Dear all,
I have a question about time-dependent covariates in a coxph model.
Specifically I am wondering whether it is possible to give more recent
events a higher weight when constructing time-dependent covariates.
Assume I have a sample of cancer patients and I would like to predict
whether the number of treatments a patient received has an impact on
survival time. For each patient in my sample I know (a) the date when a
patient is diagnosed with cancer, (b) all the dates where a treatment took
place and (c) the date of death or, alternatively, the date where the
observation window ends.
Take the following example: Bob is diagnosed with cancer on 01/01/1990, has
three treatments (on 01/01/1993, 01/01/1995 and 01/01/1997) and dies on
01/01/1999. In order to incorporate the time-dependent covariates into my
model, I transform this into four separate datapoints:
(1) Start: 01.01.1990, End: 01.01.1993, Number of treatments: 0
(2) Start: 01.01.1993, End: 01.01.1995, Number of treatments: 1
(3) Start: 01.01.1995, End: 01.01.1997, Number of treatments: 2
(4) Start: 01.01.1997, End: 01.01.1999, Number of treatments: 3
The problem is that in this formulation all treatments count the same way,
no matter when they took place. I would like to introduce some form of
discount factor that takes account of the fact that the potential impact of
each treatment decays over time. If that discount factor is d, I would like
to model the following four datapoints:
(1) Start: 01.01.1990, End: 31.12.1992, Number of treatments: 0
(2) Start: 01.01.1993, End: 31.12.1994, Number of treatments: 1
(3) Start: 01.01.1995, End: 31.12.1996, Number of treatments: 1*d^2 + 1
(4) Start: 01.01.1997, End: 01.01.1999, Number of treatments: 1*d^4 + 1*d^2
+ 1
d^n hereby accounts for the fact that the treatment was already n years ago
at the start of the observation.
My question: Is it possible to include such a formulation in a coxph model?
Is there a way to estimate the optimal d, so that I can estimate how fast
the effect of a treatment decays over time, given the data I have?
Thanks,
Michael
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