Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 4 / c

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- Solution c

Solution

The Nelson–Aalen estimator is

H (t) = \sum_{t_{j} \leq t} \frac{d _{j}}{r _{j}} .

For tied events,

d_{j} / r_{j}

uses the number of events sharing time

t_{j}

and the risk-set size just before that time.

H_{A} (5) = \frac{1}{5} + \frac{1}{4} + 1 = \frac{29}{20}, H_{B} (5) = \frac{2}{4} = \frac{1}{2} .

Their ratio is

29/10 = 2.9

.

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