DOE Response to Maximise Change Between "Negative" and "Positive" Categorical Variable

Question

I'm new to jmp and I'm trying to optimise a biochemical assay. I have multiple categorical and continuous variables to try and optimise the buffer that I am using. Then I want to add the "target" as a variable (and so have a positive or negative for this variable). Without this "target" I want to minimise the response, with it I want to maximise the response (and overall I want to maximise the fold change).

Before I was doing this by generating the conditions without this "target" variable and then manipulating the experimental design by duplicating the runs and having an extra column. However, this becomes difficult when trying to analyse the data because I feel like I am losing information if I get the mean of the "negative" and subtract it from the mean of the "positive". I was hoping for some advice on how to specify the response that I want.

Mark_Bailey · Answer

Your standard curves and control samples are for quality control, not part of the actual optimization, right?

You want high sensitivity and specificity. That performance will come from a low background (lower asymptote) and small standard deviation (blank sample). Your sample buffer will affect these parameters. The other parameters in the logistic model can be used likewise as responses. The inflection point should be minimized so your are more sensitive (more signal at lower concentrations). The slope or power parameter should be maximized so that you get more signal with a smaller increase in the analyte.

Titrating the target might not be the simplest approach but the other way is "pick the winner," not optimization. Your diagnosis is binary but your assay is quantitative. You will achieve the highest sensitivity and specificity by focusing on the quantitative characteristics. You can then trade off sensitivity and specificity of the optimized assay with the ROC curve from a logistic regression model of sample type (neg/pos) versus analyte concentration.

mc · Answer

Thank you @Mark_Bailey for the suggestions.

In terms of a standard curve, yes I will be running separate control reactions with a set amount of a known reagent that has the same response. So I can then convert all values to x units of the known reagent.

I can use more than one response, but I am unsure of how to maximise those with the "target" and minimise those without.

Yes I will have a quantitative output (fluorescence in this case) and at this point I can also titrate the target, but I feel like that might complicate the situation (since ideally I'm just maximising the difference between positive and negative).

To try and move away from being really vague, maybe it will help to explain my assay. I am developing a diagnostic assay for a particular disease. I'm optimising the buffer that I'm using so that when a patient sample is "positive" it is easily distinguished from a "negative" patient sample. My current design is a custom design with standard interactions, as well as RSM. I am running my reactions in triplicate. I am considering using "positive" or "negative" as an extra categorical variable because in my current approach I generate the runs without the "positive" and "negative" (and add it as an extra column later) but then I end up having to aggregate my "positive" triplicate runs and subtract the mean of the "negative" runs. This doesn't seem like the best way to do it (I lose information about standard deviations etc) and I would rather have the original data for jmp to use to create the optimisation model.

I just need to find a good way to specify the optimal response, or a way to specify what is the most desirable in this specific use case.

Mark_Bailey · Answer

I assume that you will run a standard curve for each of the treatments in the DOE. So, you will be able to fit a dose-response curve, such as a 4PLC. You could use more than one response. You could maximise the upper asymptote, minimize the lower asymptote. and then target the other parameters to get the dynamic range that you desire to achieve the sensitivity and specificity that you need.

Do you have a quantitative measurement for the response? Do you only have negative and positive status of samples?

I could be way off...