If the process over time is linear, then you can do this by a multilevel linear (or "mixed effects") model. In my experience the implementation of multilevel models is very crappy. I recommend doing the analysis with one of the following R packages: rstanarm, brms, lme4.

These packages also allow you to also fit Generalized MLM, which is useful if hormone concentration does not follow a Normal distribution. As hormone concentration has a lower limit, a Gamma error term could be more appropriate.

In any case, you have to make your data set long, which means one observation per row. Your table header should look like the following

Part | time | pred_1 | pred_2 | ... | pred_7 | concentration

In rstanarm, you could use the following command for estimation (I assume that your predictors vary between-subject, this is why I did not add them to the random-effects term):

M_1

If the process over time is linear, then you can do this by a multilevel linear (or "mixed effects") model. In my experience the implementation of multilevel models is very crappy. I recommend doing the analysis with one of the following R packages: rstanarm, brms, lme4.

These packages also allow you to also fit Generalized MLM, which is useful if hormone concentration does not follow a Normal distribution. As hormone concentration has a lower limit, a Gamma error term could be more appropriate.

In any case, you have to make your data set long, which means one observation per row. Your table header should look like the following

Part | time | pred_1 | pred_2 | ... | pred_7 | concentration

In rstanarm, you could use the following command for estimation (I assume that your predictors vary between-subject, this is why I did not add them to the random-effects term):

M_1

Martin's advice on R is spot on. The problem is that you have a different number of repeats in various parts of your data. I suggest you subset your data into 2 sets. One with 2 measurements and one with more than 2 repeated measurements. Run these in different runs. Excellent advice on the technical details can be found here:

https://www4.stat.ncsu.edu/~davidian/st732/notes.html

Prof. Davidian developed some of these approaches.

Examples are also included. Best wishes. David Booth

Luke -

You asked about sample size, but it isn't just sample size that matters, it's missing data among the sample cases chosen, and which ones are missing.  Is there a pattern of missing data which will result in statistical bias, whereas a small, representative sample size without missing data would only cause concern over variance?  Are missing data all data missing at random?  I don't know your subject matter or the exact mechanics of sample selection, but it sounds like imputing for missing data would result in more imputed data than anything else.  If you ignore that, results may be impacted just as much, or more.  Perhaps you can do a sensitivity analysis to try to obtain a notion as to how important this is ... or isn't.   For example, if you throw out some more of your data (at random ...

or not) you could see how much that changes your results. 

Best wishes - Jim

James R Knaub Jim, I get the impression that this is like a drug trial where for almost everybody they get a pre and post measurement but fewer followups. Some did that many did not. If that's the case, would that affect your suggestion. If this is a drug trial or something like it I would be nervous about data imputation. Your thoughts on that please. Best, David

Luke noted "There is also alot of missing data..." I was going by that.

I didn't suggest imputation, just that it would be good to see what impact a few more "missing data" might make, as a sensitivity analysis.

James R Knaub Jim thanks. I took the missing to all be after the pre-post measurements. I'm thinking of this as a drug test with the imputation in the followup portion of the data. If that was true I think I would not impute because a follow-up in a drug test I would want to be an actual measurement. What is your thinking on that? Thanks again, David

Again, I didn't suggest imputation.

I would not speculate further.

There are two important advantages of mixed or multilevel models for your situation:

1 the mixed model can handle 'categorical ' time and you specify the structure as 1st occasion, 2nd occasion, 3rd occasion within subject and moreover (unlike SEM) you can include continuous time in the fixed part and model between subject heterogeneity as a function of this detailed continuous time. Thereby making full use of the information that you have.

2: Mixed models with give unbiased estimates in the presence of missingness (imbalance) when some responses are not measured ; do not throw away subjects with just one occasion,. However, this requires the fulfilling of the assumption of Missing at Random (not the more demanding Missing Completely at Random) so it helps to put in variables to condition on. However if the missingness is informative such that it is the unobserved value of the response that is driving the missingness ( eg in a study of alcohol consumption it is the heavy drinkers that do not turn up to be measured), then the results will be biased. In practice it is very difficult to tell if these assumptions are fulfilled/ violated.

These are two very good sites with lots of resources:

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

http://www.pilesofvariance.com/