Multiple outputation for longitudinal data subject to irregular observation.

Multiple outputation is a procedure whereby excess observations are repeatedly randomly sampled and discarded. The method was originally developed to handle clustered data where cluster size is informative, for example when studying pups in a litter. In this case, analysis that ignores cluster size results in larger litters being over-represented in a marginal analysis. Multiple outputation circumvents this problem by randomly selecting one observation per cluster. Multiple outputation has been further adapted to handle longitudinal data subject to irregular observation; here the probability of being retained on any given outputation is inversely proportional to the visit intensity. This function creates multiply outputted datasets, analyses each separately, and combines the results to produce a single estimate.

Usage

mo(
  noutput,
  fn,
  data,
  weights,
  singleobs,
  id,
  time,
  keep.first,
  var = TRUE,
  ...
)

Arguments

noutput

the number of outputations to be used

fn

the function to be applied to the outputted datasets. fn should return a vector or scalar; if var=TRUE the second column of fn should be an estimate of standard error.

data

the original dataset on which multiple outputation is to be performed

weights

the weights to be used in the outputation, i.e. the inverse of the probability that a given observation will be selected in creating an outputted dataset. Ignored if singleobs=TRUE

singleobs

logical variable indicating whether a single observation should be retained for each subject

id

character string indicating which column of the data identifies subjects

time

character string indicating which column of the data contains the time at which the visit occurred

keep.first

logical variable indicating whether the first observation should be retained with probability 1. This is useful if the data consists of an observation at baseline followed by follow-up at stochastic time points.

var

logical variable indicating whether fn returns variances in addition to point estimates

...

other arguments to fn.

Value

a list containing the multiple outputation estimate of the function fn applied to the data, its standard error, and the relative efficiency of using noutput outputations as opposed to an infinite number

References

• Hoffman E, Sen P, Weinberg C. Within-cluster resampling. Biometrika 2001; 88:1121-1134

• Follmann D, Proschan M, Leifer E. Multiple outputation: inference for complex clustered data by averaging analyses from independent data. Biometrics 2003; 59:420-429

• Pullenayegum EM. Multiple outputation for the analysis of longitudinal data subject to irregular observation. Statistics in Medicine (in press)

.

See also

Other mo: outputation()

Examples

library(nlme)
data(Phenobarb)
library(survival)
library(geepack)
library(data.table)

Phenobarb$event <- 1-as.numeric(is.na(Phenobarb$conc))
data <- Phenobarb
data <- data[data$event==1,]
data$id <- as.numeric(data$Subject)
data <- data[data$time<16*24,]
i <- iiw.weights(Surv(time.lag,time,event)~I(conc.lag>0 & conc.lag<=20) +
I(conc.lag>20 & conc.lag<=30) + I(conc.lag>30)+ cluster(id),
id="id",time="time",event="event",data=data, invariant="id",lagvars=c("time","conc"),maxfu=16*24,
         lagfirst=c(0,0),first=TRUE)
wt <- i$iiw.weight
wt[wt>quantile(i$iiw.weight,0.95)] <- quantile(i$iiw.weight,0.95)
data$wt <- wt
reg <- function(data){
est <- summary(geeglm(conc~I(time^3) + log(time), id=id,data=data))$coefficients[,1:2]
est <- data.matrix(est)
return(est)
}

mo(20,reg,data,wt,singleobs=FALSE,id="id",time="time",keep.first=FALSE)
#> $est
#> [1]  1.66e+01 -6.80e-07  3.14e+00
#> 
#> $se
#> [1] 1.071052 0.000342 0.688231
#> 
#> $RE.MO
#> [1] 1.02 1.00 1.01
#> 
# On outputation, the dataset contains small numbers of observations per subject
# and hence the GEE sandwich variance estimate underestimates variance; this is why
# the outputation-based variance estimate fails. This can be remedied by using a
# sandwich variance error correction (e.g. Fay-Graubard, Mancl-DeRouen).