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© 2020 Elsevier B.V. In the end we all die, but not all at the same age and from the same cause. A competing risks analysis quantifies the occurrence over time of mutually exclusive event types. Competing risks methods are increasingly more often used in different branches of science. Yet, there remains a lot of confusion with respect to the quantities that can be estimated under specific assumptions, as well as their interpretation. Some characteristics are different from the classical time-to-event setting. With right censored time-to-event data, analysis is often based on the rate, or hazard. In the presence of competing risks, three different hazards can be defined: the cause-specific hazard, the subdistribution hazard, and the marginal hazard. The first two quantify different aspects of the competing risks process. Both can be used as basis for quantifying the risk, the cumulative event probability, although direct approaches to estimation of the risk exist as well. The marginal hazard considers the (possibly completely hypothetical) setting in which the competing risks are absent; it requires the competing risks to be independent for unbiased estimation. Using examples from the medical and epidemiological field, I explain when and how to use models and techniques for competing risks and how to interpret the results. Emphasis is on nonparametric estimation. Regression models are covered briefly. I discuss how to deal with time-varying covariables when the subdistribution hazard is the estimand. Software is readily available. In fact, many analyses can be done using standard software for time-to-event analysis.

Original publication

DOI

10.1016/bs.host.2019.11.001

Type

Book title

Handbook of Statistics

Publication Date

01/01/2020