[R] AFT-model with time-varying covariates and left-truncation

[Philipp Rappold]

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.

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, 
...).

Thanks a lot for your help!

All the best
Philipp