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Statistics

We believe the accurate interpretation of study results is critically important to a study's value. Hence, the results from studies that include a statistical design are more accurate than are those studies with no statistical approach. We promote statistical design at the study's beginning. Just as a single type of microbiological evaluation is not valid for every product, statistical analysis, too, must be specifically designed in order to allow for smaller sample sizes, unambiguous results, and lower overall cost.

We use regression analysis, including logistic regression, non-parametric statistics, t-tests, proportions, factorial designs, response surface methodology, and meta-analysis. However, the primary statistical model used at BioScience Laboratories is Analysis of Variance (ANOVA). For our clients without extensive experience in statistical application, we can also assist. Your data can be presented with a simplified approach using the Analysis of Means (ANOM). ANOM sets 95% decision levels and uses the mean values only. If any values exceed the decision levels, those factors are different. (Download the BioScience Laboratories, Inc. poster “Should you perform statistical analysis?” for a complete discussion.)

Analysis of Variance (ANOVA)

For example, suppose you want to compare these components, three products and three samples. Then, the two-factor ANOVA is:

ŷ = A + B + (A x B) + e

where:

ŷ = Reductions - Baseline

A = Products

B = Time

A x B = Interaction Term

e = Error Term

Analysis of Means (ANOM)

Many people experience fear, which leads to a misunderstanding of statistics. They simply do not know what it entails. If that is a problem you face, let us know. We will also compute the ANOMs to address this problem. Once you read the ANOM section, you will be able to understand the ANOVA.

Response Surface Methodology (RSM)

may be useful to graphically display the results of your pilot studies. RSM is particularly valuable when you collect only a small number of samples and cannot otherwise detect any differences. Many times, a customer wants to evaluate different concentrations, applications, etc. of a product to see if the kill rates are different. The problem is that they only use a few replicates. Using a statistic like the Analysis of Variance (ANOVA), no difference would be detected, because the error term is so great, due to the small sample size (Figure A).

All products are the same, because the 95% confidence intervals overlap. The way around this is to look specifically at the mean (average) values and use Response Surface Methodology (Figure B). For instance, you can see in this example, the kill rates increase until 4.0% is reached, but then they decrease. Using the response surface methodology, we would choose the 4% concentration and test to verify that it is, in fact, the best with the 3.5% and the 4.5% concentrations.

Meta-Analysis

BioScience Laboratories, Inc. has always been capable in the realm of bio-statistics, and now we offer a new service: meta-analysis. Meta-analysis is the process of integrating the data from multiple individual studies performed by different technicians at different times at different laboratories into one unified study.

By using meta-analysis, you can have the various non-FDA studies performed on your product integrated into one study to make sense of the results. This is important, for example, when one researcher finds your product to be very good, and another finds it to be not acceptable. Instead of favoring one researcher and discounting the other, meta-analysis integrates all the studies’ results into one final result.

For FDA studies, you likely will have performed more than one study on your product. Perhaps two studies were done, one pivotal and the other, confirmatory. Meta-analysis can integrate the results from these for inclusion in your FDA submission packet.

To learn more about Meta-Analysis, download a copy of Dr. Paulson's whitepaper entitled Some Basic Points Concerning Meta-Analysis and Clinical Trials.

The models are usually more difficult to make sense of, but that is why BioScience Laboratories can help you. For more information on Statistical Analysis, contact BioScience Laboratories, Inc. CEO Daryl Paulson, Ph.D. at 877-858-2754.