14  Competing Risk Analysis

$$ % Basic sets/Variables

% Probability and statistics % % Linear algebra % Math functions % Distributions

% Update symbols $$

Take for example the analysis where we are interested in observing whether a subject dies of a specific disease during the trial, then a competing risk is if the death is caused by another (specified) disease. The hazard rate for a specific type of event is noted by: \(h_j(t)\), where the overall hazard rate, with \(k\) different events, would then be described as: \(h(t) = \sum_{j=1}^k h_j(t)\).

The CIF (See Equation 8.1) for a specific event, \(F_j(t) = \mathbb{P}\left(T\leq t, C = j\right) = \int_t^t h_j(u) \cdot S(u)\,\mathrm{d}u\), describes. Similar to the overall hazard ratio, the overall CIF can be described by \(F(t) = \sum_{j=1}^k F_j(t)\).