Thanks for your super-fast reply.
I realized you're totally right: My problem is not left truncation
but missing data of time-varying covariates.
In my special case, two conditions are given by study design:
(1) A lot of subjects are missing all of their (time-varying)
covariates for a certain period of time AND...
(2) ...if this is the case, this period always starts at lifetime=0.
You say missing time-varying covariates is a problem for both AFT
and PH models. My question now is:
(a) Is there any solution to this problem (for either AFT or PH)?
(b) And if yes: It would be great if you could point me in the right
direction (eg. literature, name of method,...).
Thanks a lot for you effort, I highly appreciate it!
All the best
Philipp
Göran Broström wrote:
On Thu, Jan 28, 2010 at 2:32 PM, Philipp Rappold
<philipp.rapp...@gmail.com> wrote:
Dear Prof. Broström,
Dear R-mailinglist,
first of all thanks a lot for your great effort to incorporate time-varying
covariates into aftreg. It works like a charm so far and I'll update you
with detailled benchmarks as soon as I have them.
I have one more questions regarding Accelerated Failure Time models (with
aftreg):
You mention that left truncation in combination with time-varying covariates
only works if "...it can be assumed that the covariate values during the
first non-observable interval are the same as at the beginning of the first
interval under observation.". My question is: Is there a way to use an AFT
model where one has no explicit assumption about what values the covariates
have before the subject enters the study (see example below if unclear)? For
me personally it would already be a great help to know if this is
statistically feasible in general, however I'm also interested if it can me
modelled with aftreg.
The AFT model with time-fixed acceleration factor a is S(t; a) =
S_0(at) for some S_0.
With a time-varying a = a(t), this becomes S(t; a) = S_0(\int_0^t a(s) ds),
and in order to evaluate that you need the full history of a at each t > 0.
EXAMPLE (to make sure we're talking about the same thing):
Suppose I want to model the lifetime of two wearparts A and B with
"temperature" as a covariate. For some reason, I can only observe the
temperature at three distinct times t1, t2, t3 where they each have a
certain "age" (5 hours, 6 hours, 7 hours respectively). Of course, I have a
different temperature for each part at each observation t1, t2, t3.
Unfortunately at t1 both parts have not been used for the first time and
already have a certain age (5 hours) and I cannot observe what the
temperature was before (at ages 1hr, 2hr, ...).
The important thing here is whether you have left-truncated
_lifetimes_ or not. Your example is about missing observation(s) on a
covariate, which is a different problem. But a problem. And not only
for the AFT model, but for the PH model as well.
Göran
Thanks a lot for your help!
All the best
Philipp
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