The question mainly relates to epidemiological studies focused on pollutants exposure. Where a part of the biological samples has a pollutant concentration below the limit of detection of the analytical method.
Prof Appenzeller,
in fact there are a couple of methods when dealing with pollutants bellow the limit of detection. Two of the main popular choices are: LOD/2 and the one you cited.
I think the LOD/sqrt(2) method was created because it was found better when dealing with log-normal data.
Despite that, other more advanced approaches have been proposed. Prof Dennis R Helsel has authored some interesting papers reviewing this topic:
Article Fabricating Data: How Substituting Values for Nondetects Can...
Article Much Ado About Next to Nothing: Incorporating Nondetects in Science
Replacing LLOQ values by LLOQ/2 is almost never appropriate. The best way is to include these values into the model as left-censored. It is fairly straightforward to do using any reasonable statistical software. For example R and brms package.
fit1
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