Date: Fri, 14 May 2004 13:23:40 -0400 Stan Wheeler "SAS(r) Discussion" Stan Wheeler PROC MIXED for NL repeated meas models

Hope this is not a repeat but I think my previous attempt got lost in the ether.

I want to use PROC MIXED as part of an implementation of the 2-stage approach for estimating parameters described in the book by Davidian and Giltman.

Problem:

We have a set of M treaatments and K subjects. Subject i is assigned to one of the treatments and variable y is observed at various times. A nonlinear equation, say y=A(1-exp(B*t)), predicts the value of y at time t where A and B are unknown and depend on the Treatment. We want to estimate and make inferences about values of A and B for the Treatments.

2-Stage Approach

1. Use PROC NLIN to estimate A and B for each Treatment. Let Beta*(i) = {A*(i), B*(i)} Be the estimate of Beta(i) = {A(i),B(i)} for subject i. PROC NLIN also genrates a large-sample VC matrix C(i) for Beta*(i).

2. Let Beta be the (unknown) vector containing the true, population, values of A and B for the treatments.

3. Assume Beta*(i) = A(i)*Beta + b(i) + e(i) where A(i) is a known design matrix, b(i) is a random error with mean zero and VC matrix D and e(i) is a random error with mean zero and VC matrix C(i) which is assumed to be known (from PROC NLIN).

4. This looks like a pretty standard linear mixed model except that C(i) is KNOWN. I think that C(i) corresponds to R, in PROC MATRIX notation and D corresponds to G.

I have an IML solution for this problem using the EM approach outlined in the book but would like a PROC MIXED solution because it would be more flexible. My main problem is that I haven't figured out how to specidy the KNOWN value of C(i) in the PROC MIXED syntax.

Thanks for any ideas.

Stan Wheeler

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