Calculating limits for carcinogens: AI, PDE, and less than lifetime as per ICH M7

Any drug product is expected to have some level of mutagenic impurities, however this is not a concern when the level is below the safe limit. Now how are these acceptable limits derived for mutagenic impurities?
When this is a carcinogenic compound, a class 1 impurity as per ICH M7, it was already tested in animals in a carcinogenicity study. This is a study in which rodents are exposed to that compound in different doses, usually throughout their lifetime which is 2 years, and we observe when tumors develop.
So when we plot the results in a graph, we may see a dose-response curve like this, where in low doses we just see the background incidence of tumors, and then above a certain exposure we start to see an increase in tumor incidence. The explanation for this is that at very low levels of exposure, there are DNA repair mechanisms preventing DNA damage from becoming a mutation, and other mechanisms which avoid tumors from developing. However above a certain threshold, this higher dose exceeds the repair capacity of DNA enzymes, hence leading to mutations, and we start to actually see an increase in tumors. So this is what we call a threshold dose-response.
Now what if we don't clearly see this dose-response curve in our study? In this case, the recommended approach for mutagenic impurities has been to consider this dose-response as linear, as if any dose leads to cancer risk and there is no threshold. Here there is an assumption that we don’t have DNA repair mechanisms in place.
So which one of these will be used to find the point of departure to derive the safe limit for humans? This depends on which dose-response we have and the expected mode of action. For non-mutagenic carcinogens, we expect to have a threshold curve, so we can establish a no observed effect level – NOEL and use this value to calculate a permissible daily exposure – PDE. For mutagenic carcinogens, although some may also show a threshold dose-response [Johnson, 2009], the regulatory default approach has been to consider the curve as linear. In this case, we usually use the TD50, which is the dose causing tumors in 50%, or 1 in every 2 animals which were exposed to that compound, and then do a linear extrapolation to find the exposure corresponding to our acceptable intake, or AI.
ICH M7 describes that 1:100,000 is considered a negligible risk of cancer posed by mutagenic impurities present in drug products.
However, in these studies rodents are usually exposed for their lifetime to the compound so the TD50 and AI refer to a lifetime exposure to that impurity.
In studies when the rodents are exposed for less than their lifetime, factors are applied to estimate what would be the TD50 if they had been exposed for their lifetime.
So this lifetime AI actually applies to impurities present in a drug used for a chronic disease, which will be taken for more than 10 years.
But we know that some drugs are taken for less than a lifetime, such as some antibiotics which may be taken for only a week or two. Do we expect the same risk when the exposure to the carcinogen is so much shorter?
Actually not, many studies [Felter 2011] have shown that there is a dose and time relationship for carcinogens, analogous to the original concept in toxicology described the Haber’s law, in which toxicity equals to the concentration (or dose) versus time.
So what matters for the estimation of cancer risk is the lifetime cumulative dose of that carcinogen, and this has been described in early regulatory guidance for cancer risk assessment [EPA]: "a higher dose administered over a short duration is equivalent to a commensurately lower dose administered over a longer duration."
Based on this, ICH M7 describes the less than lifetime approach, which can be summarized in this graph.
So if 1.5 ug/day is the acceptable intake over a lifetime, if the exposure to the drug is shorter, the acceptable intake can be higher.
The line here describes a linear relationship between dose and time, however if we keep this linear shape, these higher doses administered over a short duration of exposure might overwhelm the repair capacity of DNA or saturate other detoxification pathways, because of the high rate of exposure. [Halmes 2000]
Therefore, because the uncertainty increases at higher doses, dose rate correction factors have been described in the literature [Felter], and are also applied by ICH M7.
After applying the safety factors proposed by ICH M7, the limits will be much lower, in a very conservative approach.
This graph applies when the TTC is used, for impurities of classes 2 and 3, but the same concept can be used with class 1 impurities, basically multiplying the AI by the corresponding durational factors.
So when will the LTL concept be applicable?

[continues in the comments]

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