Competing Risks Models Clause Samples

Competing Risks Models. Competing risks models are useful when there are multiple ways that an event can end, or fail, and these different types of failure events are recorded. These different failure types are said to compete with each other because only one of them can occur first and end the event of interest. Unlike with a traditional ▇▇▇ model that is used for questions about duration without a competing risk component, competing risks models can be used to determine the cause-specific hazard function and cumulative incidence function. One approach to competing risks models was developed by ▇▇▇▇ and Gray (1999). They used a semi-parametric model to determined the cumulative incidence functions. This is done by first defining a subhazard function for failure cause i as h¯i(t) = limΔt→0 = P{t ≤ T < t + Δt, f ailure f rom cause i | T > t or (T ≤ t and not cause i)} Δt For cause i, the subhazard is the probability of failure, at that time, t, from cause i, as long as there has not been a failure before time t. This also allows for the calculation of the cumulative incidence function, which is, at time t, for cause i, the probability of failing from cause i before (or up to) time t. Mathematically, this is written as CIFi(t) = 1 — exp{— t h¯i(u)du} Each possible failure outcome is treated individually and its likelihood of occurring is calculated as opposed to the alternative options. The outcome for each of these regressions gives the results in terms of subhazard ratios (SHR). With a subhazard ratio greater than one, it means that higher values of this variable are associated with higher incidence of the failure type, controlling for the other covariates and the fact that the other types of failures can occur, while a SHR less than one indicates the opposite. The calculations for the competing risks models are done in STATA using the stcrreg command.