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 |
I would consider a random coefficients model.
See
Analyzing Multilevel Models with the GLIMMIX Procedure
and
I hope this helps.
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.
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.
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.
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