Understanding competing risks: a simulation point of view

Arthur Allignol,Jan Beyersmann,Christiane Drechsler,Christoph Wanner,Martin Schumacher

doi:10.1186/1471-2288-11-86

Abstract

BackgroundCompeting risks methodology allows for an event-specific analysis of the single components of composite time-to-event endpoints. A key feature of competing risks is that there are as many hazards as there are competing risks. This is not always well accounted for in the applied literature.MethodsWe advocate a simulation point of view for understanding competing risks. The hazards are envisaged as momentary event forces. They jointly determine the event time. Their relative magnitude determines the event type. 'Empirical simulations' using data from a recent study on cardiovascular events in diabetes patients illustrate subsequent interpretation. The method avoids concerns on identifiability and plausibility known from the latent failure time approach.ResultsThe 'empirical simulations' served as a proof of concept. Additionally manipulating baseline hazards and treatment effects illustrated both scenarios that require greater care for interpretation and how the simulation point of view aids the interpretation. The simulation algorithm applied to real data also provides for a general tool for study planning.ConclusionsThere are as many hazards as there are competing risks. All of them should be analysed. This includes estimation of baseline hazards. Study planning must equally account for these aspects.

Highlights

Competing risks methodology allows for an event-specific analysis of the single components of composite time-to-event endpoints
Similar statements hold for the average of the estimated regression coefficients and the coverage probability of their confidence intervals
We find a slight increase of the competing cumulative incidence functions (CIFs) in the treatment group

Summary

Introduction

Competing risks methodology allows for an event-specific analysis of the single components of composite time-to-event endpoints. A key feature of competing risks is that there are as many hazards as there are competing risks This is not always well accounted for in the applied literature. The analysis of time-to-event data (’survival analysis’) has evolved into a well established application of advanced statistical methodology in medicine. The archetypical application analyses time until death, but combined endpoints are frequently considered. E.g., a recent literature review in clinical oncology [2] found a multitude of combined endpoints including, e.g., progression-free survival, distant metastasis-free survival, locoregional relapse-free survival, etc. Competing risks techniques allow for a more specific analysis in that they consider time until occurrence of the combined endpoint and endpoint type, e.g., progression in contrast to death without prior progression. Excellent tutorial papers in the statistical literature are [8,9]

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