Gardi, Jonathan Eyal1; Nyengaard, Jens Randel5; Gundersen, Hans Jørgen Gottlieb1
1 Stereological Research Laboratory, Faculty of Health Sciences, Aarhus University, Aarhus University2 Institute of Clinical Medicine, Faculty of Health Sciences, Aarhus University, Aarhus University3 The Department of Pathology - ÅKH, Faculty of Health Sciences, Aarhus University, Aarhus University4 Department of Clinical Medicine - Stereological Research Laboratory, Department of Clinical Medicine, Health, Aarhus University5 Department of Clinical Medicine - Stereological Research Laboratory, Department of Clinical Medicine, Health, Aarhus University
The proportionator is a novel and radically different approach to sampling with microscopes based on well-known statistical theory (probability proportional to size - PPS sampling). It uses automatic image analysis, with a large range of options, to assign to every field of view in the section a weight proportional to some characteristic of the structure under study. A typical and very simple example, examined here, is the amount of color characteristic for the structure, marked with a stain with known properties. The color may be specific or not. In the recorded list of weights in all fields, the desired number of fields are sampled automatically with probability proportional to the weight and presented to the expert observer. Using any known stereological probe and estimator, the correct count in these fields leads to a simple, unbiased estimate of the total amount of structure in the sections examined, which in turn leads to any of the known stereological estimates, including size distributions and spatial distributions. The unbiasedness is not a function of the assumed relation between the weight and the structure, which is in practice always a biased relation from a stereological (integral geometric) point of view. The efficiency of the proportionator depends, however, directly on this relation to be positive. The sampling and estimation procedure is simulated in sections with characteristics and various kinds of noises in possibly realistic ranges. In all cases examined, the proportionator is 2- to 15-fold more efficient than the common systematic, uniformly random sampling. The simulations also indicate that the lack of a simple predictor of the coefficient of error (CE) due to field-to-field variation is a more severe problem for uniform sampling strategies than anticipated. Because of its entirely different sampling strategy, based on known but non-uniform sampling probabilities, the proportionator for the first time allows the real CE at the section level to be automatically estimated (not just predicted), unbiased - for all estimators and at no extra cost to the user.
Computers in Biology and Medicine, 2008, Vol 38, Issue 3, p. 313-328