can mice() handle crr()? Fine-Gray model - r

Question

My doubt is if it is possible to pool multiple imputation data set, from "mice()", on a fit model of Fine-Gray from "crr()", and if it is statistically correct...
example
library(survival)
library(mice)
library(cmprsk)
test1 <- as.data.frame(list(time=c(4,3,1,1,2,2,3,5,2,4,5,1, 4,3,1,1,2,2,3,5,2,4,5,1),
status=c(1,1,1,0,2,2,0,0,1,1,2,0, 1,1,1,0,2,2,0,0,1,1,2,0),
x=c(0,2,1,1,NA,NA,0,1,1,2,0,1, 0,2,1,1,NA,NA,0,1,1,2,0,1),
sex=c(0,0,0,NA,1,1,1,1,NA,1,0,0, 0,0,0,NA,1,1,1,1,NA,1,0,0)))
dat <- mice(test1,m=10, seed=1982)
#Cox regression: cause 1
models.cox1 <- with(dat,coxph(Surv(time, status==1) ~ x +sex ))
summary(pool(models.cox1))
#Cox regression: cause 1 or 2
models.cox <- with(dat,coxph(Surv(time, status==1 | status==2) ~ x +sex ))
models.cox
summary(pool(models.cox))
#### crr()
#Fine-Gray model
models.FG<- with(dat,crr(ftime=time, fstatus=status, cov1=test1[,c( "x","sex")], failcode=1, cencode=0, variance=TRUE))
summary(pool(models.FG))
#Error in pool(models.FG) : Object has no vcov() method.
models.FG

Answer 1

There are a couple of things that need to be done to get this to work.
Your initial data and imputation.
library(survival)
library(mice)
library(cmprsk)
test1 <- as.data.frame(list(time=c(4,3,1,1,2,2,3,5,2,4,5,1, 4,3,1,1,2,2,3,5,2,4,5,1),
status=c(1,1,1,0,2,2,0,0,1,1,2,0, 1,1,1,0,2,2,0,0,1,1,2,0),
x=c(0,2,1,1,NA,NA,0,1,1,2,0,1, 0,2,1,1,NA,NA,0,1,1,2,0,1),
sex=c(0,0,0,NA,1,1,1,1,NA,1,0,0, 0,0,0,NA,1,1,1,1,NA,1,0,0)))
dat <- mice(test1,m=10, print=FALSE)
There is no vcov method for crr models which mice requires, however,
we can access the covariance matrix using the model$var returned value.
So write own vcov method to extract, and also need a coef method.
vcov.crr <- function(object, ...) object$var # or getS3method('vcov','coxph')
coef.crr <- function(object, ...) object$coef
There is also an error in how the model is passed to with.mids: your code has cov1=test1[,c( "x","sex")], but really you want cov1 to use the imputed data. I am not sure how to correctly write this as an expression due to the cov1 requiring a matrix with relevant variables, but you can easily hard code a function.
# This function comes from mice:::with.mids
Andreus_with <-
function (data, ...) {
call <- match.call()
if (!is.mids(data))
stop("The data must have class mids")
analyses <- as.list(1:data$m)
for (i in 1:data$m) {
data.i <- complete(data, i)
analyses[[i]] <- crr(ftime=data.i[,'time'], fstatus=data.i[,'status'],
cov1=data.i[,c( "x","sex")],
failcode=1, cencode=0, variance=TRUE)
}
object <- list(call = call, call1 = data$call, nmis = data$nmis,
analyses = analyses)
oldClass(object) <- c("mira", "matrix")
return(object)
}
EDIT:
The mice internals have changed since this answer; it now uses the broom package to extract elements from the fitted crr model. So tidy and glance methods for crr models are required:
tidy.crr <- function(x, ...) {
co = coef(x)
data.frame(term = names(co),
estimate = unname(co),
std.error=sqrt(diag(x$var)),
stringsAsFactors = FALSE)
}
glance.crr <- function(x, ...){ }
The above code then allows the data to be pooled.
models.FG <- Andreus_with(dat)
summary(pool(models.FG))
Note that this gives warnings over df.residual not being defined, and so large samples are assumed. I'm not familiar with crr so a more sensible value can perhaps be extracted -- this would then be added to the tidy method. (mice version ‘3.6.0’)