R: Plot the Penalized Profile Likelhood Function

coxphfplot {coxphf} | R Documentation

## Plot the Penalized Profile Likelhood Function

### Description

Plots the penalized profile likelihood for a specified parameter.

### Usage

    coxphfplot(formula = attr(data, "formula"), data = sys.parent(),
               profile, pitch = 0.05, limits, alpha = 0.05,
               maxit = 50, maxhs = 5, epsilon = 1e-06, maxstep = 0.5,
               firth = TRUE,  penalty=0.5, adapt=NULL, legend = "center", ...)

### Arguments

`formula` | a formula object, with the response on the left of the operator, and the model terms on the right. The response must be a survival object as returned by the 'Surv' function.
`data` | a data.frame in which to interpret the variables named in the 'formula' argument.
`profile` | a righthand formula specifying the plotted parameter, interaction or general term, e.g. `~ A` or `~ A : C`.
`pitch` | distances between the interpolated points in standard errors of the parameter estimate, the default value is 0.05.
`limits` | the range of the x-axis in terms of standard errors from the parameter estimate. The default values are the extremes of both confidence intervals, Wald and PL, plus or minus half a standard error, respectively.
`alpha` | the significance level (1-α the confidence level, 0.05 as default).
`maxit` | maximum number of iterations (default value is 50)
`maxhs` | maximum number of step-halvings per iterations (default value is 5). The increments of the parameter vector in one Newton-Rhaphson iteration step are halved, unless the new likelihood is greater than the old one, maximally doing `maxhs` halvings.
`epsilon` | specifies the maximum allowed change in penalized log likelihood to declare convergence. Default value is 0.0001.
`maxstep` | specifies the maximum change of (standardized) parameter values allowed in one iteration. Default value is 2.5.
`firth` | use of Firth's penalized maximum likelihood (`firth=TRUE`, default) or the standard maximum likelihood method (`firth=FALSE`) for fitting the Cox model.
`adapt` | optional: specifies a vector of 1s and 0s, where 0 means that the corresponding parameter is fixed at 0, while 1 enables parameter estimation for that parameter. The length of adapt must be equal to the number of parameters to be estimated.
`penalty` | strength of Firth-type penalty. Defaults to 0.5.
`legend` | if FALSE, legends in the plot would be omitted (default is TRUE).
`...` | other parameters to legend

### Details

This function plots the profile (penalized) log likelihood of the specified parameter. A symmetric shape of the profile (penalized) log likelihood (PPL) function allows use of Wald intervals, while an asymmetric shape demands profile (penalized) likelihood intervals (Heinze & Schemper (2001)).

### Value

A matrix of dimension m \times 3, with m = 1/\code{pitch} + 1. With the default settings, m=101. The column headers are:

`std` | the distance from the parameter estimate in standard errors
`x` | the parameter value
`log-likelihood` | the profile likelihood at `x`

### Author(s)

Georg Heinze and Meinhard Ploner

### References

Firth D (1993). Bias reduction of maximum likelihood estimates. Biometrika 80:27–38.

Heinze G and Schemper M (2001). A Solution to the Problem of Monotone Likelihood in Cox Regression. Biometrics 57(1):114–119.

Heinze G (1999). Technical Report 10/1999: The application of Firth's procedure to Cox and logistic regression. Section of Clinical Biometrics, Department of Medical Computer Sciences, University of Vienna, Vienna. http://cemsiis.meduniwien.ac.at/en/kb/science-research/software/statistical-software/fccoxphf/

Heinze G and Ploner M (2002). SAS and SPLUS programs to perform Cox regression without convergence problems. Computer Methods and Programs in Biomedicine 67:217-223

### See Also

coxphf

### Examples

    time<-c(1,2,3)
    cens<-c(1,1,1)
    x<-c(1,1,0)
    sim<-cbind(time,cens,x)
    sim<-data.frame(sim)
    profplot<-coxphfplot(sim, formula=Surv(time,cens)~x, profile=~x)

[Package coxphf version 1.13 Index]