Guide for Deciding on the Precision of Sampling

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During a stereological probe rules must be followed to ensure accuracy by avoiding bias, but the sampling scheme should also be carefully planned to produce the required level of precision. The precision of sampling will be affected by the heterogeneity of the distribution of the features being sampled. For distributions of features that are not homogeneous, such as those found in biological tissues, the precision will also depend on the fraction of the volume sampled. As the heterogeneity of the distribution of the features increases, you need a larger volume fraction to yield the same precision. In other words, if the features are not evenly spread out and you don’t do much sampling, there will be a large pool of all possible estimates in which you are fishing for your estimate. Conversely, if the features are more evenly spread out and/or you do a lot of sampling, you will receive your estimate from a smaller range of possible estimates. We can’t do anything about the heterogeneity of the distribution, but we can control the sampling. Using the optical fractionator as an example—the two relevant parameters that can be changed to affect the volume fraction, and therefore the precision, are section interval and disector spacing, since it is most efficient to maximize the height of the disector. How does one go about choosing these parameters?

One strategy is to search the literature. The probe you are going to use may have been employed in the same anatomical region under conditions where the heterogeneity of the distribution of the features being sampled is similar. If you trust the paper, if the authors describe the parameters they are using and why those parameters were picked, and you agree with their reasons, then certainly use those parameters. For instance, many researchers are looking at cell-birth in the hippocampus by using the optical fractionator to estimate the number of newly-born neurons (e.g., Rosanne M. Thomas, Gregory Hotsenpiller, and Daniel A. Peterson, 2007, Acute Psychosocial Stress Reduces Cell Survival in Adult Hippocampal Neurogenesis without Altering Proliferation, The Journal of Neuroscience, 27 (11): 2734 –2743).

If there is no help in the literature, then you have to be the expert or seek the help of experts in the anatomical region you are sampling. You must be or become familiar with the salient features of the region. Is there a clump of features in the direction you are sectioning that it is imperative to sample? If so then you must make the section interval small enough to include these features no matter what the random starting section turns out to be. At the section level of sampling, is the distribution of features quite heterogeneous thus warranting a larger area fraction (closer spacing of the disectors that results in more sampling)? If a person has been studying this region a long time, perhaps a mentor, and they routinely section through the region at a given interval, they will have reasons for the interval they picked and this is often a good starting point.

Once the disector spacing (area sub-fraction) and section interval (section sub-fraction) have been picked, it is wise to run a pilot study. If you are really unfamiliar with the region and don’t have any guidance to come up with an educated guess for the section and disector spacing that you think will give you the precision you require, then we recommend that you oversample and resample (also see CE and Study Design) the region in what you hope is a representative animal (see L. SLOMIANKA AND M. J. WEST, 2005, ESTIMATORS OF THE PRECISION OF STEREOLOGICAL ESTIMATES: AN EXAMPLE BASED ON THE CA1 PYRAMIDAL CELL LAYER OF RATS, Neuroscience 136 (2005) 757–767). Educate yourself as best you can about the region and pick a section interval and disector spacing, and then decrease the interval and spacing by a factor of 2 or 3. In version 9, Stereo Investigator has the ability to resample such an oversampled .dat file, resulting in graphs that compare the two sampling parameters with the range of estimates that are generated by those parameters. You can use this data to pick a ‘sweet spot’ where the disector and section spacing is close enough to make the precision high enough for your purposes, but not so close that you are doing superfluous work to arrive at an unnecessarily tight precision. If you do not oversample and resample to pick the sampling parameters, then run a pilot study and make sure that you are at least counting hundreds of features per region in a representative animal, and that the coefficients of error (CEs) are low. Most, but not all, CEs are formulas that may be good at predicting the sampling variation by looking at the variation of your counts from section to section or from disector to disector. You can see the formula and reference for CEs in our program to find out more about the individual CEs.

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