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Chapter 8

# Competing Risks Models

## 8.1 Introduction

Classical competing risks models will be discussed, as well as their modern interpretations. The basic problem is that we want to consider more than one type of event, but where exactly one will occur. For instance, consider different causes of death.

Figure 8.1

Competing risks: causes of death.

The first problem is: How can the intensities

$\begin{array}{ll}\left(\left({\alpha }_{1}\left(t\right),{\alpha }_{2}\left(t\right),{\alpha }_{3}\left(t\right)\right),\hfill & t>0\hfill \end{array}$

be nonparametrically estimated? It turns out that this is quite simple. The trick is to take one cause at at time and estimate its intensity as if the rest of the causes (events) are censorings. The real problem starts when these ...

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