md.impute: Correctly impute missing information of possible deaths using population mortality

Description

An iterative approach is used in this method to estimate the conditional distribution required to correctly impute the times of deaths using population mortality tables. Note, that simply imputing expected survival times may seem intuitive, but does not give unbiased estimates, since the right censored individuals are not a random subsample of the patients.

Usage

md.impute(data, f, maxtime, D, ratetable, iterations = 4)

Arguments

data

a data.frame in which to interpret the variables named in the formula.

a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function.

maxtime

maximum potential observation time (number of days).

where status=0 equals time.

where status=1 equals potential time of right censoring if no event would be observed.

demographic information compatible with md.survcox, md.impute and md.survnp, see md.D.

ratetable

a population mortality table, default is slopop

iterations

the number of iteration steps to be performed, default is 4

Value

an array of times with imputed times of death that can be used instead of the unavailable complete data set to get unbiased estimates, ie. in coxph.

References

Stupnik T., Pohar Perme M. (2015) "Analysing disease recurrence with missing at risk information." Statistics in Medicine 35. p1130-43. https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.6766

Examples

Run this code

# NOT RUN {
library(missDeaths)
data(slopop)

data(observed)
observed$time = observed$time*365.2425
D = md.D(age=observed$age*365.2425, sex=observed$sex, year=(observed$year - 1970)*365.2425)
newtimes = md.impute(observed, Surv(time, status) ~ age + sex + iq + elevation, 
  observed$maxtime*365.2425, D, slopop, iterations=4)

#Cumulative incidence function
cif = survfit(Surv(observed$time, observed$status)~1)
cif$surv = 1 - cif$surv
cif$upper = 1 - cif$upper
cif$lower = 1 - cif$lower
plot(cif)

#Net survival (NOTE: std error is slightly underestimated!)
surv.net = survfit(Surv(newtimes, observed$status)~1)
summary(surv.net, times=c(3,9)*365.2425)
plot(surv.net)

#Event free survival (NOTE: std error is slightly underestimated!)
surv.efs = survfit(Surv(newtimes, 1 * (observed$status | (newtimes != observed$time)))~1)
summary(surv.efs, times=c(3,9)*365.2425)
plot(surv.efs)

# }