repeated measures

[SBuc]

Dear Braintrust,

I am looking for determining the rate of elimination of an enzyme present in the serum of calves. the samples have been taken approximately 7 days apart during the 1st month of life. the big issue is that I don't have the same number of samples per subject and that the interval between 2 samples in the same subject also varies. I want to be able to predict with associated error the possible ranges of age based on the enzyme value.

I initially wanted to use PROC MIXED after log transformation of the enzyme to improve normality but definition of the covariance matrix appears difficult / impossible due to the difference interval between samples and variation of samples per subject.

Maybe you could give me some advices / clues / papers referring to that specific type of problem?

Thanks

Type of dataset

Id	age_d	enzyme_IU_L
111	1	800
111	8	90
111	18	25
234	3	1000
234	8	200
333	1	700
333	8	88
333	15	44
333	22	28

[sld]

I would consider a random coefficients model.

See

Analyzing Multilevel Models with the GLIMMIX Procedure

and

Usage Note 37109: Obtaining subject-specific parameter estimates and tests for a random coefficients...

I hope this helps.

[PGStats]

If I understand the question, the biggest issue is that you want to predict age as a function of enzyme concentration. This means, given your proposed model, that you want to get inverse confidence limits on predicted age. I really don't know where you would find those.

[SBuc]

This comment is right. I wanted to predict age based on enzyme results from animals with repeated samples at various endpoints. the big challenge here is that the day of sampling per calf may change. As well as the interval between sampling.

I was also thinking to do some Bayesian models since prediction is more easily obtained from posterior densities of the models but I am not very used with PROC MCMC.

[sld]

I had had the same thought as @PGStats initially, but I wasn't sure I was interpreting correctly.

If age is a fixed effects factor that "causes" enzyme concentration (a random variable), I would still use a random coefficients model. You can then use that model for "inverse prediction", also known as "inverse regression" or "calibration". 

I cannot say that I've ever attempted that with a random coefficients model, so at the moment the best I can offer is a few promising links:

Inverse Prediction Using SAS® Software: A Clinical Application

Approximate Graphical Methods for Inverse Regression

On Inverse Prediction in Mixed Linear Models

investr: Inverse Estimation/Calibration Functions  (R not SAS!)

I hope this helps.