# Binomial Probability best fit curve?

#### MRIAV

##### New Member
I have a probability question for some research I am doing. I think I am dealing with a binomial distribution and I was wondering if there was a way to make some sort of best fit curve for my data.

I basically have an extensive series of measurements that lead to a yes/no out come. For example, here is how the data looks: http://imgur.com/9V6Tv8e (but many more events). I know that my data trends significantly downward, but I want to know if there is some kind of model I can apply so I can say at this concentration this is your probability of cancer? Also I’m not sure if it matters but I have many more no events than yes events.

Thanks a lot for your help!

#### JohnUebersax

##### New Member
It looks to me like you might have a basic 'dose-response curve' estimation problem; this would be true whether 'concentration' is for a dose of some medicine, or for some physiological parameter.

It's been a while since I've done this, but I believe dose-response curve estimation is fairly simple using SAS (e.g., proc logistic with link=probit on the model statement - this is technically called 'probit regression'; several other SAS procs can also be used).

But basically my suggestion is to investigate whether dose-response modeling is what you want.

Hope this helps.

#### rogojel

##### TS Contributor
hi,
by the look of it this could be a nice application of a logistic regression. It will give you a curve of the probability of a yes as a function of the dose,

regards
rogojel

#### JohnUebersax

##### New Member
> by the look of it this could be a nice application of a logistic regression. It will give you a curve of the probability of a yes as a function of the dose,

Yes, logistic regression or probit regression -- they will give similar results. Both fit an S-shaped curve to concentration (x-axis) vs. probability of positive response (y-axis). The probit model, based on the cumulative normal distribution, generally has more theoretical validity. Logistic regression, a less computation-intensive method, became more popular before computer technology took off. Now it's just as easy to perform probit regression.