[Insight-users] Re: Tumor Measurements..

[Luis Ibanez]

Hi Lino,

When measuring a value there is always variability
in the outcome of the measurement.

This is due to the fact that the measurement process
itself is regulated by parameters. Some of those
parameters are under control and can be regulated,
some other parameters are not under control, and
may even be unknown.


Let's consider both cases:

1) Parameters not under control.

   When dealing with parameters of the measurement
   process that are not under control, the only way to
   estimate values is to take the measure multiple times
   and attempt to estimate the statistical distribution
   of the outcome

   In most cases, Gaussian distributions are assumed,
   usually for the lack of any other better model.

   When you follow this method, the set of values
   resulting from your measurements will have a Mean
   and a Standard Deviation. In a Gaussian distribution
   you can claim that if you randomly sample the
   distribution, X% of the samples will be at a distance
   of K*(Standard Deviations) from the Mean.  The relation
   ship between X and K is given by the erf() function.
   (the integral of the Gaussian).

   X% is called the confidence and K*STD define your interval.
   A typical common confidence value to use is 95% which
   corresponds to +-3*STD. Meaning that if you integrate the
   area of the Gaussian from  (Mean - 3*STD) to (Mean+3*STD)
   you get 95% of the total area under the full Gaussian.


   This is the typical process to follow when segmentation
   is done under human supervision, since it allows to account
   for the variability of human judgment, both in the same
   individual over time, and between multiple different
   individuals.



2) Parameters under control.

   For parameters that are under control, the uncertainty of
   the final measured value is related to the sensitivity of
   the measurement as response to perturbations of the parameters.

   For a trivial example:

   If you use a thresholding method in order to segment a tumor
   that has been made visible by Gadolinium enhancement in  an
   MRI image, the value of the threshold is a critical parameter.
   Small changes in the value of the threshold will produce
   variations on the segmentation result and therefore will affect
   the volume estimation of the tumor.

   From the point of view of Measurement Theory, the preferred
   value for the threshold should be the one that at which perturbations
   result in minimal variations of the value to be measured (in this
   case the tumor volume).

   In order to bound the range of the thresholding value, you must
   establish what are the limits in which the resulting segmentation
   is still plausible. For example, let's say that you find that
   plausible segmentations are produced when the thresholding value
   is between 150 and 180. That means that at threshold values less
   than 150 you observe that the segmentation is missing regions that
   are clearly part of the tumor, or that it is including regions of
   healthy tissue.

   At this point you can generate a population of threshold values
   that follow a uniform statistical distribution inside the plausible
   interval. For each one of those thresholding values the segmentation
   will result in a specific tumor volume.  If you collect those volumes
   and compute their Mean and Standard deviation, then you will be
   able to generate an interval around the mean that correspond to the
   confidence level that you selected.


What is challenging in most segmentation methods is that there are
many input parameters that may affect the outcome of the measurement.
Therefore, plausible ranges must be established for each parameters
and using their collective ranges, a population of segmentation can
be generated.


There are a number of tools that can help you to explore the parameter
space and estimate the statistical distribution of the measured value.



    Please let us know if you have further questions.


      Thanks


         Luis


--------------------
Lino Ramirez wrote:

> Hi Luis,
> 
> Since you pointed out that
> 
> ----------------------------------------
> Do not forget also that when you report measurement
> they must be accompanied by the uncertainty in the
> measure and the confidence of this interval.
> 
> For example,
> the tumor volume should be reported as:
> 
>       30 mm^3  +/-  5 mm^3  with  95% confidence.
> ---------------------------
> 
> Could you please provide some references on how to compute the uncertainty
> and confidence interval of the measurements obtained after using a
> segmentation method?
> 
> Thank you,
> 
> Lino
> 
> 
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