I am testing for differences in mortality from PAH mixtures based on predicted mortality from individual PAH exposures. Since single PAH testing had high variability in response between replicates, I am having trouble finding a method with statistical power to detect a difference in the mixtures response compared to predicted.
If you want to determine the toxicity of a combination of chemicals, you need to test them in combinations. I would suggest that you use a D-Optimal or I-Optimal response surface.
Using the One-Factor-At-a-TIme (OFAT) method to predict the effects of combinations is highly problematic. For the OFAT results to predict the mixture results, we have to assume that the chemicals do not interact. If you are only testing 2-4 chemicals, this might not be a bad assumption. If you have more than that, you run a high risk of your assumption being wrong.
Despite what you might have heard, it is actually a better (the best) idea to test many factors(chemicals) at many levels (doses) at the same time and test them in different combinations. There is an entire area of statistics dedicated to this idea. It is called Design of Experiments(DOE). Using good DOE methods, you can minimize the variability of your tests and minimize the number of subjects you use while maximizing the amount of information you get and maximizing the power of your tests. .
Thanks for the information! I have already concluded this research but you make a great point. I will incorporate the statistics as a limitation and discuss the uncertainty related to environmental chemical interactions.
If you look up Fixed Ratio (Mixture) Arrays, you will see that they tend to do the type of calculation you are looking for.
However, these tests make many assumptions that are not really valid for larger numbers of chemicals in the mixture.
Having spoken with dozens of Design of Experiments professionals, they see the FRMA as a poorly constructed, super saturated experiment that is essentially bogus.
How many PAHs did you test?
Here is a paper I wrote as part of my Stats thesis. I started out as a chemist/environmental scientists before I switched to Statistics and Operations Research. So, I tried to look at the toxicology tests from a chemists perspective.
This is very helpful! Thank you for the paper. I tested 4 PAHs in a fully factorial design and was able to test all possible combinations. However, high variation between replicates likely meant that if there was interaction, it was statistically undetectable. It was impossible to increase the number of replicates based on the size of the experiment. At the same time, using information on mode of action, additivity of effect was expected, which supports the finding. When I looked at other papers testing mixtures, the statistical approaches applied varied considerably across studies. I can imagine this only gets trickier the more chemicals you test! Thanks again for the information!
If you used a full factorial design, you should be able to find the interactions between the chemicals.
How did you replicate your design? Suppose that you ran 16 treatment combinations of your PAHs on week 1. Then replicated the design in Week 2, 3, 4, etc. In this case, you can use "Week" as a block. This will help eliminate some of your variability.
If your subjects came from different suppliers/batches/etc, you can use this information as blocks too. If you ran out of a stock solution and had to remake the solution, that can be a block too.
If you ran 3 replicates for each treatment combination at the same time, this can be a repeated measure design, which is a little different analysis than a typical factorial design. You could try taking the average response instead of each individual response.
What is your response? Alive/dead, Change in alleles? Blood Cell count? Survival Time? Each of these responses can be a different type of analysis.
Are you allowed to post your results? If so, I could take a look and see what I can find. If not, that is totally understandable too.
We ran 3 replicates for each treatment, with mortality as the response. The problem is the high variability between those replicates obscuring the ability to detect responses that deviate from additivity. I can't post the results here because the work is currently being published through Environmental Toxicology and Chemistry. The final publication should be available soon. Thanks for the additional information!
Will the publication have your raw data? If so, let me know when it gets published. I'll check it out then.
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