How to add a random effect in the multiple linear regression model of Plackett-Burman DOE?

[#1]

Hi community,

I have conducted a Plackett-Burman DOE for 9 continuous factors measuring 3 different responses (viability, proliferation, gene expression). For one of the responses (gene expression), I actually measure the response three times for each treatment - so these are not independent replicates. I would like to add a random effect in the model that JMP fits for this response. How can I do this practically? Or is this not possible on the JMP platform?

Thank you very much

Sara

[#2]

Hi @SaraA,

Repetition and Replication are two different techniques that can be combined to reduce costs and variation. Repetition is about making multiple response measurements on the same experimental run (same sample without any resetting between measurements), while replication is about making multiple independent randomized experimental runs (multiple samples with resetting between each runs) for each treatment combination.

• Repetitions only reduce the variation from the measurement system (for example by using the average of the repeated measurements).
• Replications reduce the total experimental variation (process + measurements) in order to provide an estimate for pure error and reduce the prediction error (with more accurate parameters estimates).

I'm not entirely sure how/why you would treat the repetition as a random effect ?

What is your problem or reason behind using several repeated measurements for this response ? 

There might be multiple ways to deal with your repetitions :

• If you have high variation from measurement system, you can try using the average of the three runs to reduce the measurement variability. 
• You can also use a Mixed Model for repeated measurements : Example of Repeated Measures
• You can also use the repetition (number) as a random effect in your model. It will give you an information about the variance related to the response and its significance, and help identify fixed effects more easily.

If you would like to have more guidance, it would be helpful to have more context and possibly a toy dataset to test.

Hope this answer will help you,

[#3]

Hi @Victor_G 

For two of my responses (cell viability and cell proliferation), I have replicated runs. For each replicated run, I measure the the response with resetting between each run. This is fine.

However, the problem I have is for the third response (gene expression) where I have repetition, i.e. 1 run where I measured the response 3 times. Therefore, when I input the data in my DOE table, I don't think it is correct to consider these measurements as replicates because there are not independent of each other. So this is why I was thinking to treat repetition as a random effect in my model. I therefore added an additional column (named 'well') to my DOE table (please see the file in attachment) to treat is a random effect and analyze the data using mixed model. However, I don't know if JMP can do this (or if I need to go to JMP Pro or SAS). I did find that I can go to Fit Model > Attributes and select Random effect.

I do not have a high variation in my measurement system because this is measured using quantitative PCR which is quite precise but I also do not want to loose the information that I could get from these repetitions.

I understand also from @Mark_Bailey that computing a mean with a log standard deviation is another option apart from mixed model. But how do I input this into my DOE table?

Thank you your suggestions.

Kind regards,

Sara

[#4]

I also just realised that I am using JMP Pro

[#5]

Hi @SaraA : I think your idea for gene expression to include Well as a random effect makes sense;  it's effectively a split-plot design via hard-to-change factors. So, I guess my question is, why wouldn't you include Well as a random effect?

Edit: Well, in this context, is a block. 

[#6]

@MRB3855 

I added well as a random effect using the Fit Model platform > attribute. I am not sure why it is a block instead of a random effect in this context. Could you explain a bit more?

Kind regards,

Sara

[#7 · Accepted solution]

Hi @SaraA : The JMP model is the same no matter how you think of it: block or random effect. However, thinking of it as a block recognizes that variability between Wells is something to be accounted/controlled for when measuring the impact of the other factors, and not an "effect" in the same way the others are. This is the same thing that is done in a paired t-test. In a paired t-test, you can think of subject as a block (a "random effect" in the model), so that variability between blocks is removed before making the appropriate within subject comparisons. 

https://www.lexjansen.com/pharmasug/2004/Posters/PO05.pdf

https://www.stat.purdue.edu/~kuczek/stat514/Split%20plot%20example.pdf

[#8]

Hi @SaraA : For completeness, and as @statman said, you could choose to analyze the Well means rather than include Well as a block. If you do, you will get nearly identical results as including Well as a random effect (block). And, the results would be identical if there were 3 observations per Well (Wells 8 and 16 had two each, while the others had three). But, including Well as a block is more informative so that's what I usually recommend in these types of situations.    

[#9]

I did not look at the data set, but if Well is a block, you should not take the mean of Wells for analysis.  You do have options in planning.  If you know what factors are confounded with a block, and you can assign them to the block, you may be able to treat the block as a fixed effect and estimate both block and block by factor interactions which is a measure of robustness. If you have not identified what noise factors are associated with the block and therefore have not assigned factors to the block, the block effect should be treated as a random effect (JMP will do this by default).

[#10]

I would add just a bit to Victor's response.  For the response variable in question (repeated measures), there are a couple of things you can do, but it does depend on how you got the 3 data points.  Were they multiple measures of the same sample (e.g., measurement system)?  Were they 3 samples within treatment (e.g., within batch)?  Here are some options:

1. Plot the 3 data points for each treatment (Variability plot of Graph Builder).  Are there any unusual data points?  Are there any patterns?

2. Assess the consistency of those data points with a Range control chart. Are there any outliers?

3. After looking at the data, perhaps the appropriate summary statistics are mean and standard deviation.  Both responses (or some transform of those) can be modeled.  The mean would reduce the variation of the 3 repeated measures (perhaps reducing that measurement error) and the standard deviation would quantify the variation of the 3 data points.

In any case, there would be no reason to add a random term to account for the 3 measures.