Statistical toxicological samples

There are three assumptions about sampling which are common to most of the statistical analysis techniques that are used in toxicology. These are that the sample is collected without bias, that each member of a sample is collected independently of the others and that members of a sample are collected with replacements. Precluding bias, both intentional and unintentional, means that at the time of selection of a sample to measure, each portion of the population from which that selection is to be made has an equal chance of being selected. Ways of precluding bias are discussed in detail in the section on experimental design. 

Two of the major points to be made throughout this chapter are (1) the use of the appropriate statistical tests, and (2) the effects of small sample sizes (as is often the case in toxicology) on our selection of statistical techniques. Frequently, simple examination of the nature and distribution of data collected from a study can also suggest patterns and results which were unanticipated and for which the use of additional or alternative statistical methodology is warranted. It was these three points which caused the author to consider a section on scattergrams and their use essential for toxicologists. 

The use of a new statistical approach, the limiting distribution, which is based upon the assumption of lognormality, generally leads to correct conclusions on the basis of few samples relative to the number required by tolerance sets. Limiting distributions may also be indexed to the toxicological and environmental realities so that they can be made as conservative as desired. 

Ronco, A., Gagnon, P., Diaz-Baez, M.C., Arkhipchuk, V., Castillo, G., Castillo, L.E., Dutka, B.J., Pica-Granados, Y., Ridal, J., Srivastava, R.C. and Sanchez, A. (2002) Overview of results from the WaterTox intercalibration and environmental testing phase II program Part 1, statistical analysis of blind sample testing, Environmental Toxicology 17 (3), 232-240. 

There are three assumptions about sampling which are common to most of the statistical analysis techniques that are used in toxicology. These are that the sample is collected without bias, that each member of a sample is collected independently of the others,... 

It is certainly possible to pool the data from several identical toxicological studies. One approach to this is meta-analysis, considered in detail later in this chapter. For example, if an acute inhalation study was performed where only three treatment group animals survived to the point at which a critical measure (such as analysis of blood samples) was taken, there would not be enough data to perform a meaningful statistical analysis. In such a case, the protocol could be repeated with new control and treatment group animals from the same source. At the end, after assurances that the two sets of data are comparable, the data from survivors of the second study could be combined (pooled) with those from the first. 

Precision and accuracy With method established perform three runs Perform at least six runs Apply appropriate statistics Evaluate reproducibility of incurred samples in each toxicology species Clearly defined and acceptable Evaluate reproducibility of incurred samples in key studies... 

As one attempts to assign risks that are acceptable to humans (1 in 10 or 10 ), it is clear that an enonnous sample size is needed. Actual statistical sensitivity of the toxicology tests is dependent upon the number of animals used, the background incidence of the tumors seen and the doses administered. 

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