BACKGROUND: In studies of all-cause mortality, the fundamental epidemiological concepts of rate and risk are connected through a well-defined one-to-one relation. An important consequence of this relation is that regression models such as the proportional hazards model that are defined through the hazard (the rate) immediately dictate how the covariates relate to the survival function (the risk). METHODS: This introductory paper reviews the concepts of rate and risk and their one-to-one relation in all-cause mortality studies and introduces the analogous concepts of rate and risk in the context of competing risks, the cause-specific hazard and the cause-specific cumulative incidence function. RESULTS: The key feature of competing risks is that the one-to-one correspondence between cause-specific hazard and cumulative incidence, between rate and risk, is lost. This fact has two important implications. First, the naïve Kaplan-Meier that takes the competing events as censored observations, is biased. Secondly, 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. An example with relapse and non-relapse mortality as competing risks in a stem cell transplantation study is used for illustration. CONCLUSION: The two implications of the loss of one-to-one correspondence between cause-specific hazard and cumulative incidence should be kept in mind when deciding on how to make inference in a competing risks situation.
BACKGROUND: In studies of all-cause mortality, the fundamental epidemiological concepts of rate and risk are connected through a well-defined one-to-one relation. An important consequence of this relation is that regression models such as the proportional hazards model that are defined through the hazard (the rate) immediately dictate how the covariates relate to the survival function (the risk). METHODS: This introductory paper reviews the concepts of rate and risk and their one-to-one relation in all-cause mortality studies and introduces the analogous concepts of rate and risk in the context of competing risks, the cause-specific hazard and the cause-specific cumulative incidence function. RESULTS: The key feature of competing risks is that the one-to-one correspondence between cause-specific hazard and cumulative incidence, between rate and risk, is lost. This fact has two important implications. First, the naïve Kaplan-Meier that takes the competing events as censored observations, is biased. Secondly, 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. An example with relapse and non-relapse mortality as competing risks in a stem cell transplantation study is used for illustration. CONCLUSION: The two implications of the loss of one-to-one correspondence between cause-specific hazard and cumulative incidence should be kept in mind when deciding on how to make inference in a competing risks situation.
Authors: A Gratwohl; J Hermans; J M Goldman; W Arcese; E Carreras; A Devergie; F Frassoni; G Gahrton; H J Kolb; D Niederwieser; T Ruutu; J P Vernant; T de Witte; J Apperley Journal: Lancet Date: 1998-10-03 Impact factor: 79.321
Authors: Irene J Zaal; John W Devlin; Marijn Hazelbag; Peter M C Klein Klouwenberg; Arendina W van der Kooi; David S Y Ong; Olaf L Cremer; Rolf H Groenwold; Arjen J C Slooter Journal: Intensive Care Med Date: 2015-09-24 Impact factor: 17.440
Authors: Marloes G M Derks; Cornelis J H van de Velde; Daniele Giardiello; Caroline Seynaeve; Hein Putter; Johan W R Nortier; Luc Y Dirix; Esther Bastiaannet; Johanneke E A Portielje; Gerrit-Jan Liefers Journal: Oncologist Date: 2019-01-03
Authors: Salvatore T Scali; Catherine K Chang; Dan Raghinaru; Michael J Daniels; Adam W Beck; Robert J Feezor; Scott A Berceli; Thomas S Huber Journal: J Vasc Surg Date: 2012-12-12 Impact factor: 4.268