Glaser E M, Wilson P D
MicroBrightField, Inc., Baltimore, MD 21209, USA.
J Microsc. 1998 Nov;192(Pt 2):163-71. doi: 10.1046/j.1365-2818.1998.00417.x.
The optical fractionator is a design-based two-stage systematic sampling method that is used to estimate the number of cells in a specified region of an organ when the population is too large to count exhaustively. The fractionator counts the cells found in optical disectors that have been systematically sampled in serial sections. Heretofore, evaluations of optical fractionator performance have been made by performing tests on actual tissue sections, but it is difficult to evaluate the coefficient of error (CE), i.e. the precision of a population size estimate, by using biological tissue samples because they do not permit a comparison of an estimated CE with the true CE. However, computer simulation does permit making such comparisons while avoiding the observational biases inherent in working with biological tissue. This study is the first instance in which computer simulation has been applied to population size estimation by the optical fractionator. We used computer simulation to evaluate the performance of three CE estimators. The estimated CEs were evaluated in tests of three types of non-random cell population distribution and one random cell population distribution. The non-random population distributions varied by differences in 'intensity', i.e. the expected cell counts per disector, according to both section and disector location within the section. Two distributions were sinusoidal and one was linearly increasing; in all three there was a six-fold difference between the high and low intensities. The sinusoidal distributions produced either a peak or a depression of cell intensity at the centre of the simulated region. The linear cell intensity gradually increased from the beginning to the end of the region that contained the cells. The random population distribution had a constant intensity over the region. A 'test condition' was defined by its population distribution, the period between consecutive sampled sections and the spacing between consecutive sampled disectors. There were 1000 independently simulated cell populations for each test condition, and a 'trial' was conducted for each of these cell populations. In each trial we calculated the (unique) true CE of the population size estimate and the three CE estimates obtained by applying the Scheaffer-Mendenhall-Ott (SMO) and both Gundersen-Jensen (GJ) estimators. We compared the estimated CEs with the true CEs for each population distribution. We found that the CE estimates obtained by the SMO estimator were closer to the true CEs and had less scatter than those of the nugget-modified GJ estimator. Both had small positive bias. The CE estimates obtained by the unmodified GJ estimator exhibited widely varying bias and large scatter. In all the population distributions we tested, the average true CE was very nearly proportional to 1/square root of QT, where QT is the average number of cells counted in the two-stage systematic sample.
光学分割器是一种基于设计的两阶段系统抽样方法，当总体数量太大而无法详尽计数时，用于估计器官特定区域内的细胞数量。分割器对在连续切片中系统抽样的光学解剖区域中发现的细胞进行计数。在此之前，光学分割器性能的评估是通过对实际组织切片进行测试来进行的，但使用生物组织样本很难评估误差系数（CE），即总体大小估计的精度，因为它们不允许将估计的CE与真实的CE进行比较。然而，计算机模拟确实允许进行这样的比较，同时避免处理生物组织时固有的观察偏差。本研究是首次将计算机模拟应用于通过光学分割器进行总体大小估计的实例。我们使用计算机模拟来评估三种CE估计器的性能。在三种非随机细胞总体分布类型和一种随机细胞总体分布的测试中评估估计的CE。非随机总体分布因“强度”差异而不同，即每个解剖区域的预期细胞计数，这取决于切片以及切片内解剖区域的位置。两种分布是正弦曲线型的，一种是线性增加的；在所有三种分布中，高强度和低强度之间存在六倍的差异。正弦曲线分布在模拟区域中心产生细胞强度的峰值或谷值。线性细胞强度从包含细胞的区域开始到结束逐渐增加。随机总体分布在该区域内具有恒定的强度。“测试条件”由其总体分布、连续抽样切片之间的间隔以及连续抽样解剖区域之间的间距定义。对于每个测试条件，有1000个独立模拟的细胞总体，并且对每个这些细胞总体进行一次“试验”。在每次试验中，我们计算总体大小估计的（唯一）真实CE以及通过应用谢弗 - 门登霍尔 - 奥特（SMO）和两种冈德森 - 詹森（GJ）估计器获得的三种CE估计值。我们比较了每种总体分布的估计CE与真实CE。我们发现，SMO估计器获得的CE估计值比矿块修正的GJ估计器的更接近真实CE，并且散布更小。两者都有小的正偏差。未修正的GJ估计器获得的CE估计值表现出广泛变化的偏差和大的散布。在我们测试的所有总体分布中，平均真实CE几乎与1/√QT成正比，其中QT是两阶段系统样本中计数的细胞平均数。
