Unable to fit a 4PL curve after applying weighting (1/y^2)

[#1]

I am attempting to analyze a data set that utilizes raw signal points (y, response) and concentration (x, predictor formula) for an ELISA type assay using a logistic 4P model on the data. Once I apply a 1/y^2 weighting to the raw signal points column, the graph can no longer fit giving an R = ~0.45. This same plate has been analyzed with another software okay, so I am wondering what is happening here. Any help is appreciated! 

weighting calculation: 

[#2]

It's difficult to discern what the issue is without data, could you provide the example of what you're discussing?

Thanks,
Ben

[#3]

Hi Ben, 

I appreciate your response! Below are the numbers I am working with. It's a simple dilution series that I am trying to get to fit with the "ave signal col 1 and 2" on my Y axis and "Theoretical Concentration" as my X. The weighting column is from using the above formulation in the original post. After analyzing with a non-linear model, the 4PL doesnt fit (it does when weighting is removed) 

[#4]

Hi @CurseOfCheetah8 ,

The L4P seems to be working as intended with the weighting, it is just struggling because the weighted data is a poor fit for a 4 parameter model, which you can see in the parameter estimates table:

It might be that the equation in your software is different to the one JMP uses? If so you could try and bring that over and use the Non-linear platform.

Let me know if there are differences and I can send some more resources to help.

Thanks,

Ben

[#5]

Is it reasonable to model this data with any 4PLC when the response is essentially linear to the change in concentration?

[#6]

I agree the linear fit works with the way this is weighted. Unfortunately, this is a pre-validated assay that specifies to use a 4PL with a 1/y^2 weighting so I am limited with how I can analyze it. I am trying to understand why a 4PL would look so different between two softwares (MSD WorkBench and JMP). Thanks for your help on this, it sounds like next steps for me is to try to see what equation the other software is using.  

[#7]

Hi @CurseOfCheetah8 : Looking here we can see what MSD WorkBench is doing.

https://www.mesoscale.com/~/media/files/manuals/discovery%20workbench%20v4%20users%20guide.pdf?la=en

MSDW is using what is listed below as "United States Pharmacopeia: USP <1034>".  JMP uses what is listed as "European Pharmacopoeia".

https://www.quantics.co.uk/blog/what-is-the-4pl-formula/

So, they are paramaterized differently.

That said...for your data, I'd abandon the 4PL model no matter what your protocol says (i.e., the data doesn't nearly follow the sigmoidal shape of the 4PL model).

Also, you say "This same plate has been analyzed with another software okay". What exactly do you mean by "okay"?

Edit: Good discussion here as well.

https://community.jmp.com/t5/Discussions/4PL-fit-4-parameter-logistic/td-p/15836

[#8]

Hi @CurseOfCheetah8 ,

I had a crack at bringing in the formula from Meso to JMP (look at the formula column on here) and trying to run it through the non-linear platform - it does converge, although the result is poor in terms of fit - have a look at the estimated values that your other software came out with for each parameter, is it similar? You might need to set suitable ranges for each parameter for NL to properly converge.

Thanks,
Ben