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The present work focuses on modelling the event-specific hazard which is not directly interpretable as the marginal hazard function.
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For each of these three LWA models, λ 0 t is an unspecified marginal baseline hazard function considered as common for all the pairs, so for the whole population.
In section Methods, we first introduce an example of a simple interplay between two markers (effect modification) that leads to marginal crossing hazard functions and has prompted us to derive a novel pseudo-R2 measure for such non-proportional situations.
The hazard function of the marginal distribution of each T i is usually called the cause-specific hazard.
The hazard function of the marginal model for the j t h event for the i t h subject is h ij (t ) = h 0 j (t ) exp (β j ′ Z i (t ) ).
Therefore, it will lead to bias if we use a marginal hazard ratio to estimate a hazard ratio.
Under this study design, we developed weighted estimating procedures for model parameters in marginal multiplicative intensity models and for the cumulative baseline hazard function.
We examined the impact of four factors on the statistical power function: number of observed events, prevalence of treatment, the marginal hazard ratio, and the strength of the treatment-selection process.
An alternative approach for studying competing risks is to model the subdistribution hazard function [ 14], which permits estimating covariate effects that are directly interpretable in terms of marginal probabilities.
Hazard function.
Integrated hazard function.
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