Data Analysis with Competing Risks and Intermediate States

P(t T < t + ∆t, E = k T t)

λ

k

(t) = lim

≤ | ≥

, (2.1)

Δt 0

∆t



K

K

P(t T < t + ∆t, E = e T t)

λ

e

(t) = lim

e=1

≤ | ≥

Δt 0

∆t

e=1

↓

P(t T < t + ∆t T t)

= lim

≤ | ≥

= h(t) . (2.3)

Δt↓0

∆t

60 Data Analysis with Competing Risks and Intermediate States

you can skip Section 2.4 from 2.4.2 onwards. In Section 2.5 we describe how

to obtain confidence intervals and in Section 2.6 we introduce the competing

risks analogues of the log-rank test, one for each type of hazard.

We refer to Section 1.7 for all the notation that is used. Unless specified

otherwise, we assume that the entry and