[R-sig-dyn-mod] Help to fit a dynamic model - irregular time
Bernardo Rangel Tura
tura at centroin.com.br
Thu Dec 10 10:15:59 CET 2009
On Wed, 2009-12-09 at 08:27 -0500, Setzer.Woodrow at epamail.epa.gov wrote:
> Dr. Tura,
> I wonder if you need to specify the model a little more clearly. As
> written, A() is an unknown function such that A(t+1) - A(t) = b +
> Error2. But, you have times on a finer time scale, since the first
> three times do not even span the time from 0 to 1. Your model does not
> give any way to interpolate to shorter time intervals.
> I can see how you might modify the recursion for A() to small time
> increment dt (A(t + dt) ~ A(t) + b*dt + Error2), but it is not so clear
> how rate should change over a short interval.
> Maybe something like:
>
> log(rate(t+dt)) - log(rate(t))= log(A(t))*dt + log(Error1)
>
> When dt = 1, this gives you the expression you gave us.
>
> You need to decide how or whether the error variances should depend on
> time, too. If they are the result of some process that you are thinking
> of as stochastic, then the variance probably depends on the time
> interval.
>
> You also need to tell us what A(0) ought to be, though I guess that
> could be estimated, also.
>
> Woody
Hi Woody,
First i extract the data from a plot published.
This work is about 180-days follow-up of patients with a cardiovascular
disease so 0.16 is same 5 days (30 days * .16), .25 is same 8 days (30
days*.25), 1.3 is same 39 days (30*1.3) etc
Is very difficult have precision of information in scale less than 1
day in this type of study.
I think the risk of clinical event will modify with the time (likely a
log curve), but the information is cumulative incidence of event.
Because this i suggest the model
rate(t+1) ~ A(t)*rate(t)*Error1 --> d rate/dt ~ A(t)*Error1
A(t+1) ~ A(t) + b + Error2 -> dA/dt ~ b + Error2
In early time (first days) the rate (cumulative incidence) will grow
fast - so b is positive, after this the rate will grow slow - b is
positive but decreasing in relation a initial times
Well, the number of patients in the study will reduce over time - by
death, other clinical events or lost of follow-up - so the error
variances will increase with time but is reasonable to think that
correlate
--
Bernardo Rangel Tura, M.D,MPH,Ph.D
National Institute of Cardiology
Brazil
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