How to create a survival curves (non-linear regression) using the linear-quadratic model?

[#1]

I am completely new to JMP and I want to use the linear-quadratic model of cell death by radiation to fit my survival data (survival fraction) to the applied dose. 

The function is the following:  Y = exp(-1*(A*X + B*X^2))

Y = survival fraction 

X = (radiation) dose 

A = linear component represents cell death  due to a single lethal hit to the DNA

B = quadratic component represents cell death that only happens with two hits.

Does anyone have some insights or some advice? Thanks

[#2]

Hi @JGru  and welcome. The easiest way way would be to linearize:

Y = exp(-1*(A*X + B*X^2)) is the same as:

• ln(Y)  = -1*(A*X+B*X^2)
• ln(1/Y) = A*X+B*X^2

So, if that is your model, you could use Fit Model and  make the sure the "No intercept" option is selected.

Just create a new column called Y2 (or any other name you like) and put the function Ln(1/Y) in that column. In Fit Model, put Y2 in as "Y", and X and X*X in as "Model Effects". 

Also, you will want to de-select "Center Polynomials" using the red triable next to Model Specification.

[#3]

Thank you very much. Helps a lot. 
I have an additional question. In total I have n=12 sampels per dose point, so that means per dose I have 12 survival fractions. How can I include this in the formula / in the analysis? 

Thank you

[#4]

Hi @JGru . To make sure I understand, you have a different curve for each of the 12 samples? Is that correct?

[#5]

Hello, no I d'ont have a different curve for the 12 samples. I have 12 samples and therefore 12 survival fractions per dose point (x-axis) and these are plotted and displayed as the mean to the Linear quadratic model. In the attachement I added the the survival curve that I obtained from prism and the error barrs indicating the SD of the 12 survival fractions. 

[#6]

Hi @JGru : OK, as I understand it you have several observed fractions at each dose-point. There are a few ways to get what you want. If you are mostly interested in parameter estimation (estimating A and B) you can do just as I suggested in my previous post. Then once you know A and B you can separately plot whatever you want. However, if you want estimates, and plots etc similar to those you've produced before, all in one analysis, then the most direct and flexible option might be the Nonlinear Regression platform. Come back if you have questions.

Nonlinear Regression