METHODOLOGY

An Introduction to Competing Risks Beenish S. Manzoor, MPH1, Sruthi Adimadhyam, MS1, Surrey M. Walton, PhD1,2, 1Department of Pharmacy, Systems Outcomes and Policy; 2Center for Pharmacoepidemiology and Pharmacoeconomic Research, University of Illinois at Chicago, College of Pharmacy, Chicago, IL, USA

Survival analysis, or time-to-event analysis, complement of the Kaplan-Meier function (1 Beenish S. is a cornerstone of health outcomes minus Kaplan-Meier function) is appropriate. Manzoor, MPH research. Common examples include studies However, in the presence of competing of treatment related effects related to risks, the Kaplan-Meier estimate upward progression-free survival in cancer patients, biases the estimation of incidence [2-6] time to stroke in patients with atrial by treating competing events as censored fibrillation, or time to receiving a transplant and removing censored observations from in dialysis patients. Almost always, data the risk sets in subsequent time points. In KEY POINTS . . . sets used for conducting survival analyses contrast, the Cumulative Incidence Function Competing risks are events which include censored observations where (CIF) uses the censored competing event to prevent the occurrence or modify the patients are lost to follow up or the study inform event-free survival probability and risk of the primary event or outcome period ends before the event of interest has consequently, overall survival probability. of interest. occurred. Conventional methodology used As such, the incidence derived from CIF is in , based on the standard interpreted as the probability of experiencing Cumulative incidence function Kaplan-Meier method, typically relies on the the primary event conditioned upon not should be used in the presence assumption of non-informative censoring experiencing either event (primary or of competing risks to avoid which asserts that censoring occurs competing) until that time. Given this, the overestimation and bias that occurs independently of the risk for the outcome of CIF appropriately calculates incidence by using the traditional Kaplan-Meier interest [1,2]. Violation of this assumption correctly handling competing events, instead method. introduces bias in the analysis. In a cohort of just censoring them. of patients where the main outcome is In the presence of competing risks, cardiovascular death, patients surviving to In traditional survival analysis, the overall the analyst may determine cause- the end of the study are censored and this (and its complement, specific or subdistribution hazards censoring is typically assumed to be non- cumulative incidence) describes the based on their research question. informative. data. One way to determine the effect of covariates on the survival function is using Of note, however, is that if a patient a Cox proportional hazards model (CPH) is deemed to have died from a non- which assumes that hazard functions are cardiovascular event during the study proportional over time. In a CR framework, period, then the patient is also considered data is described using CIF; and the effect censored when using the Kaplan Meier of covariates is determined by using either survival function to evaluate the incidence of two different hazard functions: cause- of cardiovascular death. This latter case of specific or Fine and Gray/ subdistribution. censoring is called a competing risk and The cause-specific hazard function often results in informative censoring. The represents the instantaneous rate of use of a Kaplan-Meier survival function occurrence of the kth event in patients that in presence of competing events violate have not experienced any event and the Fine the assumption of independent censoring and Gray subdistribution hazard function whenever the competing event results in represents the instantaneous rate of failure informative censoring. from the kth event in patients that have not experienced any event, plus patients that This article will provide a brief introduction have experienced a competing event [2]. to methods for describing competing Given our previous example above, the risks, methods to account for competing cause-specific hazard of cardiovascular risks in survival analysis, and practical death describes the instantaneous rate of considerations when using a competing risks cardiovascular death in patients that have framework. not experienced any event. Similarly, the subdistribution hazard function describes Methods for Competing Risks the instantaneous rate of cardiovascular Competing risks (CR) are events which death in patients that have not experienced prevent the occurrence or modify the risk of any event and those who have experienced the primary event or outcome of interest [2]. death due to non-cardiovascular events. In the absence of CR, estimating cumulative Both of these hazard functions can be incidence of events over time via the employed in hazard regression models, >

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Table 1: Recommendations for Analyzing Competing Risks [2]

• A cumulative incidence function (CIF) should be used in the presence of competing risks to avoid overestimation and bias using the Kaplan-Meier method in traditional survival analysis • Depending on the objective of the study, analysts should decide which of the two competing risk hazard functions to use. • The Cause-specific hazard function is more appropriate for etiologic research objectives. • The Subdistribution hazard function is more appropriate for prognostic research objectives.

Adapted from Austin et al.[2]

and practical considerations of their presence of CR. Furthermore, two CR use are centered on the objective of the related hazard functions may be employed research being conducted. Regression in hazard and should using a cause-specific hazard function be chosen given the research question. will render a coefficient that describes the These CR analysis options are available relative effect of a covariate on the relative in statistical software packages including increase in the rate of the primary event in SAS, STAT and R, and recommendations for observations that are event-free, lending to analysis of CR appear in Table 1. the examination of the casual relationship between risk factors and an event, and References therefore more appropriate for etiologic [1] Satagopan JM, Ben-Porat L, Berwick M, research objectives including treatment Robson M, Kutler D, Auerbach AD. A note on competing risks in survival . Br J effects [2-3,8]. Whereas regression Cancer. 2004;91:1229–1235. [2] Austin PC, using the subdistribution hazard function Lee DS, Fine JP. Introduction to the analysis of describes the effect of covariates on the survival data in the presence of competing risks. ADVERTISE incidence and this may be more in-line Circulation. 2016;133:601–609. [3] Lau B, with predicting the rate of occurrence Cole SR, Gange SJ. Competing risk regression of events [2,7]. Of course, it may be models for epidemiologic data. Am J Epidemiol. HERE! best to utilize both methods for a full 2009;170:244–256. [4] Putter H, Fiocco M, understanding of the impact of particular Geskus RB. Tutorial in : competing risks Value & Outcomes Spotlight covariates and/or treatments. and multi-state models. Stat Med. 2007;26:2389– 2430. [5] Varadhan R, Weiss CO, Segal JB, Wu AW, fosters dialogue within the Scharfstein D, Boyd C. Evaluating health outcomes global health economics and The use of a Kaplan- in the presence of competing risks: a review of “ statistical methods and clinical applications. Med outcomes research (HEOR) Meier survival function Care. 2010;48(6 suppl):S96–S105. [6] Berry in presence of SD, Ngo L, Samelson EJ, Kiel DP. Competing risk community by reviewing the of death: an important consideration in studies of impact of HEOR methodologies competing events older adults. J Am Geriatr Soc. 2010;58:783–787. violates the assumption [7] Koller MT, Raatz H, Steyerberg EW, Wolbers on health policy and health M.Competing risks and the clinical community: care delivery to ultimately of independent irrelevance or ignorance? Stat Med. 2012;31:1089– 1097. [8] Noordzij M, Leffondré K, van Stralen improve decision making censoring. KJ, Zoccali C, Dekker FW, Jager KJ. When do we need competing risks methods for survival analysis for health globally. ” in nephrology? Nephrol Dial Transplant. 2013 Conclusion Nov;28(11):2670-7. n Datasets used in survival analysis may We are now offering this often lend themselves to CR. When new ad space size-option informative censoring is related to the treatment or underlying risk factors, then opportunity in 2017. it becomes problematic in measuring For further info on this ad treatment effects. CR can also be issue in space opportunity accurately forecasting events in a decision size and rate, go to: or markov model. The CIF, accounting for censored observations in its risk set, avoids www.ispor.org/ overestimation compared to the traditional Kaplan-Meier estimate, and is the preferred ValueOutcomes method of measuring incidence in the Spotlight

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