Here a comment about a specific problem in statistics which is often ignored by (mostly) non-mathematicians.
I originally intended to leave the comment in a mathematicians forum where this problem is discussed. As an example I looked at the glyphosate Renewal Assessment Report from 2013 where I think this ignorance leads to very problematic conclusions. Warning: some details about the animal test results are rather explicit.
Here the comment:
I haven’t found a remark to the problem of sample size and p-value. I hope I haven’t overlooked something.
For obvious reasons drug testing with animals is usually done with not so many animals, so testing for significance only (and not also for the concrete values) seems highly problematic.
However this seems to be a common method if I look for example at animal experiments in 2013 with glyphosate. The updated 2015 version (which seems not public) of this report is (as explained here in german) one of the main “scientific” ingrediences for the WHO recomendations about Glyphosate and also for the European EFSA. The main “rapporteur of member state” (RMS) was here Germany, so I think most of this was done at the Bundesinstitut für Risikobewertung.
The report is about 1000 pages long, but sofar any random reading within the study gave me my hair stand on end.
The report gathered studies and tried to excerpt major findings. As a matter of fact it seems the big majority of the studies was done by chemical companies, but I didnt count.
In the report excerpts from respective animal studies with glyphosate were briefly documented and then “evaluated” in a comment by the RMS (in italics).
But back to the p-values. Again I didnt count but it seems that in all evaluations of the RMS “significance testing” was a key element for evaluation. However the number of tested animals is often not even listed.
A randomly picked example (in which some animal numbers are listed) for illustrating how the evaluation took place:
2007 Glyphosate technical: 52-week Toxicity Study by
Oral Route (Capsule) in Beagle Dogs
Data owner: Nufarm
In Table B.6.3-32 one sees that at doses (which are 500 mg/kg bw/day or below) a weight loss can be seen (and if I didnt oversee something also in all other of the few dog studies, where explicit numbers were displayed). The number of dogs here is not mentioned but in the table below a number of 4 dogs is mentioned. The mean weight decrease is not significant (p<0.05) and so the RMS comments:
This study is considered acceptable. It is agreed
to set the NOAEL at the highest dose level of 500 mg/kg bw/day. It can be confirmed that the alterations in clinical chemistry parameters were mostly not statitically significant and, if so, did not show a dose response. The only possible exception is a lower blood calcium level in high dose males that was observed in other studies with glyphosate, too. However, without any concomitant findings, e.g, on bones, this perhaps treatment-related effects is not considered adverse.
It should be mentioned that for example the EFSA luckily did not use this NOAEL in order to set the accepted daily intake, but then I dont know though what this “uncertainty factor” means and in particular what it implies for allowed dosages:
The acceptable daily intake (ADI) of glyphosate is 0.5 mg/kg bw per day, based on the maternal and developmental NOAEL of 50 mg/kg bw per day from the developmental toxicity study in rabbits and
applying a standard uncertainty factor (UF) of 100
They can’t mean the NOAEL, because a factor 100 would mean a NOAEL at 5000 mg/kg bw !
The comment of the RMS goes on and in particular comments on another dog study of the same company where they used the double dose of 1000 mg per kg bodyweight (1000 mg/kg bw) – I will therefore before citing the rest of the comment cite some information about that study.
2007 Glyphosate Technical: 13-Week Toxicity Study By
Oral Route (Capsule) In Beagle Dogs
Laboratory Study No.: 29646 TCC
Data owner: Nufarm
In the study (p.265) it is said:
Mortality: Two unscheduled sacrifices (one male and one female) were necessary in animals given 1000 mg/kg bw/day:
One male was sacrificed on Day 61 on humane grounds. Vomiting was seen once in Week 7 (before dosing) and liquid faeces were noted on many occasions in Weeks 8 and 9. Prior to sacrifice, signs of poor clinical condition including thin appearance, dehydration, and pallor of lip mucosa, coldness to the touch, hypothermia (34 to 35 °C) and hypoactivity were observed. These signs were associated with a body weight loss between Weeks 7 and 9 (-34 %) and reduced food consumption from Week 7 (generally only 25 to 50 % of this animal’s
daily ration was consumed), followed by an absence of food intake on the day before death. Medical care (Smecta® and Lactate Ringer®) was given in order to stop the diarrhoea and rehydrate the animal.
One female was sacrificed on Day 72 for humane reasons. This animal showed liquid or soft faeces on many occasions from Week 4 and dehydration from Week 9. Vomiting was observed once in Week 10. These signs were accompanied by a body weight loss between Weeks 8 and 11 (-22 %) and decreased food consumption from Week 8 (generally only 25 to 50 % of this animal’s daily ration was consumed), followed by an absence of food intake on the two days prior to sacrifice. Medical care (Smecta® and lactate Ringer®) was given in many occasions.
The following treatment-related clinical signs were reported in animals given 1000 mg/kg/day (excluding those killed in extremis, which are discussed separately): liquid or soft faeces on several occasions in all animals, vomiting in 2/3 females on one occasion within 30 minutes or 3 to 5 hours after treatment, thin appearance in 1/3 males and all females, dehydration in 1/3 males and 2/3 females, pallor of ears and mouth in 1/3 females.
The comment of the RMS to this study:
The study is considered acceptable and the NOAEL is agreed. At the top dose level, the MTD was clearly exceeded. It was noticed that high dose effects of glyphosate administration in this study were particularly severe, much more pronounced and rather different from what
was seen in other dog studies or other species. Thus, because of the clinical signs and pathological changes, its results do not fit into the toxicity profile of glyphosate as it was established in the majority of studies. In the study by (1990, TOX9552384) that is decribed in detail in the original DAR (1998, ASB2010-10302), the same high dose of 1000 mg/kg bw/day was administered also in capsules causing only minor effects.
So if I see this correctly the “majority of studies” concerning dogs is (1990, TOX9552384).
Now the rest of the RMS comment to the lower dose experiments:
This study was run in the same laboratory and under similar conditions as the 90-day study by (2007, ASB2012-11454) in which severe adverse effects were seen upon treatment of Beagle dogs with glyphosate at a high dose level of 1000 mg/kg bw/day. It is clear now that these adverse reaction to treatment was in fact confined to an exaggerated dose level and that the NOAEL is higher than 300 mg/kg bw/day as established in that previous study.