Methods and Techniques Discussion => Image Analysis => Topic started by: rumc on October 07, 2005, 06:47:52 PM

Title: Which Coefficeint of Error value to use in Stereology
Post by: rumc on October 07, 2005, 06:47:52 PM

I was wondering if anyone has input on which coefficent of error (CE) to use for stereology. Particularly, I use the optical fractionator. The data output gives you multiple types of CEs to choose from and multiple CEs of the same type to choose from.

If anyone knows the situations in which one is more advantageous than another and why that would be great.

Papers in my field don't really say which CE was used and if they do indicate it is usually Gundersen's CE. How does this compare to the Schmitz-Hof CE, and why use one or the other?

Title: Which Coefficeint of Error value to use in Stereology
Post by: richard03 on October 09, 2005, 10:03:30 PM
Are you using Stereo Investigator or Stereologer?

If you used Stereo Investigator,  the Coefficient of Error (Gundersen) should be used.

Title: Which Coefficeint of Error value to use in Stereology
Post by: rumc on October 12, 2005, 01:18:56 PM
I use stereoinvestigator.
Is there somewhere I can find or do you know why Gundersen's should be used? Also, why are the others not good to use?  

Unfortunately, the manual for stereoinvestigator does not really help in deciding which CE to use. The manual mentions that Scheaffer's is an alternative CE to Gundersen's. However, the objects being counted have to be randomly distributed and the ROI must be accurately traced for Scheaffer's CE to remain unbiased. So, why would one want to use Gundersen's CE over this CE?  

Thanks for the help,
Title: Which Coefficeint of Error value to use in Stereology
Post by: richard03 on October 12, 2005, 07:15:45 PM
I used Gundersen's CE according to our statistician. I do not know the theory behind this (sorry). The other thing I would like to mention is that our ROI is striatum where the objects are uniformly distributed. You may consult with some statistician in your institution to see which one is more appropriate for your particular project.

Title: which CE
Post by: hokie on May 24, 2006, 09:09:15 AM
The appropriate CE is the one that models your work. The Gundersen CE is more properly called the Matheron transitive technique. It incorporates the idea that sampling is done in a systematically uniform random manner. The Scheaffer CE is based on the idea that the samples are independent random. It is unlikely that your work is ever independently random.

If you read Scheaffer's book you see that the examples are things like sampling animals taken in traps. This differs from the situation where the population is fixed as in cells on a tissue slice.

The distribution of the particles does not affect the unbiased nature of the estimate, but the CE methods are all model-based. It is important to use formulas correctly. The Matheron transitive technique and the Scheaffer method apply to different situations. The Scheaffer CE is not an alternative to the Matheron method.  They are used in very different situations. Also, to claim that the objects being counted have to be randomly distributed is incorrect. Claiming that the ROI has to be accurately traced is also incorrect. Claiming that a CE estimate is unbiased is also incorrect.

Hope this helps out
Title: Which Coefficeint of Error value to use in Stereology
Post by: rumc on June 20, 2006, 01:54:55 PM
Thanks for all the helpful info.

What are your thoughts on when to use the Schmitz-Hof CE and how this CE compares to the Gundersen CE (or Matheron transitive technique)?
Some papers in the literature use the Schmitz-Hof CE in similar situations as I am using stereology, but do not give the reason for their choice.

Thanks again.
Title: CE choice
Post by: hokie on June 20, 2006, 09:59:52 PM
There have been a number of attempts of determining a means of estimating the CE. Methods by Cruz-Orive and Braendgarrd and Roberts aas well as others have been largely passed by with the Matheron transitive method.

The Schmitz-Hof method is basically a pair of values. That makes little sense. The range is so wide so as to be useless unless the larger value is used. That worst case is exactly the CE based on independent random sampling. That does not apply. So maybe the smaller value should be used. The formula is based on curve fitting and not a derivation. The curve fitting was done by collecting data from a few simulations.

I would stick with what has been derived. The derivations have been done and redone in Australia, France, Spain, the UK, Denmark, the US, and plenty of other places. You might want to read or gloss over the comments in:

Cruz-Orive, L.M., García-Fiñana, M., A review of the article: Comments on the shortcomings of predicting the precision of Cavalieri volume estimates based upon assumed measurement functions, by Edmund Glaser, Journal of Microscopy, Vol. 218, Pt. 1, 2005, pp. 6-8

These few pages point out how proponents of other methods are missing the basic idea when it comes to the practical and theoretical concepts involved in this work.

You also might find it instructive to look at Scheaffer's book Elementary Sampling Theory. You need to get the 1990 edition. Look at chapters 4 and 7. You will see that he lists the important assumption that the samples are independent of each other. This is an easy to miss assumption.

I ran some simulations testing some of these CE formulas. I find that the m=1 (the 1/240) estimate is usually a slight underestimate of the CE. The Scheaffer method is way off. The Schmitz-Hof has such a large range as to be of no practical value.

Last but not least think of it this way. You are working on a project. You want to publish. Do you want to defend your biological work or do you want to defend a statistical method not adopted by your peers in your field of interest? That might happen if you decide to use an alternative method. The Matheron method is today's standard. I would go with the flow.

Good luck with your work. The fact that you are taking the time to learn about all of these different ideas suggests that you are going to do a fine job.