time series modeling with uncertain observation times

[Linas Mockus]

Hi,

I would like to model the PK profile of multidose oral administration in stan.  However the times when blood plasma levels were measured are uncertain (they are within known 30 min window).  Can anybody suggest a reference how to incorporate the uncertain measurement times into Bayesian framework?

Thank you,
Linas

[Luc Coffeng]

How about modeling the time for each observation as a random variable, conditioned on the "observed" time and some expected range or standard deviation? And then us the random time variable in the rest of your model.

[Linas Mockus]

Luc,

Thank you.  If there are 100 patients and each has 10 observations and observation times for each patient are independent from observation times of other patients we will end up with quite a bit of random variables.  Maybe there is a better way?

Thank you,
Linas
765-494-0090 

On 8/13/2014 6:45 PM, Luc Coffeng wrote:

How about modeling the time for each observation as a random variable, conditioned on the "observed" time and some expected range or standard deviation? And then us the random time variable in the rest of your model.

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[Luc Coffeng]

One way or another, you need to integrate / marginalize over all potential true values of the observation times. Unless you know of a way to do this analytically, you will need to do it numerically, i.e. by specifying a latent variable for the true timing of each observation.

[Linas Mockus]

Luc,

Thank you.  Can this latent variable be distributed uniformly within observation windows for each patient?  Then perhaps I can say that the time of measurement is the start of observation window + random variable?  Or is it better to start with some different distribution?

Thank you,
Linas
765-494-0090

On 8/14/2014 2:26 AM, Luc Coffeng wrote:

One way or another, you need to integrate / marginalize over all potential true values of the observation times. Unless you know of a way to do this analytically, you will need to do it numerically, i.e. by specifying a latent variable for the true timing of each observation.

[Luc Coffeng]

That's really a judgment call you have to make yourself. I'd say, choose a prior that reflects your prior beliefs. Unexpected, I know. :)