Question on Repeated Measures with Multiple Continuous Variables

[#1]

Hi everyone,

I'm a new JMP user (and not at all a statistics expert!) with a question about repeated measures. I have a data set with 10 subjects, who were each measured between 4-6 times over several weeks, before and after exposure to a pathogen. At each measurement point, binding potential was calculated and a complete blood count was ALSO taken (there were also a couple of times when complete blood count was taken in the absence of binding potential). What we are hoping to find out is which variables in the CBC are most associated with changes in binding potential. Because all our variables are continuous, I haven't found a tutorial that matches my data (the dogs one doesn't really fit). I am not totally sure how to make JMP look at each animal separately (or if I need to do that), and how to make JMP factor in whether the data came from pre- or post-exposure. Right now I've organized my data in the "tall" format, and I'm not sure it would work to do a "wide" one (or, at least, it would result in about 200 columns). Any insight would really be appreciated.

[#2]

There might be more than one way to analyze your study. We might need more background information as we go along.

JMP can perform a repeated measures analysis several different ways. The fact that you are interested in correlation between the responses suggested that partial least squares analysis (PLS) might also be useful.

So CBC and binding potential are both responses. There is one factor (exposure). Did you study the time course before exposure or only measure a baseline?

You will need a column for subject ID and another for the factor level.

[#3]

Thanks so much for your response Mark! I’ll look more at the partial least squares analysis. 

The factor is exposure, yes. Prior to exposure we collected two baseline timepoints. 

Right now I have a column with subject ID, with several rows for each ID representing different time points. For factor level, could that be a continuous variable (i.e. days of infection, where baseline is represented as a negative number)? For example, this is analogous to how my data is organized at the moment, but the numbers are made up:

Subject ID	Infection Day (factor level)	Variable x	Variable y	Variable z
1	-10	1.5	5	0
1	2	6	5	0
1	10	8	1	2
2	-10	.7	6	0
2	2	2	7	2
2	10	5	3	4
3	-10	1.2	4	1
3	2	6	1	4

[#4]

Do you take duplicate measurements at all time points (baseline and after exposure)?

I think that your factor is implicitly included in the time point (exposure = no if time is 0, exposure = yes if time > 0). you can include a data column for the factor but i am not sure it is explicitly required by the analysis.

Why would 'infection day' be negative?' Do you monitor daily for 10 days prior to exposure and then daily afterward? I thought you only took baseline measurements (time = 0).

I believe that you could use a PLS model with all 3 responses versus the 1 predictor, time.

[#5]

Hi Mark,

Sorry if I was unclear! I did take two baseline time points at separate times: 10 and 5 days prior to exposure (which is why I initially put the negative values). The other time points don't have duplicate measurements. I'll adjust both baseline 'infection day' factor levels to 0. Partial Least Squares looks interesting, and I've been playing with the options on JMP, but I can't tell if it will account for repeated measures.

Thanks so much for bearing with me!

[#6]

If I understand you correctly, you have at least two responses over time and you want to study/test/model their correlation. That is exactly what PLS will do for you. I suggest that you get the book, "Discovering Partial Least Squares with JMP," which explains PLS in the context of solving real problems (case studies). It is a wonderful book about this important technique.

[#7]

I am not so sure now that PLS is the answer. It is a multivariate analysis of numeric data and you must include Dog, which is categorical. Moreover, the Dog effect is random. You might instead consider a mixed effects model, as your study could be viewed as a split-plot design in which each dog is the whole plot. I set up a simple example:

I obviously don't have response values. I used CBC 1 and CBC 2 to represent two of the counts - you probably have more. Let's treat all the CBC results as factors/predictors with fixed effects. Select Analyze > Fit Model and enter the columns into these roles:

Notice that Dog is indicated to have a random effect. (Select Dog in the Effects list, click the red triangle next to Attributes, and select Random.)

You can include more terms in the linear predictor such as other CBC columns or transformations such as interactions or powers as needed.

[#8]

Hi Mark!

Thanks so much for working with me! I am making progress.

I had a question about another aspect of this analysis. From what I understand, the Animal ID [Random] function gives us random intercepts. Is there a way to also get random slopes (I think this is called random coefficients, right?)? I believe that JMP Pro offers this -- can I also do this with a non-pro version of JMP? I've been trying to answer this question myself but I haven't been able to with certainty.  

Again, many thanks for your time!