Competing risks: you only die once

Abstract

The current study uses recent developments in competing risks methodologies that have not yet been applied to large scale meta-analyses.

Readers of this journal are familiar with the challenges associated with the competing risks between mortality and end-stage renal disease (ESRD), especially in elderly patients where the provision of conservative management is weighed against the benefits and costs of preparing for and providing renal replacement therapy [1–4].

In the current issue, Sud et al. [5] focused on progression from Stage 3 chronic kidney disease (CKD) to Stage 4 CKD, and considered the competing risks for hospitalization, acute kidney injury (AKI) and death in a retrospective cohort study of 1609 Canadian patients with Stage 3 CKD referred for tertiary nephrology care between 2001 and 2008. Progression to Stage 4 CKD was assessed by two independent outpatient estimated glomerular filtration rate (eGFR) values <30 mL/min/1.73 m². The primary outcomes included death, first AKI hospitalization and first all-cause hospitalization prior to ESRD, where AKI hospitalization included the first admission with an AKI diagnosis code as a primary or secondary diagnosis. This analysis is reminiscent of that published by Go et al. [6], which described increased risks for death, hospitalization and cardiovascular events in a large population-based study, and noted the increased risks associated with Stage 3B CKD compared with Stage 3A CKD. The current analysis shows that patients who progressed to Stage 4 CKD had significantly increased risks of death, AKI and hospitalization. The final eGFR was a better predictor of outcome than the magnitude of the previous change in eGFR. This provocative finding has obvious implications about risk assessments for patients going forward, even if information about the previous renal status is not readily available, and is consistent with previous work by O'Hare et al. [7]. This observation has also recently been confirmed by a large-scale meta-analysis by the CKD Progression Consortium [8].

Competing risks occur in survival analysis when a subject is at risk of more than one type of event. A competing risk is an event that either hinders the observation of the event of interest or modifies the chance that this event occurs [9]. A classic example is consideration of different causes of death. If a subject dies of one particular cause they are no longer at risk of death from any other cause. Another example is the probability of Staphylococcus infection during a hospital admission; censoring may occur due to death or hospital discharge. Hospital discharge is a non-fatal competing event that prevents the event of interest from occurring as a first event [10].

The usual approaches to survival analysis, such as the Kaplan–Meier method and standard Cox proportional hazards regression, may be inappropriate in the presence of competing risks, and alternative methods specifically designed for analyzing competing risks models have been developed. Two specific examples in the nephrology world that require competing risk analysis are comparisons of mortality risk in patients with CKD compared with the mortality risks of patients who have progressed to ESRD, because the risk of mortality is different for patients who reach ESRD than for those who do not progress [11]. In studies of mortality among dialysis patients, renal transplantation is a competing event for the primary event of interest (e.g. death). Another relevant example is a reinterpretation of the reported ‘protective effects’ of β-blockers in patients with prostate cancer [12]. Patients who take blockers are at increased risk of dying from other causes, hence the apparent protective effect against prostate cancer. Competing risk analysis may not be appropriate if outcome ‘events’ are not mutually exclusive, and if these events are better described as effect modifiers of the primary risk of interest rather than a competing outcome event. The consideration of cause-specific hazard rate, which can be estimated using standard survival techniques by censoring competing events, may fall somewhere in between and requires consideration on a case-by-case basis.

The standard approaches to competing risk analyses are not computationally efficient even when subjects have competing events with well-behaved proportional hazards. Non-proportional hazard issues, time-dependent interactions and large data sets are a challenge because the estimation procedure requires that time-dependent weights be calculated for those with a competing event. Computation efficiency is compromised by the way weighting terms for time–covariate interactions are estimated; the data sets are expanded with nodes at the times of the unique event for all individual who have events. Improved computational algorithms that require a single expansion of the data sets before estimation of the weighted parameters are much more efficient. After restructuring the data and incorporating weights, the standard tools for survival analysis can be used for analysis of competing risk data. P.C. Lambert (submitted for publication) has recently developed a similar approach in STATA to that described by Geskus in R [13, 14], as has Kohl et al. [15] in SAS.

The current article [5] uses the implementation in R, and also provides graphs of the competing incidence functions in the Supplementary data. Cause-specific cumulative incidence functions give the absolute (or crude) risk of the event accounting for the fact that it is impossible to have the event if a competing event occurs first. The one-to-one correspondence between cause-specific hazard and cumulative incidence, between rate and risk, is lost with competing risk analysis [16]. As a direct consequence, the way in which covariates are associated with the cause-specific hazards may not coincide with the way these covariates are associated with the cumulative incidence. Cause-specific hazards as well as cumulative incidence functions should be reported for all competing risk analyses [17], and the distinction between sub-hazard ratios and cause-specific hazard ratios been to be better defined than was done in the article by Sud et al. [5].

The current view is that the sub-distribution hazards described by the Fine and Gray approach are the most appropriate method to use for prognostic studies [9, 18]. There is a bit of awkwardness about the interpretation of sub-hazards for different causes of death. The sub-hazard function includes subjects who have had a competing event in the risk set; a patient is still considered at risk of death from cancer even after they have died from cardiovascular disease. Thus, the sub-hazard ratios are not a standard epidemiological rate and should not be interpreted in a similar way to a standard hazard ratio. The Fine and Gray model is a useful way to get predictions of the competing incidence functions, but the interpretation of the parameters should not be unduly emphasized, nor should causal inferences be drawn. Alternative approaches to cause-specific analysis have been described [12, 16], but the fundamental concern about drawing causal inferences from epidemiologic associations studies in an important limitation.

The progression of CKD may reflect multiple bouts of AKI with incomplete recovery of kidney function [19, 20]. The analysis by Sud et al. [5] analyzed the competing risks of death, developing AKI or hospitalization in a cohort of CKD patients who progressed from Stage 3 to Stage 4 CKD. Siew et al. [20] recently analyzed the competing risks of death compared with recurrent AKI. Recurrent AKI is not a hard endpoint like death or ESRD, yet having suffered a previous bout of AKI could well increase the risks of subsequent adverse events like death, progression to ESRD or even another episode of AKI. These questions might be better approached with a conditional risk assessment [21] or multi-state illness-death models [10, 22] than with competing risk analysis.

In an example from stem cell transplant for acute leukemia [17], with competing endpoints of relapse, treatment-related death or other causes at the end of the 2 year follow-up period, two different treatment protocols were considered as effect modifiers. The analysis is ‘right censored’ after some pre-specified time interval. Applying this approach to CKD patients, other effect modifiers could be considered analogous to the treatment strata in the acute leukemia study, such as age strata, gender, race, baseline estimated glomerular filtration rate, and past or present cardiac events and past or present AKI. The individual strata could then be compared with cumulative incidence functions rather than the more problematic comparisons of risk coefficients derived from sub-hazard functions. As mentioned above, the article by Sud et al. [5] includes cumulative incidence function graphs in their Supplementary data, Figure S3A shows the cumulative incidence functions for death before ESRD compared with ESRD. For this cohort of patients with advanced CKD, the probability of death before ESRD by 5 years was 0.2 compared with the probability 0.04 for progression to ESRD by 5 years. Supplementary data, Figure S3C shows an early increase in the probability of developing AKI that is not evident in the sub-hazard ratios plotted in Supplementary data, Figure S4. The statistical significance of differences between cumulative incidence curves can be tested using modified log-rank tests (P.C. Lambert, submitted for publication).

In summary, Sud et al. [5] described the competing risks for death, all-cause and AKI-related hospitalization and ESRD among a cohort of patients with Stage 3 CKD who progressed to State 4 CKD. The final eGFR, rather than the rate of progression from Stage 3 to Stage CKD appears to be a more important predictor of outcome. The current analysis uses recent developments in competing risks methodologies that have not yet been applied to large-scale meta-analyses [8].

CONFLICT OF INTEREST STATEMENT

None declared. (See related article by Sud et al. Progression to Stage 4 chronic kidney disease and death, acute kidney injury and hospitalization risk: a retrospective cohort study. Nephrol Dial Transplant 2016; 31: 1122–1130)