Combine profile likelihoods from imputed-data model fits

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Description

This function uses CLIP (combination of likelihood profiles) to compute the pooled profile of the posterior after multiple imputation.

Usage

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CLIP.profile(obj = NULL, variable, data, which, firth = TRUE, weightvar, 
   control = logistf.control(), offset = NULL, from = NULL, to = NULL, 
   steps = 101, legacy = FALSE, keep = FALSE)

Arguments

obj

Either a list of logistf fits (on multiple imputed data sets), or the result of analysis of a mice (multiply imputed) object using with.mids.

variable

The variable of interest, for which confidence intervals should be computed. If missing, confidence intervals for all variables will be computed.

data

A list of data set corresponding to the model fits. Can be left blank if obj was obtained with the dataout=TRUE option or if obj was obtained by mice.

which

Alternatively to variable, the argument which allows to specify the variable to compute the profile for as righthand formula, e.g. which=~X.

firth

If TRUE, applies the Firth correction. Should correspond to the entry in obj.

weightvar

An optional weighting variable for each observation.

control

control parameters for logistf, usually obtained by logistf.control()

offset

An optional offset variable.

from

Lowest value for the sequence of values for the regression coefficients for which the profile will be computed. Can be left blank.

to

Highest value for the sequence of values for the regression coefficients for which the profile will be computed. Can be left blank.

steps

Number of steps for the sequence of values for the regression coefficients for which the profile will be computed.

legacy

If TRUE, only R code will be used. Avoid.

keep

If TRUE, keeps the profiles for each imputed data sets in the output object.

Details

While CLIP.confint iterates to find those values at which the CDF of the pooled posterior equals the confidence levels, CLIP.profile will evaluate the whole profile, which enables plotting and evaluating the skewness of the combined and the completed-data profiles. The combined and completed-data profiles are available as cumulative distribution function (CDF) or in the scaling of relative profile likelihood (minus twice the likelihood ratio statistic compared to the maximum). Using a plot method, the pooled posterior can also be displayed as a density.

Value

An object of class CLIP.profile with items

beta

the values of the regression coefficient

cdf

the cumulative distribution function of the posterior

profile

the profile of the posterior

cdf.matrix

An imputations x steps matrix with the values of the completed-data CDFs for each beta

profile.matrix

An imputations x steps matrix with the values of the completed-data profiles for each beta

call

the function call

Author(s)

Georg Heinze and Meinhard Ploner

References

Heinze G, Ploner M, Beyea J (2013). Confidence intervals after multiple imputation: combining profile likelihood information from logistic regressions. Statistics in Medicine, to appear.

Examples

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#generate data set with NAs
freq=c(5,2,2,7,5,4)
y<-c(rep(1,freq[1]+freq[2]), rep(0,freq[3]+freq[4]), rep(1,freq[5]), rep(0,freq[6]))
x<-c(rep(1,freq[1]), rep(0,freq[2]), rep(1,freq[3]), rep(0,freq[4]), rep(NA,freq[5]),
   rep(NA,freq[6]))
toy<-data.frame(x=x,y=y)


# impute data set 5 times
set.seed(169)
toymi<-list(0)
for(i in 1:5){
  toymi[[i]]<-toy
  y1<-toymi[[i]]$y==1 & is.na(toymi[[i]]$x)
  y0<-toymi[[i]]$y==0 & is.na(toymi[[i]]$x)
  xnew1<-rbinom(sum(y1),1,freq[1]/(freq[1]+freq[2]))
  xnew0<-rbinom(sum(y0),1,freq[3]/(freq[3]+freq[4]))
  toymi[[i]]$x[y1==TRUE]<-xnew1
  toymi[[i]]$x[y0==TRUE]<-xnew0
}


# logistf analyses of each imputed data set
fit.list<-lapply(1:5, function(X) logistf(data=toymi[[X]], y~x, pl=TRUE, dataout=TRUE))

# CLIP profile
xprof<-CLIP.profile(obj=fit.list, variable="x", keep=TRUE)
plot(xprof)

#plot as CDF
plot(xprof, "cdf")

#plot as density 
plot(xprof, "density")