Repeated mesurements with continous time and censored Y

[petter]

I have x variables describing water properties that I want to correlate to water pollution (Y). Data are from different water utilities with repeated measurements with irregular time intervals.

I don’t expect any linear time effect on Y in the long run (the sampling were done for more than one year) but I would like model the correlation between the repeated measurements within each water utility.

Is this the SAS syntax to accomplish this? 

Proc Mixed Data=water_qual;

class water_util;

Model y = x1 x2  x3 x4 water_util/ solution DDFM=kr;

Random days / Subject=water_util type=un solution;

Run;

Another problem I have is that Y is left-censored. I can't find any mixed model repeated measurement that takes censored data into account. Anyone has suggestion? If the Null Model Likelihood Ratio Test for the model above (for the non-censored data) is close to 1 it means that it is not necessary to model the covariance structure of the data at all and I can use a tobit model (in proc lifereg) to deal with the censored data. But how to deal with the censored data if the Null Model Likelihood Ratio Test is significant?

Thanks

[SteveDenham]

WARNING: I have not done this, but it looks like it is possible.

Perhaps PROC MCMC will work.  You would have to specify the repeated measures as something like a G side matrix.  There is something like a repeated measures analysis in the Details: MCMC Procedure > Functions of Random-Effects Parameters.

Then it comes down to specifying distributions and priors and a whole lot of art.

I think checking for structure of the repeated measures is a logical way to proceed, followed by the tobit regression if it looks like there is no real structure to the data.

Steve Denham

[petter]

Hi Steve,

And thanks for the idea of using a Bayesian approach. I will certainly give PROC MCMC a try.

Petter Lindgren