Dose Response Parameter Fitting

[ptc-1368288]

We have been on that for > 3 months and over 200 threads, all valid work done version 11. "Save as" at least as low as 11. No point to direct you to the previous work, I can't even retrieve my own work sheet in the collab ... the search tool is scrap. Don't forget to include the source if you have, a valid source in order to limit all backward argumentation in case the "paper" is just a "paper".

I'm sure, an idea will come out before midnight.

jmG

[ChemEng]

Thank you for your response. Yeah the search engine here is a joke. It is cool to see how many Mathcad users are out there. Take care!

[ptc-1368288]

On 8/19/2009 5:13:37 PM, Stevenlee wrote:
>Thank you for your response.
>Yeah the search engine here is
>a joke. It is cool to see how
>many Mathcad users are out
>there. Take care!
_______________________________

159 threads you can read, but that is a fraction since the beginning of the "Dose response" because there were so many different kinds of data. At least, the attached is the very last version as file in my models. And, there was never any data set about "clearance", a big word with no data and nothing less than nothing from zillion papers. So, as you can see, I made my own "clearance", but I'm not a doc [maybe good thing as I would have ended manufacturing crystal balls].

Just the data set will tell a lot.
How many Mathcad users ~ 3 millions
How many collab readers ?
A while ago, Mike Griffin had a chart

The attached as is, not sure if the last post in the collab.

http://collab.mathsoft.com/read?126991,17e#126991
http://collab.mathsoft.com/read?126991,17e#126991

Your Mathcad 14 might have digestion problem(s) with this sheet

jmG

[TomGutman]

You might be interested in the long thread at http://collab.mathsoft.com/read?72586,17 on fitting probability distributions includig MLE.

I can't make much sense out of your worksheets. You have several data sets, all inconsistent. I can't even tell if you are trying to fit a PDF or a CDF.
__________________
� � � � Tom Gutman

[ptc-1368288]

>I can't even tell if you are trying to fit a PDF or a CDF<<br> _____________________________

Bad news for a bed time reading, then !

[ChemEng]

My apologies for the sloppy mcd sheets. The function I am wanting to fit is P(x,alpha,beta) = 1 + (1-x/beta)^-alpha. You could call it a CPF function since it is Dose (x-axis) versus Probability of Illness (y-axis). I trying to get a fit that resembles the S curve.

[TomGutman]

That is a different equation from what you have in the sheets. And the two sheets have different data and different equations.

If you are looking for an s shaped logistic curve, start by plotting your function for some reasonable values of the parameters and see if you get the correct shape. You have to have reasonable guess values for the parameters, and a function that reasonably approximates the data, before you can even start doing curve fitting.

Curve fitting is best done using minerr directly. Various forms of first calculating the SSE are cumbersome, slow, and inaccurate.
__________________
� � � � Tom Gutman

[TheodoreM.Bones]

I have 3 fitting techniques that process this data very well.

[ChemEng]

I was able to take points and from all your comments and was able to solve for the dose resonse parameters using the genfit function. One mistake I was making was trying to fit the parameters using the log dose. I get the right parameters if I do not log the dose. Please let me know if you know of a better approach from what I did in the attached sheet. If there is a better way to minimize the summaation of the square errors. Thanks for all your help, you guys are great!

[TomGutman]

Minerr is usually an easier way to set up fits.

If you need to plot over a large range, you need logarithmically spaced points, not linearly spaced points.

.XMCD files are oversized. For posting, I suggest .XMCDZ (compressed format) files, without rendered images. Note the file sizes of the various posted files.
__________________
� � � � Tom Gutman

[ptc-1368288]

>You could call it a CPF <<br> __________________________

What's that invention CPF ?

PDF, CDF are known. If you mean CPF is CDF, then it is CDF. The CDF being the normalized cumulative integral of the PDF, it can't be that erroneous. That was my point in the previous reply. The other crucial point is that you should supply the PDF ... why ? because we have lot more PDF from the tool box than CDF. What that means is that the effort to fit the CDF is a reverse engineering process, not worth a dime with such a poor data set. What you must understand is that no matter how many fits can be proposed, none can be declared. Check for typos.

jmG

[ChemEng]

My apologies for the sloppy mcd sheets. The function I am wanting to fit is P(x,alpha,beta) = 1 + (1-x/beta)^-alpha. You could call it a CPF function since it is Dose (x-axis) versus Probability of Illness (y-axis). I trying to get a fit that resembles the S curve.

[ChemEng]

My apologies for the sloppy mcd sheets. The function I am wanting to fit is P(x,alpha,beta) = 1 + (1-x/beta)^-alpha. You could call it a CPF function since it is Dose (x-axis) versus Probability of Illness (y-axis). I trying to get a fit that resembles the S curve.

[ChemEng]

My apologies for the sloppy mcd sheets. The function I am wanting to fit is P(x,alpha,beta) = 1 + (1-x/beta)^-alpha. You could call it a CPF function since it is Dose (x-axis) versus Probability of Illness (y-axis). I trying to get a fit that resembles the S curve.

[ptc-1368288]

>The function I am wanting to fit is ...<<br> ____________________________

There is nothing to fit. Your data set is too erroneous ! Less data you have, more exact they must be and they are just out of the blue. Pure waste of time up until now. If you want continued collaboration and extended expertise,"Save as 11" or lower version. Your data set does not make sense from inspection, or there is more behind that you have no knowledge ... no source ?
The biphasic is however the most tempting.



jmG

[ChemEng]

Please see my last attachment. How do I plot the full range of the dose. I reach a maximum number of points to plot.

[ptc-1368288]

>Please see my last attachment<<br> _______________________________

No attachment to see because not readable in version 11, the version I use. What you explain does not make sense , you are not applying "Data reduction" in the sense of "Data reduction". Read my previous replies.

jmG

[ChemEng]

jmG,

My apologies and thanks for bearing with me on my lack of details to my questions. I'll be more specific in my responses. As requested, the Mathcad 11 sheet is attached. There is probably a more comprehensive way of doing this rather than using the black box functions in Mathcad.

[ptc-1368288]

The 2nd data set does not make any sense at all. Too much about it that is unknown and not enough data. For the first one, the model proposed is very good and makes sense, but it refuse the 0.14 value. That means this value is incorrect and I just put one that validates the fit.
That is just a tentative fit. I played a bit with the values within the round off of the collection and within the digitization error. A damned good fit !

jmG

[TheodoreM.Bones]

Where does the final XY data file comes from? I see you inserted it backwards from your logistical response fit. So it fits very well?

[ptc-1368288]

On 8/20/2009 8:22:54 AM, study wrote:
>Where does the final XY data
>file comes from? I see you
>inserted it backwards from
>your logistical response fit.
>So it fits very well ?
______________________________

No idea where the data set comes from !
I think it comes from your work sheet, Theodore !

Jean

[ChemEng]

The data set is from the following website:
http://www.fao.org/docrep/009/a0238e/A0238E04.htm

See table 4.1 and Figure 4.7. I am preparing some exercises for a risk assessment workshop using @RISK software and Mathcad. I using this data as an example to fit dose response parameters. I should of provided this up front which I do next time. Thanks for the coaching.

[TomGutman]

Any idea as to how they calculated the "best fit"? Their parameters differ from the ones calculated by Mathcad, and the SSE for their parameters is distinctly larger than the SSE for the ones found by Mathcad. The very even value for α (.25) suggests that they may have arbitrarily fixed α and fitted just β. But even forcing α to .25 gives a β of 15.2, not 16.2.
__________________
� � � � Tom Gutman

[ChemEng]

Good question. The method used for finding the parameters was the maximum likelihood estimation. Most of the parameter fitting for microbial dose response curves refer to this approach. I have not tried it for this data.

[ptc-1368288]

On 8/20/2009 3:39:59 PM, Stevenlee wrote:
>Good question. The method used
>for finding the parameters was
>the maximum likelihood
>estimation. Most of the
>parameter fitting for
>microbial dose response curves
>refer to this approach. I have
>not tried it for this data.
_______________________________

Please read my post just above. In short, when data don't ride over the possible shape(s) of the model: there is no fit and no likelihood. What's likelihood when there is lies in the data ? just answer that to yourself. Data fitting is an art [F.B. Hildebrand], statistics are lies (damned lies). With a bit of touching, you could get 2 dozens of sigmoidal fit ! No one can be declared better unless the data are carefully collected, but how can you expect that from unfamiliar personal and under designed test bench.

Enjoy

jmG

[TomGutman]

Yep. MLE reproduces their values exactly.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 8/20/2009 9:27:18 PM, Tom_Gutman wrote:
>Yep. MLE reproduces their
>values exactly.
>__________________
>� � � � Tom Gutman
...................

i.e: same as equating minmax residuals
[� 0.105] on the plot

[ptc-1368288]

Steven,

Thanks for the link, and the source of the data. The data are there just to be there ! They surely don't make sense unless measured with a "nosemeter" [kid type nosemeter near the ice cream shelve]. The proof they don't make sense is the fact there is no Minerr no nothing to help a fit. Your equation makes sense however. So, the attempted fit is manual and that's it. You will find the Log(xmin,xmax,npts) in order to get a complete plot on the range. Note that with a more valid data set and more populated, the function should Minerr. I didn't care Genfit because Minerr does better and a lot simpler. If you want to confirm to yourself about the Minerr, if it would ... simple: take the function as is attached, add noise and try to fit Minerr.

Hope you benefit from visiting the collab.
Sorry, I have scraped your Genfit.

jmG

[ptc-1368288]

Back to your 1rst visit, the two data set attached. About the Beta Poisson model and the data set and the paper, you can probably conclude that about any curve can fit any data set. Look at the 4th order poly fit ! You can suppose that a model function is the function to fit, you can suppose from the system knowledge, but why pass (the paper) a totally uncorrelated data set and so skinny. It does have a puzzling effect but is not "curve fitting educative". It's like telling the moon is square because it appears circular. If you wish, you can add the MLE on the sheet. In case you have more "Dose Response", welcome ... there are so many "Dose Response" that anything is a "Dose Response", even the humor of the cat, elections ... etc.

jmG