BEproff Senior Russia, 20151124 08:13 Posting: # 15658 Views: 2,952 

Hi All, Is it possible to detect cumulation of a substance using "classic" PKparameters (AUC, Cmax, Tmax, etc)? Maybe additional metrics to be calculated? 
Helmut Hero Vienna, Austria, 20151124 13:41 @ BEproff Posting: # 15662 Views: 2,387 

Hi BEproff, » Is it possible to detect cumulation of a substance using "classic" PKparameters (AUC, Cmax, Tmax, etc)? Not sure what you mean. According to the “Superposition Principle” linear pharmacokinetics could be tested by a comparison of AUC_{0τ} (steady state) with AUC_{0∞} (single dose). Generally this is done in a study where after the single dose profile the drug is administered until steady state is reached.* The comparison is done by a paired test – which assumes no period effects. I have never seen a crossover in 35 years… Would be a logistic nightmare. If the 90% CI of AUC_{0τ}/AUC_{0∞} is outside the acceptance range, nonlinear PK is proven. See also this lengthy thread. The superposition principle is applicable to AUCs only (that’s why Friedrich Hartmut Dost called it “Gesetz der korrespondierenden Flächen” – Law of Corresponding Areas back in 1953). Comparisons of C_{ss,max}/C_{max} and t_{ss,max}–t_{max} are possible but of doubtful value. » Maybe additional metrics to be calculated? Whichever you might think of. A common one is the “Accumulation Index”: R = 1/(1 – 2^{–ε}), where ε = τ/t_{½}. Phoenix/WinNonlin uses a different formula R = 1/(1 – ℯ^{–λz·τ}), which gives the same result (homework: why?). R gives you an idea how much higher average concentrations in steady state are if compared to a single dose. Example: Halflife 12 h (λ_{z} 0.05776) and dosing interval 24 h ⇒ R 1.333 (i.e., concentrations in steady state will be ⅓ higher than after a single dose). If you decrease the dosing interval to t_{½}, R will be 2. I’m not a big fan of R since it might be difficult to obtain a reasonably good estimate of λ_{z} / t_{½} in steady state. In the BEcontext we don’t sample beyond τ. If you are interested in a good estimate of λ_{z} (e.g., in phase I studies of new drugs) you might sample longer. Furthermore, R is strictly valid only for the onecompartment model. For more compartments it is approximate (since based on the elimination phase only).
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