Help with design/analysis of repeated-measures protocol

[#1]

Hello,

I am preparing to design experiments for my research protocol and I am trying to settle on a model to analyze my data with. Below is my design setup:

Response variable: heart-rate

Random factor: subject

Fixed factor: treatment (control, treatment A, treatment B)

Goal: determine statistically significant factor/interaction effects deviating from baseline heart-rate

Protocol:

1. Record baseline heart-rate for 60 minutes prior to administration of treatment
2. Record heart-rate for 20 minutes during 20 minutes of treatment administration
3. Record heart-rate for 60 minutes after treatment administration

I am confused because there are a variety of approaches used in the literature and there seems to be conflicting advice online regarding repeated-measures data analysis. I have read about the major benefits of using a Generalized Linear Mixed Model (GLMM) as opposed to a repeated-measures ANOVA. I am just a bit stuck with the practical application of this GLMM with data collected using my protocol.

I was thinking of averaging the recorded heart-rate into 5 minute bins, which would give me 12 baseline, 4 during treatment, and 12 post-treatment data points per subject. No real rhyme or reason why I picked 5 minutes. Most of the literature normalizes subject heart-rates by the first 5 minute bin (%) before analyzing but I am weary to do this as it does not allow for subject-to-subject comparisons of heart-rate levels.

Now, I am kind of stuck and don't know how to proceed or understand what kind of model I have.

Hoping that there might be someone out there familiar with this type of protocol that could lend a hand.

Any help is much appreciated.

Thanks,

JP

[#2 · Accepted solution]

Given your response variable, heart rate, is continuous, I would start the analysis with linear mixed models, which is available in JMP Pro (Analyze => Fit Model and choose Mixed Model as Personality). The data must be in a tall format, that is, each observation is identified by Subject and Time columns.

In the JMP Mixed Model a random subject effect can be specified using the Random Effects tab, while the correlations between the repeated measures are handled by Repeated Structure tab. Of course, use Fixed Effects tab to specify fixed effects such as treatment, etc.

With JMP Pro 13 there are many different variance-covariance structures to choose from. You would try with several and evaluate the models fit before deciding on the "best" structure. For more info, please refer to the documentation http://www.jmp.com/support/help/13/Fit_Model_Launch_Window_2.shtml#999895

[#3]

Hello Jian,

Thank you for your reply. I literally just finished watching your JMP Pro Mixed Model for repeated measures tutorials prior to checking back on this discussion. They were very helpful.

As a follow-up, I have two questions:

1) Is it best that the response variable (heart-rate) is kept in its raw form for performing this Mixed Model analysis or can one normalize heart-rate (within-subject over time) as either a percentage change from time zero or difference from time zero before running the analysis? My gut tells me that normalizing is probably not a good idea as it wont allow for between-subject comparison, but I am curious of your opinion.

2) In my case, each subject has 30 response data points measured in time within three ordered groups of time, namely: pre-infusion of treatment (12 data points), during infusion treatment (6 data points), and post-infusion of treatment (12 data points). How can I add this information into the Mixed Model platform?

Thank you!

[#4]

1. You could transform all of measurements as the differences (or as % changes) from "time at zero". Whether to transform should be guided in part by your study objectives.

2. The information from the repeated measures is used in estimating treatment effects that you will include in your model as well as repeated structure. As a caution, since you've recorded 30 response points, there may be too many variance-covariance parameters to estimate for structures such as UN.   I suggest you start with Exchangeable or AR(1).  

[#5]

Since each of the 30 response measurements are effectively a summary (average) of each 5 minute window, I could condense this to summarizing into 10 minute windows to cut down the number of data points, thought I will look into the Exchange and AR1 structures.

As a more pointed question, do I need to create a column for 'Time Group' where it has three possible levels: 'pre-treatment', 'during treatment', and 'post-treatment', and use this as a factor in my Mixed Model?

The reason I ask is because these types of studies usually have a time zero response data point right before the treatment is administered and then all data points following are considered to be time after treatment. In my case my treatment is being administered continuously for 30 minutes before it is stopped, so there is also a 'during treatment' time period that needs to be defined.

Thank you!

[#6]

You will need to create a Time column (e.g., 0, 10, 20, 30, etc.).  Together with a Subject ID column, the two uniquely identify each heart rate measurement. And these two ID columns are required when you specify a Repeated Structure. (Note: for AR(1), the Time column should be defined as continuous. For others, it is categorical. See "the Repeated Covariance Structure Requirements" section http://www.jmp.com/support/help/13/Fit_Model_Launch_Window_2.shtml#999895.  

You will also need to create a separate three-level treatment column to be used as a fixed effect. 

Finally, in addition to the JMP documentation I highly recommend this book https://www.sas.com/storefront/aux/en/spmixedmodel/59882_toc.pdf. Chapter 5 is about the analysis of repeated measures. 

[#7]

Thank you, I will definitely check out the text.

So to sum up, would a simplified sample version of my stacked data look like the following:

Sub.	Treat.	Time Group	Time from first data point (min)	Heart-rate (bpm)
1	A	Pre-Treatment	0	62
1	A	Pre-Treatment	5	60
1	A	During Treatment	10	64
1	A	During Treatment	15	67
1	A	Post-Treatment	20	65
1	A	Post-Treatment	25	64
2	B	Pre-Treatment	0	71
2	B	Pre-Treatment	5	72
2	B	During Treatment	10	78
2	B	During Treatment	15	76
2	B	Post-Treatment	20	76
2	B	Post-Treatment	25	75
...	...	...	...	...

[#8]

How many treatment levels? For Time Group levels, they should be like pre-1, pre_2, during_1, during _2, ..., etc. Check out the sample data, Cholesterol Stacked.jmp, which is used in the JMP Documentation’s repeated measures example. That data is similar in format and layout to yours.

[#9]

There are two treatment levels (A=low dose, B=high dose).

Based on the Cholesterol Stacked.jmp example, this is how I think I need to setup my dataset and analysis:

• Platform: Fit Model
• Personality: Mixed Model
• Y, Response: Heart-rate (bpm) --> continuous
• Fixed Effects: Treat., Time Region, Reg. Inst. --> all categorical

Under the Repeated Structure tab if I want to use 'Unstructured':

• Subject: Subject
• Repeated: Time Reg./Inst. Concat. --> categorical

Under the Repeated Structure tab if I want to use 'AR(1)':

• Subject: Subject
• Repeated: Time (min) --> continuous

Sub.	Treat.	Time Region	Reg. Inst.	Time Reg./Inst. Concat.	Time (min)	Heart-rate (bpm)
1	A	Pre-Treatment	1	Pre-Treatment_1	0	62
1	A	Pre-Treatment	2	Pre-Treatment_2	5	60
1	A	During Treatment	1	During Treatment_1	10	64
1	A	During Treatment	2	During_Treatment_2	15	67
1	A	Post-Treatment	1	Post-Treatment_1	20	65
1	A	Post-Treatment	2	Post-Treatment_2	25	64
2	B	Pre-Treatment	1	Pre-Treatment_1	0	71
2	B	Pre-Treatment	2	Pre-Treatment_2	5	72
2	B	During Treatment	1	During Treatment_1	10	78
2	B	During Treatment	2	During Treatment_2	15	76
2	B	Post-Treatment	1	Post-Treatment_1	20	76
2	B	Post-Treatment	2	Post-Treatment_2	25	75
...	...	...	...	...	...	...

Does the 'Repeated Structure' subject field make my 'Sub.' column a random effect or do you need to specifiy that in the 'Random Effects' tab? Also, using the 'unstructured' option, how does the model know the order of each time point if the 'Time (min)' column is not used for that case?

Thanks!

[#10]

No, it does not. RE and Repeated Structure represent two different sources of variation. However, for certain repeated structures such as UN, RE is no longer estimable--you would get an error message if you attempt to do so. AR(1) works with a random subject effect.

The time order doesn't matter for UN.