Parallel dose-response curves in combination experiments |
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Authors: | Jürgen Sühnel |
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Institution: | (1) Institut für Molekulare Biotechnologie, Postfach 100813, D-07708 Jena, Germany |
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Abstract: | A possible experimental design for combination experiments is to compare the doseresponse curve of a single agent with the
corresponding curve of the same agent using either a fixed amount of a second one or a fixed dose ratio. No interaction is
then often defined by a parallel shift of these curves. We have performed a systematic study for various types of doseresponse
relations both for the dose-additivity (Loewe additivity) and for the independence (Bliss independence) criteria for defining
zero interaction. Parallelism between doseresponse curves of a single agent and those of the same agent in the presence of
a fixed amount of another one is found for the Loewe-additivity criterion for linear doseresponse relations. For nonlinear
relations, one has to differentiate between effect parallelism (parallel shift on the effect scale) and dose parallelism (parallel
shift on the dose scale). In the case of Loewe additivity, zero-interaction dose parallelism is found for power, Weibull,
median-effect and logistic doseresponse relations, given that special parameter relationships are fulfilled. The mechanistic
model of competitive interaction exhibits dose parallelism but not effect parallelism for Loewe additivity. Bliss independence
and Loewe additivity lead to identical results for exponential doseresponse curves. This is the only case for which dose parallelism
was found for Bliss independence. Parallelism between single-agent doseresponse relations and Loewe additivity mixture relations
is found for examples with a fixed doseratio design. However, this is again not a general property of the design adopted but
holds only if special conditions are fulfilled. The comparison of combination doseresponse curves with single-agent relations
has to be performed taking into account both potency and shape parameters. The results of this analysis lead to the conclusion
that parallelism between zero interaction combination and single-agent doseresponse relations is found only for special cases
and cannot be used as a general criterion for defining zero-interaction in combined-action assessment even if the correct
potency shift is taken into account. |
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