Gardi J E, Nyengaard J R, Gundersen H J G
Stereology and Electron Microscopy Research Laboratory and MIND Center, University of Aarhus, Ole Worms Allé 1185, Aarhus C, Denmark.
Comput Biol Med. 2008 Mar;38(3):313-28. doi: 10.1016/j.compbiomed.2007.11.002. Epub 2007 Dec 27.
The proportionator is a novel and radically different approach to sampling with microscopes based on the 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 is 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 2-15-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.
比例采样器是一种基于著名统计理论（概率与大小成比例 - PPS 抽样）的新型且截然不同的显微镜采样方法。它使用具有大量选项的自动图像分析，为切片中的每个视野分配一个与所研究结构的某些特征成比例的权重。这里研究的一个典型且非常简单的例子是结构的颜色特征量，用具有已知特性的染色剂进行标记。颜色可能是特定的，也可能不是。在所有视野的权重记录列表中，所需数量的视野会根据权重按比例自动进行概率抽样，并呈现给专家观察者。使用任何已知的体视学探针和估计器，这些视野中的正确计数会得出所检查切片中结构总量的简单、无偏估计，进而得出任何已知的体视学估计值，包括大小分布和空间分布。无偏性并非权重与结构之间假定关系的函数，从体视学（积分几何）角度来看，在实际中这种关系总是存在偏差。然而，比例采样器的效率直接取决于这种关系为正。在具有可能实际范围内的特征和各种噪声的切片中模拟了采样和估计过程。在所有检查的案例中，比例采样器的效率比常见的系统均匀随机采样高 2 至 15 倍。模拟还表明，对于均匀采样策略而言，由于视野间变化导致的误差系数（CE）缺乏简单预测器是一个比预期更严重的问题。由于其基于已知但非均匀采样概率的完全不同的采样策略，比例采样器首次允许在切片级别自动估计（而不仅仅是预测）真实的 CE，对所有估计器而言都是无偏的，且对用户无需额外成本。
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