# Is there a way to model left truncated and interval censored data in R or SAS?

We have a study where our participant underwent some surgery at time = 0, but at various ages. Our follow-up is based only on Medicare age-eligible people, so we have to wait until they reach the age of 65 to observe them. Then, based on Medicare data (which won't exist below the age of 65) we can narrow down the time of their event to some interval (say, somewhere between a couple days and a couple months). So the data are truncated at the age of 65 (or date they turned 65) and because we can't observe anything until they are Medicare age-eligible. And it is censored to the narrowest interval that we can determine the event happened.

I'd like to use the intcox package in R, but it seems that I can either do interval censored OR left truncated in the Surv() function.

Some code I was using to test this:

library(intcox)
library(survival)

n<-100
dat<-data.frame(death=rbinom(n,1,0.5),entry.age=rnorm(n,50,3),group=(1+rbinom(n,1,.6))/2)

dat$left <- with(dat,entry.age+rexp(n,dat$group+0.5))
dat$right <- ifelse(dat$death,dat$left+rexp(n,dat$group+0.5),NA)

coxph(Surv(entry.age,left,death,type='counting')~group,data=dat)
intcox(Surv(left,right,type='interval2')~group,data=dat)

It seems that the same place I would specify left-truncation is the same place you specify the left end of the interval for IC. Does anyone know if this is possible to model, or if there are workarounds that I could use? I'm pretty sure that this is not possible in SAS, but not sure about R.

• The statement of your question is confusing because "censoring" and "truncation" are distinctly different things. Are you perhaps trying to use both words synonymously? What exactly do you intend them to mean? – whuber Feb 9 '15 at 22:26
• Our data are both censored and truncated. They are interval censored because we only know that each event happened within a certain time interval, which could be a day, a month, a year, or larger for some people. The data are left truncated because each person entered the study at a different age/time. We are only able to observe events after the start of the study. To complicate things even more, we are truly only able to observe events after some variable amount of time has passed since the start of the study. – rjweyant Feb 10 '15 at 12:36
• Thank you for that clarification! I do not understand why the variable time of entry should be considered truncation instead of left censoring. If you think this is a key element of your problem you might want to explain that aspect of your model more fully. – whuber Feb 10 '15 at 13:50
• Thanks, I made some edits in the main post, not enough space here. Main issue is that there is some delay before we can observe the people. After we are able to observe them, the best we can determine when the event happened was in a window, which happened after they became eligible. – rjweyant Feb 10 '15 at 14:41
• Are the observations truncated at the time (age) of surgery? Or would you split the survival time of each person in "no surgery" and "surgery"? – swmo Feb 12 '15 at 17:35