coxphftest: Penalized Likelihood Ratio Test in Cox Regression

In coxphf: Cox Regression with Firth's Penalized Likelihood

Penalized Likelihood Ratio Test in Cox Regression

Description

Performs a penalized likelihood ratio test for hypotheses within a Cox regression analysis using Firth's penalized likelihood.

Usage

coxphftest(
  formula,
  data,
  test = ~.,
  values,
  maxit = 50,
  maxhs = 5,
  epsilon = 1e-06,
  maxstep = 0.5,
  firth = TRUE,
  adapt = NULL,
  penalty = 0.5
)

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.
test	righthand formula of parameters to test (e.g. ~ B + D). As default the null hypothesis that all parameters are 0 is tested.
values	null hypothesis values, default values are 0. For testing the hypothesis H0: B1=1 and B4=2 and B5=0, specify test= ~ B1 + B4 + B5 and values=c(1, 2, 0).
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 todeclare 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.

Details

This function performs a penalized likelihood ratio test on some (or all) selected parameters. It can be used to test contrasts of parameters, or factors that are coded in dummy variables. The resulting object is of the class coxphftest and includes the information printed by the proper print method.

Value

testcov	the names of the tested model terms
loglik	the restricted and unrestricted maximized (penalized) log likelihood
df	the number of degrees of freedom related to the test
prob	the p-value
call	the function call
method	the estimation method (penalized ML or ML)

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.

Examples

library(survival)
testdata <- data.frame(list(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8),
stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17),
event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0),
x1    =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0),
x2    =c(0, 1, 1, 1, 0, 0, 1, 0, 1, 0),
x3    =c(1, 0, 1, 0, 1, 0, 1, 0, 1, 0)))

summary( coxphf( formula=Surv(start, stop, event) ~ x1+x2+x3, data=testdata))

# testing H0: x1=0, x2=0

coxphftest( formula=Surv(start, stop, event) ~ x1+x2+x3, test=~x1+x2,  data=testdata)



# How to test total effect of a variable with time-dependent effect

# NOT RUN (works)
#fitt<- coxphf( formula=Surv(start, stop, event) ~ x1+x2+x3*stop, data=testdata, pl=FALSE)

#test <- coxphf(formula=Surv(start, stop, event) ~ x1+x2+x3*stop, data=testdata, adapt=c(1,1,0,0))

# PLR p-value for x3 + x3:stop
#pchisq((fitt$loglik[2]-test$loglik[2])*2, 2, lower.tail=FALSE)

#NOT RUN (does not work)
#test <- coxphf(formula=Surv(start, stop, event) ~ x1+x2+x3*stop, data=testdata, test=~x3+stop:x3)

coxphf documentation built on Aug. 11, 2023, 5:06 p.m.