Psi_par: psi
In CompetingRisk: The Semi-Parametric Cumulative Incidence Function

Description Usage Arguments Details References

This function computes psi_kl(t;z_0).

1	Psi_par(formulas, kk, ll, CIFest, data, newdata, group, event, save, group.in.train)

`formulas`	A list of length K contains formula objects, where K is the number of types of failures. Each element is a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function.
`kk`	The k^th type of failure.
`ll`	The l^th type of failure.
`CIFest`	The point estimator of the cumulative incidence function.
`data`	A data frame with n observations and p number of covariates.
`newdata`	A data frame or a matrix used for prediction. If not specified, the original data will be used instead.
`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`.
`event`	This is an internal binary indicator to specify if any type of failure occurs at a given time.
`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{ψ}_{kl}(t; z_{0}) = \frac{1}{n}∑_{i=1}^{n}(\hat{F}_{k}(t; z_{0}) - \hat{F}_{k}(\tilde{T}_{i}; z_{0}))(z_{0}- \bar{Z}(\hat{β}_{l}, \tilde{T_{i}}))\frac{\exp(\hat{β}_{l}^{T}z_{0})δ_{li}I(\tilde{T}_{i} ≤ t)}{S^{(0)}(\hat{β}_{l}, \tilde{T}_{i})}

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.