Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 35 / 7 / 3

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- Solution 3

Solution

Integrate the type-A first-event density from zero to

t

. The type-A cumulative incidence is

F_{A} (t) = Pr (T \leq t, J = A) = \int_{0}^{t} α e^{- (α + β) u} d u = \frac{α}{α + β} (1 - e^{- (α + β) t}) .

This is the cumulative incidence function in the competing risks model, distinct from the hypothetical net risk

1 - e^{- α t}

obtained by removing B.

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