# Fit a Cox model with a ridge penalty on all covariates

### Description

Fits a simple Cox model with a ridge penalty on all coefficients. The penalty weight can be optimized using a REML-type likelihood method or be chosen by the user.

### Usage

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### Arguments

`formula` |
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. |

`lambdaFixed` |
when TRUE the function does not seek to optimize the penalty weight. |

`lambda` |
When lambdaFixed is FALSE lambda is a scalar giving the starting value for the weight of the penalty. When lambdaFixed is true lambda is the chosen weight of the penalty. |

`eps` |
a small value. The criterion of convergance. |

`data` |
an optional data frame containing the variables named in the formula. |

`iter.max` |
maximum number of iterations, default is 200. |

`mon` |
when true the function prints out the computed lambda weigh in each iteration. |

### Value

`cox.ridge`

returns an object of class "cox.ridge"
The function print.cox.ridge is used to obtain and print a summary of the results.
An object of class "cox.ridge" is a list containing the following components:

`call ` |
function call. |

`coef ` |
the vector of coefficients. |

`loglik ` |
the penalized log-likelihood of the model. |

`time ` |
a vector with failure/censoring times. |

`death ` |
a vector of status indicator. |

`X` |
a matrix of covariates. |

`iter ` |
number of iterations used to maximise likelihood at a fixed lambda. |

`inter.it ` |
number of iterations used to find optimal lambda.' |

`lambda ` |
optimal weight of the penalty. |

`Hat ` |
the hat matrix at convergance. |

`hess` |
the Hessian matrix of second derivatives. |

### Note

The function at the current form cannot handle missing values. The user has to take prior action with missing values before using this function.

### Author(s)

Aris Perperoglou

### References

Perperoglou A.(2013)*Cox models with dynamic ridge penalties on
time varying effects of the covariates*. Statistics in Medicine, to appear

### See Also

coxph, Dynamic.Ridge

### Examples

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