screen.main.cox: Adaptive function for screening main effects and performing a Cox model

Description

The adaptive function selects the most important main effects and performs a Cox proportional hazards model for the usage in the argument screen.main in the function sprinter. For time-to-event data two methods are available for the screening step: Either a Cox proportional Hazards model with variable selection by adjusted univariate p-values (fit.uniCox) can be performed or a model is build via CoxBoost (fit.CoxBoost).

Usage

fit.uniCox(time, status, x, unpen.index = NULL, 
             method = 'bonferroni', sig = 0.05,...)

fit.CoxBoost(time, status, x, unpen.index = NULL, 
             seed = 123, 
             stepno = NULL,
             K = 10, 
             criterion = 'pscore', 
             nu = 0.05,
             maxstepno=200,
             standardize = T, 
             trace = T, ...)

Arguments

time

vector of length n specifying the observed times.

status

censoring indicator, i.e., vector of length n with entries 0 for censored observations and 1 for uncensored observations.

n * p matrix of covariates.

unpen.index

vector with indices of mandatory covariates, where parameter estimation should be performed unpenalized.

seed

Seed for random number generator.

stepno

number of boosting steps.

number of folds to be used for cross-validation. If K is larger or equal to the number of non-zero elements in status, leave-one-out cross-validation is performed.

criterion

indicates the criterion to be used for selection in each boosting step. "pscore" corresponds to the penalized score statistics, "score" to the un-penalized score statistics. Different results will only be seen for un-standardized covariates ("pscore" will

value for evaluating the penalty for the update of an individual element of the parameter vector in each boosting step (penalty = sum(status)*(1/nu-1)).

maxstepno

maximum number of boosting steps to evaluate, i.e, the returned "optimal" number of boosting steps will be in the range [0,maxstepno].

standardize

logical value indicating whether covariates should be standardized for estimation. This does not apply for mandatory covariates, i.e., these are not standardized.

trace

logical value indicating whether progress in estimation should be indicated by printing the name of the covariate updated.

method

method for adjusting p-values. A variable is selected if its adjusted p-value is less than sig.

sig

selection level. A variable is selected if its adjusted p-value is less than sig

...

further arguments passed to methods.

Value

The adaptive function returns the following values:
modelCox proportional Hazards model. fit.uniCox returns an object of class coxph and fit.CoxBoost returns an object of class CoxBoost.
xnamesvector of length p containing the names of the covariates.
indmainvector of length p containing the indices of the selected covariates.
betavector of length p containing the coefficients of the selected covariates.

Details

fit.uniCox and fit.CoxBoost are adapted functions for the usage of screening main effects in the function sprinter for time-to-event data. Both approaches fit a multivariate Cox proportional hazards model. fit.uniCox{ fit.uniCox fits a multivariate Cox proportional hazards model after a variable selection step. Therefore univariate Cox proportional hazard models are performed for each variable. All variables with univariate adjusted p-values less than sig are selected for the multivariate model. The variables with indices unpen.index are mandatory for the multivariate Cox model. } fit.CoxBoost{ fit.CoxBoost fits a Cox proportional hazards model by using CoxBoost. If the number of boosting steps is not specified in stepno the step number is evaluated by cross validation. See more information about fitting a Cox proportional hazards model by CoxBoost in CoxBoost. } Implementing new functions for the argument screen.main{ New functions for screening potential main effects can be implemented by the user. Therefore, the function must be constructed in a way that a Cox proportional Hazards model is generated. This model should be returned together with the names of the variables used in the model, called xnames, and their corresponding indices, called indmain. The following arguments must be enclosed in this function: ll{ time vector of length n specifying the observed times. status censoring indicator, i.e., vector of length n with entries 0 for censored observations and 1 for uncensored observations. x n * p matrix of covariates. unpen.index vector with indices of mandatory covariates. } With this instructions the user can create new functions for screening main effects. To set further arguments for this function create a list of arguments, which can be quoted in args.screen.main. In the next step the screened main effects will be used for orthogonalizing the data by computing residuals corresponding to the selected main effects and the mandatory covariates. }

References

Andersen, P. and Gill, R. (1982). Cox's regression model for counting processes, a large sample study. Annals of Statistics 10, 1100-1120. Binder, H., Allignol, A., Schumacher, M., and Beyersmann, J. (2009). Boosting for high-dimensional time-to-event data with competing risks. Bioinformatics, 25:890-896.