Comparing two curves with peaks

[AndreyMyslivets]

Hello!

I have a question about analysis method and I would be very grateful for the help!

So, I have two groups: Active and Placebo, each group is measured for 20 different concentrations (from 1 to 20) 6 times (response_1 - response_6).

pic.1 Active resoults.

pic.2 Placebo resoults.

As you can see there are 3 peaks for every responses of Active group.

Do any statistical methods exist to

  1) find correct concentrations of this peaks

  2) prove that the peaks are not random, that it is the peaks but not the noise or some kind of outlier.

  3) compare Active and Placebo groups for whole curves or particular concentrations

What analysis should I use for solve this problems?

The attached file is RAW data in .csv format with ',' as delimiter.

Best regards!

[SteveDenham]

I'd like to ask two design questions.  First, are the 20 concentrations blinded/masked values for some true concentration?  The reason I ask is that a tri-modal response just doesn't occur very often, in my experience.  However, if the 20 concentrations behind the labeled values of 1 to 20 were rearranged by increasing or decreasing true values, I would expect a pretty reasonable response curve.

Another design question: What do response_1 thru 6 represent?  Are they separate samples taken at each concentration, or are they different measurements on a single sample taken at each concentration, or are they six different "subjects" measured at each of the concentrations?  The proper analysis would need to recognize which of these situations apply.

With those two questions addressed, I think the analysis would be pretty straightforward for any single scenario.  We just need more info to identify which scenario applies.

Steve Denham

[AndreyMyslivets]

Hi Steve! Thanks for such quick answer!

I made up data for this example and 20 concentrations are blinded values for true concentrations arranged by increasing.

About second question, in my example this is the separate samples of drugs taken at different days and by different operators, but another representation is interesting for me too.

It would be great if you suggest methods for both situations.

Cheers!

[Rick_SAS]

I am assuming that Steve is correct and that Concentration is actually a dummy variable rather than a true concentration such as grams per milliliter.  However, I will volunteer that there are statistical techniques for determining whether a peak in density is real or whether it is an artifact.  The SiZer technique of Steve Marron and his colleagues (1999-2007) was created to address this question: Introduction to SiZer