# [R] Plotting survival curves after multiple imputation

Robert Long W.R.Long at leeds.ac.uk
Thu Feb 14 15:07:34 CET 2013

```I am working with some survival data with missing values.

I am using the mice package to do multiple imputation.

I have found code in this thread which handles pooling of the MI results:
https://stat.ethz.ch/pipermail/r-help/2007-May/132180.html

Now I would like to plot a survival curve using the pooled results.

Here is a reproducible example:

require(survival)
require(mice)

set.seed(2)

dt <- colon

fit <- coxph(Surv(time,etype)~rx + sex + age, data=colon)

dummy <- data.frame(sex=c(1,1,1),rx=c("Obs","Lev","Lev+5FU"),age=c(40,40,40))
plot(survfit(fit, newdata=dummy) )

# now create some missing values in the data
dt <- colon
dt\$rx[sample(1:nrow(dt),50)] <- NA
dt\$sex [sample(1:nrow(dt),50)] <- NA
dt\$age[sample(1:nrow(dt),50)] <- NA

imp <-mice(dt)

fit.imp <- coxph.mids(Surv(time,etype)~rx + sex + age,imp)
# Note, this function is defined below...

imputed=summary.impute(pool.impute(fit.imp))
print(imputed)

# now, how to plot a survival curve with the pooled results ?

coxph.mids <- function (formula, 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]] <- coxph(formula, data = data.i, ...)
}

object <- list(call = call, call1 = data\$call,
nmis = data\$nmis, analyses = analyses)

return(object)
}

pool.impute <- function (object, method = "smallsample") {

if ((m <- length(object\$analyses)) < 2)
stop("At least two imputations are needed for pooling.\n")

analyses <- object\$analyses

k     <- length(coef(analyses[[1]]))
names <- names(coef(analyses[[1]]))
qhat  <- matrix(NA, nrow = m, ncol = k, dimnames = list(1:m,names))
u     <- array(NA, dim = c(m, k, k),
dimnames = list(1:m, names, names))

for (i in 1:m) {
fit       <- analyses[[i]]
qhat[i, ] <- coef(fit)
u[i, , ]  <- vcov(fit)
}

qbar <- apply(qhat, 2, mean)
ubar <- apply(u, c(2, 3), mean)
e <- qhat - matrix(qbar, nrow = m, ncol = k, byrow = TRUE)
b <- (t(e) %*% e)/(m - 1)
t <- ubar + (1 + 1/m) * b
r <- (1 + 1/m) * diag(b/ubar)
f <- (1 + 1/m) * diag(b/t)
df <- (m - 1) * (1 + 1/r)^2

if (method == "smallsample") {

if( any( class(fit) == "coxph" ) ){

### this loop is the hack for survival analysis ###

status   <- fit\$y[ , 2]
n.events <- sum(status == max(status))
p        <- length( coefficients( fit )  )
dfc      <- n.events - p

} else {

dfc <- fit\$df.residual
}

df <- dfc/((1 - (f/(m + 1)))/(1 - f) + dfc/df)
}

names(r) <- names(df) <- names(f) <- names
fit <- list(call = call, call1 = object\$call, call2 = object\$call1,
nmis = object\$nmis, m = m, qhat = qhat, u = u,
qbar = qbar, ubar = ubar, b = b, t = t, r = r, df = df,
f = f)

return(fit)
}

summary.impute <- function(object){

if (!is.null(object\$call1)){
cat("Call: ")
dput(object\$call1)
}

est  <- object\$qbar
se   <- sqrt(diag(object\$t))
tval <- est/se
df   <- object\$df
pval <- 2 * pt(abs(tval), df, lower.tail = FALSE)

coefmat <- cbind(est, se, tval, pval)
colnames(coefmat) <- c("Estimate", "Std. Error",
"t value", "Pr(>|t|)")

cat("\nCoefficients:\n")
printCoefmat( coefmat, P.values=T, has.Pvalue=T, signif.legend=T )

cat("\nFraction of information about the coefficients
missing due to nonresponse:","\n")
print(object\$f)

ans <- list( coefficients=coefmat, df=df,
call=object\$call1, fracinfo.miss=object\$f )
invisible( ans )
}