MICE for Cox model

I encountered this problem about 18 months ago. I contacted Prof. Fox 
and Dr. Malewski (the R package maintainers for mice) but they referred 
me to Prof. van Buuren. I wrote to Prof. van Buuren but am unable to 
find his reply (if he did reply).

Here are the functions I used at that time, if you want to take it with 
lots of salt. Let me know if you find anything fishy with it.

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)

   oldClass(object) <- if (.SV4.) "mira" else c("mira", "coxph")
   return(object)
}

And in the function 'pool', the small sample adjustment requires 
residual degrees of freedom (i.e. dfc). For a cox model, I believe that 
this is simply the number of events minus the regression coefficients. 
There is support for this from middle of page 149 of the book by Parmer 
& Machin (ISBN 0471936405). Please correct me if I am wrong.

Here is the slightly modified version of pool :

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

   call <- match.call()
   if (!is.mira(object)) stop("The object must have class 'mira'")

   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)
   oldClass(fit) <- if (.SV4.) "mipo" else c("mipo", oldClass(object))
   return(fit)
}

print.miro only gives the coefficients. Often I need the standard errors
as well since I want to test if each regression coefficient from
multiple imputation is zero or not. Since the function summary.mipo does
not exist, can I suggest the following

summary.mipo <- 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 )

}

Hope this helps.

Regards, Adai

MICE for Cox model

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