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Monday, April 06, 2020 1:33:59 AM

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rmitra should help confirm and explain my findings in more detail, but I believe I have identified another potential factual error in Judge Du's bench order. It feels rather glaring to me, but best to have some corroboration from those familiar in statistics, and rmitra should be able to explain it in a much clearer manner.

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:
Quote:
A POSA would have understood that Hayashi includes at least one patient with triglyceride levels > 500 mg/dL in light of Hayashi’s data. (ECF No. 367 at 725:21-727:1.) Table I reports that at baseline, the patients in the study had a triglyceride level of 300 ± 233 mg/dl. (Ex. 1532 at 5.) Dr. Heinecke11 explained that while “there is some ambiguity in this paper about what the meaning is of the plus minus 233[,] . . . overwhelmingly, in the medical literature, that would be a standard deviation.” (ECF No. 367 at 725:21-727:1.)

The standard deviation is the average spread of the data around the mean value of 300 mg/dl (for a normal distribution of data, two-thirds of the data points are within one standard deviation of the mean). (Id.) Accordingly, as Dr. Heinecke explained, “[ b]ecause there’s a value of plus or minus 233, there was at least one patient in that study who had a value of greater than 300, and because that’s only encompassing two-thirds of the data, one-sixth of the patients would likely have been above 533.” (Id.) Although Dr. Lavin initially told the PTO12 that not even one patient in Hayashi would have had triglyceride levels > 500 mg/dL, Dr. Lavin later testified that he would “rewrite” his declaration on this point, explaining that in Hayashi “you know that there must be at least one subject” with triglyceride levels > 500 mg/dL, and that it is “likely that you have one or two observations above 533.” (Lavin Dep. Tr. at 102:24-103:21.) Dr. Toth13 did not “offer any type of statistical opinion to corroborate what Dr. Lavin told the patent office.” (ECF No. 371 at 1868:13-16.)

Dr. Heinecke explained that there is an alternative theory that Hayashi’s reference to 300 ± 233 mg/dl instead refers to the range of triglyceride values, rather than the standard deviation. (ECF No. 367 at 725:21-727:1.) But “this would be very unusual,” and in any case, under that interpretation there would still be “at least one patient in the study that had a value of 533.” (Id.) Therefore, under either interpretation of Hayashi, at least one patient had triglyceride levels > 500 mg/dL. (Id. at 727:2-6.)


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:
Quote:
“[ b]ecause there’s a value of plus or minus 233, there was at least one patient in that study who had a value of greater than 300, and because that’s only encompassing two-thirds of the data, one-sixth of the patients would likely have been above 533.”


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,
Quote:
A POSA would have understood that Hayashi includes at least one patient with triglyceride levels > 500 mg/dL in light of Hayashi’s data. (ECF No. 367 at 725:21-727:1.)


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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