Compute_Omega: Omega_k
In CompetingRisk: The Semi-Parametric Cumulative Incidence Function

Description Usage Arguments Details References

This function computes Omega_k.

1	Compute_Omega(est, x, y, kk, event, group, save, group.in.train)

`est`	The model fitting details from the k^th cause-specific hazards model.
`x`	The design matrix associated with the k^th type of failure, of dimension n observations * p_k covariates.
`y`	The survival response associated with the k^th type of failure.
`kk`	The k^th type of failure.
`event`	This is an internal binary indicator to specify if any type of failure occurs at a given time.
`group`	The name of the group covariates (if any). If specified, the cumulative hazards will be estimated for each group seperately. Default is `group=NULL`.
`save`	An option to save the computed S0 and S1. It is highly recommended for large-scale dataset to improve the computational efficiency. Default is `save=FALSE`.
`group.in.train`	This argument is valid only when the group argument is specified. If group is presented in both data and newdata, use `group.in.train=T`; If group is presented in only newdata but not data, use `group.in.train=F`.

This function computes

\hat{Ω}_{k} = \frac{1}{n}∑_{i=1}^{n}\bigg(\frac{S^{(2)}(\hat{β}_{k}, \tilde{T}_{i})} {S^{(0)}(\hat{β}_{k}, \tilde{T}_{i})} - \bar{Z}(\hat{β}_{k}, \tilde{T_{i}})^{\otimes 2} \bigg)δ_{ki}

Cheng, S. C., Jason P. Fine, and L. J. Wei. "Prediction of cumulative incidence function under the proportional hazards model." Biometrics (1998): 219-228.

CompetingRisk documentation built on May 30, 2017, 2:54 a.m.