Monday, April 06, 2020 1:33:59 AM
On page 26 of the bench order (https://www.courtlistener.com/recap/gov.uscourts.nvd.118340/gov.uscourts.nvd.118340.381.0_1.pdf), the judge states:
Essentially, based on testimony by the experts, and given that patients in the study had a triglyceride level of 300 +- 233 mg/dL, the judge concludes that there exists at least one subject with triglycerides level >500mg/dL.
Based on my understanding of statistics and probability distributions, that conclusion does not follow, and is mathematically incorrect.
Given N=25 mean=300 and SD=233, it is mathematically incorrect to claim that there exists at least one N with value >500. What would be correct instead, is to state that there exist a certain probability that some values might exist >500, but it is not necessary that the data set has values above >500.
To put it in another way, it is entirely possible to construct a data set such that we get the properties N=25 mean=300 and SD=233, yet there are no data points with values >500. Note also that the normal distribution has two tails, but the experts derive their conclusions assuming that only one tail matters.
Dr. Heinecke (defendant's expert) states:
That is somewhat misleading because we can't readily know if the bolded "would likely" part is true (rmitra can probably derive the exact probability for it) and the judge most definitely misinterpreted it when she states,
It is rather unfortunate that the expert witnesses made such errors and the judge readily accepted their claims, even when they are mathematically incorrect. I'm not sure how such things are legally dealt with.
As further support for my point, relying solely on Hayashi, et al., Decreases in Plasma Lipid Content and Thrombotic Activity by Ethyl Icosapentate Purified from Fish Oils, 56(1) Curr. Therap. Res. 24-31 (1995), available here https://sci-hub.tw/https://www.sciencedirect.com/science/article/pii/0011393X95850163
Observe Figure 2 on page 28 of Hayashi
It shows the distribution of the triglyceride levels of almost all the patients in the study (n=28) and none are above 500. Note that in Figure 2, n=25 and n=22 for the triglycerides chart probably because some measurements could not be taken (see Figure 1 caption).
Those two charts in Figure 2, together with our mathematical argument above, most definitely suggest that no patients in the study have TG levels above 500.
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