The proportionator is the most efficient unbiased stereological method used to estimate population size in samples. A typical application is counting the number of cells in an organ. The proportionator is related to the optical fractionator and physical dissector methods that also estimate population. The optical and physical fractionators use a sampling method called systematic uniform random sampling, or SURS. Unlike these two methods the proportionator introduces sampling with probability proportional to size, or PPS. With SURS all sampling sites are equal. With PPS sites are not sampled with the same probability. The reason for using PPS is to improve the efficiency of the estimation process. Efficiency is the notion of how much is gained by a given amount of work. A more efficient method provides better results for the same amount of work. The proportionator provides a better estimate, that is a more precise estimate, than either of these two methods: the optical fractionator and physical dissector . The PPS is implemented by assigning a value to a sampling site. This value is the characteristic of the sampling site. The proportionator becomes the optical fractionator if the characteristic is constant, i.e. the same, for all sampling sites. If there is no difference between sampling sites, then the proportionator behaves the same as the optical fractionator. In actual sampling, the characteristic varies across the tissue being studied. Information about the distribution of the characteristic is used to refine the sampling. The greater the variance of the characteristic, the greater the efficiency of the proportionator. What this means to the stereologist is simple: if you need to count more and more to get the CE needed to publish just stop and switch to the proportionator. The proportionator is a patented process that is not generally available. The only current licensee for the patent is Visiopharm.
Introduction The proportionator is the de facto standard method used to count cells in large projects. The increased efficiency provided by the proportionator makes more work intensive methods such as the optical fractionator less attractive except in small projects. A common misconception in the stereological literature is that design based methodologies require that all objects of interest must have the same probability of being selected. It is true that making such a design decision ensures an unbiased result, but it is not necessary. The use of nonuniform sampling is often used in stereological work. The point sampled intercept method selects cells using a point probe. The result is a volume-weighted estimate of the size of the cells. This is not a biased result. A sampling method known as probability proportional to size, or PPS, selects objects based on a characteristic that differs between objects. An excellent example of this is the selection of trees based on their diameter, or selecting a cell based on volume. The PSI selects cells with points. DeVries estimators select trees with lines. Sections select objects based on their height. These are examples of objects being selected in a varying probability by probes. In these examples the characteristic is a function of the objects themselves. That does not have to be the case. The proportionator applies PPS to counting cells. The PPS is employed to gain efficiency in the sampling, and not to produce a weighted estimate, such as a volume weighted estimate. The optical fractionator is the older standard for estimating the number of cells in an unbiased manner. The optical fractionator, and other sampling methods, has some statistical uncertainty. This uncertainty is due to the variance of the sampling even though the result is unbiased. The efficiency of the sampling can be determined by use of the coefficient of error, or CE. This value describes the variance of the sampling method. Often, biological sampling is done at a CE of .05. The efficiency of a sampling method is the amount of work it takes to obtain a desired CE. A more efficient method is one that requires less work to obtain a desired CE. A method is less efficient if the same amount of work results in a larger CE. Suppose that every sample always gave the same result. There would be no difference between samples. This means that the variance in this case is 0. No more than 1 sample would be required to obtain a good result. (Understand that this might not be efficient if the sampling requires a great deal of work and there is no need for a CE this low.) If samples differ, then the variance is positive, and so is the CE. The typical method of controlling the CE is to do more counting. The literature on the optical fractionator recommends methods of deciding where to increase the workload: more slices, or more optical dissectors. In keeping with this notion some amount of effort has been made to perform automatic image acquisition and counting to facilitate the process. The proportionator provides a superior result by avoiding more counting.
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