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#' @title Cumulative incidence estimation for interval censored competing risks data using multiple imputation
#' @author Marc Delord \email{<mdelord@@gmail.com>}
#' @description Uses multiple imputation to compute the cumulative incidence function for interval censored competing risks data
#' @param k An integer, indicates the number of iteration to perform
#' @param m An integer, indicates the number of imputation to perform at each iteration
#' @param status The name of the column where status are to be found
#' @param trans Denomination of the event of interest in the status column
#' @param data The input data (see details)
#' @param conf.int Logical, computes the confidence interval
#' @param cens.code Censor indicator in the status column of the data
#' @param alpha Parametrize the confidence interval width
#' @examples
#' res <- MI.ci(k = 5, m = 5, status = 'status', trans = 1 , data = ICCRD,
#' conf.int = TRUE, cens.code = 0 , alpha = 0.05)
#' res
#' print(res)
#' plot(res)
#' @export
#' @import survival
#' @return \code{est} A data frame with estimates
#' @return \code{\dots} Other objects
#' @details This function uses a multiple imputation approach to estimate a cumulative incidence function for interval censored competing
#' risks data.
#' Estimates are computed using Rubin's rules (Rubin (1987)). The cumulative incidence is computed as the mean of
#' cumulative incidences over imputations. The variance is computed at each point by combining the within imputation variance and the
#' between imputation variance augmented by an inflation factor to take into account the finite number of imputations.
#' At each iteration, the cumulative incidence is updated and multiple imputation is performed using the updated estimate.
#' If \code{conf.int} is required, the log-log transformation is used to compute the lower confidence interval.
#'
#' Print and plot methods are available to handle results.
#'
#' The \code{data} must contain at last three columns: \code{left}, \code{right} and \code{status}. For interval censored data, the
#' \code{left} and \code{right} columns indicates lower and upper bounds of intervals, respectively. \code{Inf} in the
#' \code{right} column stands for right censored observations. When an observation is right censored, the \code{status} column must
#' contain the censor indicator specified by \code{cens.code}. The transition of interest must be specified by the \code{trans}
#' parameter.
#'
#' @references Delord, M. & Genin, E. Multiple Imputation for Competing Risks Regression with Interval Censored Data Journal of Statistical
#' Computation and Simulation, 2015
#' @references PAN, Wei. A Multiple Imputation Approach to Cox Regression with Interval-Censored Data. Biometrics, 2000, vol. 56, no 1,
#' p. 199-203.
#' @references Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys.
#' @references Schenker, N. and Welsh, A. (1988). Asymptotic results for multiple imputation. The Annals of Statistics pages 1550-1566.
#' @references Tanner, M. A. and Wong, W. H. (1987). An application of imputation to an estimation problem in grouped lifetime analysis.
#' Technometrics 29, 23-32.
#' @references Wei, G. C., & Tanner, M. A. (1991). Applications of multiple imputation to the analysis of censored regression data.
#' Biometrics, 47(4), 1297-1309.
#' @seealso \link[survival]{Surv}, \link[survival]{survfit}
MI.ci<-function( k , m , data , status , trans , cens.code , conf.int = F , alpha = 0.05 ){
if( !is.numeric(k) ) stop('k must be an integer')
if( !is.numeric(m) ) stop('m must be an integer')
if( !is.data.frame(data) ) stop('data must be a data.frame')
if( !is.logical(conf.int) ) stop('conf.int must be logical')
if( alpha <= 0 | alpha >= 1 ) stop('alpha must be in ] 0 , 1 [')
#if(k <= 1) stop('You may consider the MI.ci function')
cl<-match.call()
prep <- preproc.crreg( data = data , m = m , trans = trans , status = status , cens.code = cens.code )
data_int <- prep$data2
data_fix <- prep$data1
or <- prep$or
I <- prep$I
r2 <- as.character( rep( data[ , status ] , m ) )
r2 <- replace( r2 , r2 == cens.code , 0 )
r1 <- as.character( data[ , status ] )
r1 <- replace( r1 , r1 == cens.code , 0 )
#Multiple Imputation
CI <- MI.ci_1( m = m , status = status , trans = trans , cens.code = cens.code,
data = data , conf.int = F , alpha = alpha , ntimes = NULL )$est
CI$diff <- c(0 , diff( CI$est ) )
for(i in 1:k){
ss1<-apply(data_int , 1 , function(x ) subset( CI , time >= as.numeric(x['left']) & time <= as.numeric(x['right']) ) )
tk2<-lapply(seq_len(nrow(data_int)) ,function(X) ss1[[X]]$time)
samples<-t( sapply( seq_len(nrow(data_int)) , function(X) {
pk2 <- ss1[[ X ]]$diff
sapply( 1:m , function(x){
if( sum( pk2 ) & length( pk2 ) > 1 ) sample( tk2[[ X ]] , size = 1 , prob = pk2 )
else mean( tk2[[ X ]] ) } ) } ) )
samples2<-rbind(samples,data_fix)[or,]
times<-as.vector(samples2)
ci<-Surv( time = times , event = r2 , type = 'mstate')
fitCI<-survfit( ci ~ 1 , weights = rep( 1 , length( times ) ) / m , conf.type = 'none')
w <- which( fitCI$states == trans )
sd <- fitCI$std.err[ , w ]
pr <- fitCI$pstate[ , w ]
t0 <- fitCI$time
CI<-unique(rbind(c(time = 0 , est = 0 ) , data.frame( time = t0 , est = pr ) ))
CI$diff <- c(0 , diff( CI$est ) )
}
sap<-lapply( 1:m , get_est_mi , trans = trans , imp_sets = samples2 , data = data , r2 = r1 )
#obtain data frame of standard errors and point estimates
cis <- sapply(sap,function(x) x[['est']])
t3 <- sapply(sap,function(x) x[['time']])
#get standard errors and point estimates at single times
cis_at_times<-sapply( 1:m , get_values_at_times , values = cis , times = t3 , at = t0 , list = is.list(cis) )
cis_at_times <- get_z( cis_at_times )
CI <- post_point_est_CI( beta = cis_at_times , sd = sd , times = t0 , conf.int = conf.int , alpha = alpha )
if(conf.int){
colnames(CI)<-c('time','prev','sd','uci','lci')
CI <- unique(replace(CI , is.na(CI) , 0 ))
}else{
colnames(CI)<-c('time','prev')
CI <- unique(replace(CI , is.na(CI) , 0 ))
}
ret<-list( est = CI , call = cl , data = data , cens.code = cens.code , status = status , conf.int = conf.int )
class(ret) <- 'MI_ci'
return(ret)
}
#' @export
print.MI_ci <- function (x , ... )
{
cat('\nCumulative incidence estimation for interval censored data using data augmentation and multiple imputation\n')
cat( "\nCall:\n", paste( deparse(x$call) , sep = "\n" , collapse = "\n" ) , "\n\n" , sep = "")
cat('Interval-censored response for cumulative incidence estimation:\n\n')
n<-nrow(x$data)
data<-x$data
cens <- x$cens.code
status <- x$status
cat('No.Observation:', n , '\n')
cat('Patern:\n')
stat<-ifelse(data[,status]==cens,'unknown (right-censored)',as.character(data[,status]))
type<-ifelse(data$right==data$left , 'exact' , NA )
type<-ifelse(data$right!=data$left & data$right!=Inf , 'interval-censored' , type )
type<-ifelse(data[,status]==cens , 'right-censored' , type )
print(table('Cause'=stat, type))
cat('\n')
cat('$est\n')
dimest<-paste(dim(x$est)[1] , 'x' , dim(x$est)[2])
cat(paste('A',dimest,'data frame of required estimates\n'))
print(head(x$est))
}
#' plot method for MI_ci objects
#' @param x A MI_ci object
#' @inheritParams plot.MI_surv
#' @export
plot.MI_ci <- function ( x, xlab = 'Time', ylab = 'Cumulative incidence' , ... )
{
data <- x$est
conf.int = x$conf.int
plot( data$time , data$prev , xlab = xlab , ylab = ylab , type = 's' , ylim = c(0,1) , bty ='l')
if(conf.int){
lines( data$time , data$uci , lty = 2 , type = 's' )
lines( data$time , data$lci , lty = 2 , type = 's' )
}
}
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