Aggregation over multiple available hazard characterisations

In some scenarios, it may be that for a given substance and effect there are multiple available hazard characterisations. This can happen, for instance, if there are two different NOAELs originating from different studies. In such cases, a single hazard characterisation should be derived from the available candidates.

A conservative approach is to choose the lowest hazard characterisation (\(\operatorname{HC}\)) of the available hazard characterisations. I.e.,

\[\operatorname{HC} = \min_{i=1,\ldots,n} \operatorname{HC}_i\]

Alternatively, it is possible to aggregate the candidates into a new “average” hazard characterisation. For this, the harmonic mean, also used for obtaining central value estimates in the imputation of missing hazard characterisations, is a suitable approach.

\[\operatorname{HC} = \left( \sum_{i}^{n} \frac{1}{\operatorname{HC}_i} \right) ^{-1}\]