Variation of fractionator estimates and its prediction

Over the last decade the so-called 'fractionator' has become widespread in anatomical and pathological research for obtaining unbiased estimates of total numbers of particles in biological specimens. Several methods have been proposed for predicting the precision (i.e., the variation) of the estimated total numbers of particles using the fractionator (i.e., for predicting the precision of fractionator estimates). However, the validity of these predicting methods has not been tested so far. As it is impossible to do so with biological experiments, it was carried out here by using a computer simulation. Specimens containing particles, with various particle distributional patterns, were modeled, and the total number of particles in the specimens was estimated repeatedly with various modeled sampling schemes. It could be shown that the empirically estimated precision of the modeled fractionator estimates depend on both the particle distributional pattern in a modeled specimen as well as on the applied sampling scheme. Furthermore, considerable differences between the predicted and the empirically estimated precision of the modeled fractionator estimates were found. This was due partly to an incorrect assumption, which serves as the basis for one of the proposed predicting methods, partly to the fact that for some of the proposed predicting methods important contributions to the variation of fractionator estimates have not been considered, and partly to the fact that the mathematical theory, which serves as the basis for all predicting methods proposed so far, can in principle not be the optimum basis for predicting the precision of fractionator estimates. Based on the results of the computer simulation, a new, simple method is proposed for predicting the precision of fractionator estimates.