Saturday, May 30, 2009

Pharmacokinetics: Verify the Steady State Under Multiple Doses

For a multiple-dose regimen, the amount of drug in the body is said to have reached a steady state level if the amount or average concentration of the drug in the body remains stable. At steady state, the rate of elimination = the rate of administration.

To determine whether the steady state is achieved, statistical test can be performed on the trough levels. The predose blood sampling should include at least three successive trough level samples (Cmin).

In FDA's guidance for industry: Bioequivalence Guidance, it stated " determine a steady state concentration, the Cmin values should be regressed over time and the resultant slope should be tested for its difference from zero." For example, we can use the logarithm of last three trough measurements to regress over time. If the 90% CI for the exponential of slope for time is within (0.9, 1.1), then we will claim SS. The limit of (0.9, 1.1) is arbitrarily decided.

Similarly, in FDA's guidance for Industry: Clozapine Tablets: In Vivo Bioequivalence and In Vitro Dissolution Testing, it stated "...The trough concentration data should also be analyzed statistically to verify that steady-state was achieved prior to Period 1 and Period 2 pharmacokinetic sampling."

Typically, the verification of the steady state can simply be the review of the trough levels at time points prior to the PK sampling without formal statistical testing. If the PK blood samples are taken after 4-5 dose intervals, it can be roughly assumed that the (approximately or near) steady state has been reached.
The trough and peak values of plasma concentrations are also used to determine whether the steady state has been reached. The peak to trough ratio is usually used as an indicator of fluctuation of drug efficacy and safety. A relatively small peak to trough ratio indicates that the study drug is relatively effective and safe.

In their book "Design and analysis of bioavailability and bioequivalence studies", Chow and Liu described the univariate analysis and multivariate anaysis approaches to test the steady state formally.

Hong also proposed a non-linear procedure to test for steady state.

A note about trough and Cmin:

The characteristic Cmin has been associated with the concentration at the end of te dosing interval, the so-called pre-dose or trough value. However, for prolonged release formulations which exhibit an apparent lag-time of absorption, the true minimum (trough) concentration may be observed some time after the next dosing, but not necessarily at the end of the previous dosing interval.

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