CLIP.confint: Confidence Intervals after Multiple Imputation: Combination...

In logistf: Firth's Bias-Reduced Logistic Regression

Confidence Intervals after Multiple Imputation: Combination of Likelihood Profiles

Description

This function implements the new combination of likelihood profiles (CLIP) method described in Heinze, Ploner and Beyea (2013). This method is useful for computing confidence intervals for parameters after multiple imputation of data sets, if the normality assumption on parameter estimates and consequently the validity of applying Rubin's rules (pooling of variances) is in doubt. It consists of combining the profile likelihoods into a posterior. The function CLIP.confint searches for those values of a regression coefficient, at which the cumulative distribution function of the posterior is equal to the values specified in the argument ci.level (usually 0.025 and 0.975). The search is performed using R's optimize function.

Usage

CLIP.confint(
  obj = NULL,
  variable = NULL,
  data,
  firth = TRUE,
  weightvar = NULL,
  control = logistf.control(),
  ci.level = c(0.025, 0.975),
  pvalue = TRUE,
  offset = NULL,
  bound.lo = NULL,
  bound.up = NULL,
  legacy = 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
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()
ci.level	The two confidence levels for each tail of the posterior distribution.
pvalue	If TRUE, will also compute a P-value from the posterior.
offset	An optional offset variable
bound.lo	Bounds (vector of length 2) for the lower limit. Can be left blank. Use only if problems are encountered.
bound.up	Bounds (vector of length 2) for the upper limit. Can be left blank. Use only if problems are encountered.
legacy	If TRUE, will use pure R code for all model fitting. Can be slow. Not recommended.

Details

For each confidence limit, this function performs a binary search to evaluate the combined posterior, which is obtained by first transforming the imputed-data likelihood profiles into cumulative distribution functions (CDFs), and then averaging the CDFs to obtain the CDF of the posterior. Usually, the binary search manages to find the confidence intervals very quickly. The number of iterations (mean and maximum) will be supplied in the output object. Further details on the method can be found in Heinze, Ploner and Beyea (2013).

Value

An object of class CLIP.confint, with items:

variable	The variable(s) which were analyzed
estimate	The pooled estimate (average over imputations)
ci	The confidence interval(s)
pvalue	The p-value(s)
imputations	The number of imputed datasets
ci.level	The confidence level (input)
bound.lo	The bounds used for finding the lower confidence limit; usually not of interest. May be useful for error-tracing.
bound.up	The bounds used for finding the upper confidence limit
iter	The number of iterations (for each variable and each tail)
call	The call object

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.

See Also

logistf() for Firth's bias-Reduced penalized-likelihood logistic regression.

Examples

#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))
  
 # CLIP confidence limits
 CLIP.confint(obj=fit.list, data = toymi)
 

logistf documentation built on Aug. 18, 2023, 5:06 p.m.