![]() ![]() ![]() Predictions from the fitted model may then be returned as either a relative risk prediction, X β ^ or exp ( X β ^ ), or h 0 is also estimated and a survival distribution is predicted as h ^ ( t ) = h ^ 0 ( t ) exp ( X β ^ ). In practice, software fits the model by estimating the coefficients, β ^. Less abstractly, consider the Cox Proportional Hazards (CPH) model ( Cox, 1972): h ( t ) = h 0 ( t ) exp ( X β ) where h 0 is the ‘baseline’ hazard function, X are covariates, and β are coefficients to be estimated. This prediction may be presented in one of three ways, as a: (i) time-to-event, Y ∈ ℝ > 0, which represents the time until the event takes place (ii) a relative risk, ϕ ∈ ℝ, which represents the risk of the event taking place compared to other subjects in the same sample or (iii) the probability distribution for the time to the event, S ∈ Distr ( ℝ > 0 ), where Distr ( ℝ > 0 ) is the set of distributions over ℝ > 0. ![]() Predictive survival models estimate the distribution of the time until an event of interest takes place. ![]()
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