Stanley Deming, Ph.D., President, Statistical Designs recently sat down with us to go over some of the topics he'll be presenting on during the Development, Validation and Maintenance of Biological Assays event taking place this coming May. Today, he answers the question:
Some characteristics of an assay are not normally distributed, often because there is a physical barrier – such as %RSD which is limited by 0. How do we set these SPC limits? If we need to transform the data to get a normal distribution, what in your experience is the best transformation?
Rates and proportions (such as %RSD) are different because the measured quantities are bounded, usually by 0 and 1, or by 0 and 100%. Thus, the statistics required to construct confidence intervals about point estimates (and thus to make statistical decisions involving uncertainty) must take these usually asymmetrical bounds into account.
An excellent introduction to the statistics required for dealing with rates and proportions is a chapter in the text by Stanton a. Glantz, Primer of Biostatistics, McGraw-Hill, New York, NY, 2002. A more complete text is J. L. Fliess, B. Levin, and M. C. Paik, Statistical Methods for Rates and Proportions, 3rd ed., John Wiley & Sons, New York, NY, 2003.
Methods described in these references can be used to set SPC limits on rates and proportions. The use of p-charts (instead of the usual x-bar and r charts) is one example where proportions are used to set SPC limits.
There are other situations where non-normal data are encountered. In bioassay work, these are usually log-normal distributions that can be “normalized” by simply working with the logarithm of the measured quantities instead of working with the measured quantities themselves. A familiar example is relative potency – it is usually the logarithms of the relative potencies that are normally distributed, not the relative potencies themselves. Plotting the logarithm of the relative potencies on the usual x-bar and r charts often works well for setting statistical process control limits for bioassay results.
Dr. Deming will be leading the workshop Process Capability and Variance Components Analysis on May 14, 2013. For more information on this session and the rest of the program, download the Bioassays agenda. If you'd like to join us May 14-16, 2013 in Seattle, as a reader of this blog, when you register to join us and mention code IBA13JP, you'll save 20% off the standard rate! Have any questions? Feel free to email Jennifer Pereira.
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