dear allstatters
i have a problem with survival data that are interval censored at both
ends. i am working on a large observational database, where for each
patient i know the value of a boolean variable X at various times T.
The starting value at baseline is 'True', so the data for one individual
might look like this:
T X
t_0 True
t_1 True
t_2 False
t_3 False
t_4 True
The observation times t_0, t_1, ... are irregularly spaced through time,
and are not the same for each individual.
I am interested in three survival outcomes for these data, but have so
far only been able to look at the first two:
Outcome 1. the time from t_0 until X becomes 'False' - this is simple
survival analysis with an interval censored survival time, in this
example the outcome occurs in the interval (t_1, t_2), and i can use SAS
or s-plus to fit a variety of parametric survival models allowing for
left/right/interval censoring. The log-likelihood contribution for the
example individual above would be S(t_2) - S(t_1), where S(.) represents
the survivor function.
Outcome 2. the time from t_0 until X becomes 'True' after being 'False'
(so this is conditional on X being 'false' at some point after t_0).
Again, this is interval censored survival data, and SAS or s-plus can be
used, although there is an issue about truncation if individuals who are
always 'True' are excluded.
Outcome 3. the time from X becoming 'False' until it becomes 'True'
again - the "rebound" time. In this case, I know that the minimum
possible rebound time is (t_3 - t_2), and the maximum possible rebound
time is (t_4 - t_1), but how can i analyse these data? What about
rescaling the time axis to allow this individual to contribute the term
[ S(t_4 - t_1) - S(t_3 - t_2) ] to the log-likelihood?
thanks for any help
i'll summarise any responses and post to the list.
Ben
--
Ben Cowling
Department of Infectious Disease Epidemiology
Division of Primary Care and Population Health Sciences
Faculty of Medicine
Imperial College London
Norfolk Place
London
W2 1PG
email: [log in to unmask]
|