (based on “eyeballed” annual values from their Supplementary Figure S2). (b) Proper nonparametric cause-specific conditional cumulative incidence curves for the whole cohort in Stewart et al. CIF, cumulative incidence function; DDKT, deceased donor kidney transplant; LDKT, living donor kidney transplant.

Figure 2

(a) Nonparametric cause-specific Kaplan-Meier curves for the whole cohort in Hart et al. (based on “eyeballed” annual values from their Figure 1a). (b) Nonparametric cause-specific cumulative incidence curves for the whole cohort in Hart et al. (based on “eyeballed” annual values from their Figure 1b). (c) Nonparametric cause-specific 1 − Kaplan-Meier curves for the whole cohort in Hart et al. (d) Nonparametric cause-specific conditional cumulative incidence curves for the whole cohort in Hart et al. (e) Nonparametric cause-specific cumulative hazard curves for the whole cohort in Hart et al. CIF, cumulative incidence function; DDKT, deceased donor kidney transplant; LDKT, living donor kidney transplant.